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PD Dr.Ing. habil. Stefan KollmannsbergerTeam Leader: Simulation in Applied MechanicsRoom: 3165 Email: Diese EMailAdresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein! Tel: +49 89 28925021 Fax: +49 89 28925051 
Research
 Simulation in Applied Mechanics
 ORCID orcid.org/0000000308238649
 ResearcherID: E22962015
Submitted preprints

Korshunova, N.; Alaimo, G.; Hosseini, S.B.; Carraturo, M.; Reali, A.; Niiranen, J.; Auricchio, F.; Rank, E.; Kollmannsberger, S. Show abstract Bending behavior of additively manufactured lattice structures: numerical characterization and experimental validation
submitted to Materials & Design x (x), pp. xx, 2021
DOI: x
Selective Laser Melting (SLM) technology has undergone significant development in the past years providing unique flexibility for the fabrication of complex metamaterials such as octettruss lattices. However, the microstructure of the final parts can exhibit significant variations due to the high complexity of the manufacturing process. Consequently, the mechanical behavior of these lattices is strongly dependent on the processinduced defects, raising the importance on the incorporation of asmanufactured geometries into the computational structural analysis. This, in turn, challenges the traditional meshconforming methods making the computational costs prohibitively large. In the present work, an immersed imagetoanalysis framework is applied to efficiently evaluate the bending behavior of AM lattices. To this end, we employ the Finite Cell Method (FCM) to perform a threedimensional numerical analysis of the threepoint bending test of a lattice structure and compare the asdesigned to asmanufactured effective properties. Furthermore, we undertake a comprehensive study on the applicability of dimensionally reduced beam models to the prediction of the bending behavior of lattice beams and validate classical and strain gradient beam theories applied in combination with the FCM. The numerical findings suggest that the SLM octettruss lattices exhibit size effects, thus, requiring a flexible framework to incorporate highorder continuum theories.

Jomo, J.; Oztoprak, O.; de Prenter, F.; Zander, N.; Kollmannsberger, S.; Rank, E. Hierarchical multigrid approaches for the finite cell method on uniform and multilevel hprefined grids
submitted to Computer Methods in Applied Mechanics and Engineering x (x), pp. xx, 2020

Korshunova, N.; Alaimo, G.; Hosseini, S.B.; Carraturo, M.; Reali, A.; Niiranen, J.; Auricchio, F.; Rank, E.; Kollmannsberger, S. A CTbased numerical characterization of tensile behavior of additively manufactured octettruss structures and its experimental validation
submitted to Additive Manufacturing x (x), pp. xx, 2020  Status: Preprint / submitted

Carraturo, M.; Kollmannsberger, S.; Reali, A.; Ferdinando, F.; Rank, E. An immersed boundary approach for residual stress evaluation in SLM processes
submitted to Additive Manufacturing x (x), pp. xx, 2020
DOI: x
JournalPapers

Kudela, László; Kollmannsberger, Stefan; Almac, Umut; Rank, Ernst Show abstract Direct Structural Analysis of Domains Defined by Point Clouds
Computer Methods in Applied Mechanics and Engineering 358, 2020  Status: Verlagsversion / published
This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a highorder immersed boundary technique that computes on a regular background grid of Finite elements and requires only insideoutside information from the geometric model. It is shown that oriented point clouds provide sufficent information for these pointmembership classifications. Further, we address a tessellationfree formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Twodimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Threedimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.

Schröder, J.; Wick, T.; Reese, S.; Wriggers, P.; Müller, R.; Kollmannsberger, S.; Kästner, M.; Schwarz, A.; Igelbüscher, M.; Viebahn, N.; Bayat, H. R.; Wulfinghoff, S.; Mang, K.; Rank, E.; Bog, T.; D'Angella, D.; Elhaddad, M.; Hennig, P.; Düster, A.; Garhuom, W.; Hubrich, S.; Walloth, M.; Wollner, W.; Kuhn, C.; Heister, T. A selection of benchmark problems in solid mechanics and applied mathematics
Archives of Computational Methods in Engineering, 2020

Coradello, Luca; D'Angella, Davide; Carraturo, Massimo; Kiendl, Josef; Kollmannsberger, Stefan; Rank, Ernst; Reali, Alessandro Hierarchically refined isogeometric analysis of trimmed shells
Computational Mechanics, 2020
DOI: https://doi.org/10.1007/s00466020018586

Carraturo, M.; Jomo, J.; Kollmannsberger, S.; Rank, E.; Reali, A.; Auricchio, F. Show abstract Modeling and experimental validation of an immersed thermomechanical partscale analysis for laser powder bed fusion processes
Additive Manufacturing, 2020
DOI: https://doi.org/10.1016/j.addma.2020.101498  Status: Verlagsversion / published
The capability of correctly predicting part deflections after support removal is important to asses the quality of a final artifact produced by laser powder bed fusion (LPBF) technology. The finite element method is usually employed to perform partscale thermomechanical analysis to estimate the final distortion of 3D printed parts. Due to the high flexibility of LPBF additive manufacturing, most of the components produced by means of such a technology have an optimized shape and complex geometrical features. Consequently, the process of generating an analysis suitable mesh starting from the original 3D virtual model turns out to be a nontrivial task. Immersed boundary methods represent a possible solution to perform accurate process simulation without the meshing burden. In this work, an immersed numerical framework to perform thermomechanical partscale analysis is experimentally validated by means of part deflection measurements obtained for a singlecantilever structure after support removal. The comparison between simulation and experiment shows that the proposed numerical framework is able to deliver results with an almost perfect correlation to the measured data and a maximum relative error below 5%.

Carraturo, M.; Lane, B.; Yeung, H.; Kollmannsberger, S.; Reali, A.; Auricchio, F. Numerical evaluation of advanced laser control strategies
Integrating Materials and Manufacturing Innovation  (10), pp. , 2020
DOI: 10.1007/s40192020001913  Status: Verlagsversion / published

Korshunova, N.; Jomo, J.; Lékó, G.; Reznik, D.; Balázs, P.; Kollmannsberger, S. Show abstract Imagebased material characterization of complex microarchitectured additively manufactured structures
Computers and Mathematics with Applications, 2020
DOI: 10.1016/j.camwa.2020.07.018  Status: Verlagsversion / published
Significant developments in the field of additive manufacturing (AM) allowed the fabrication of complex microarchitectured components with varying porosity across different scales. However, due to the high complexity of this process, the final parts can exhibit significant variations in the nominal geometry. Computer tomographic images of 3D printed components provide extensive information about these microstructural variations, such as processinduced porosity, surface roughness, and other undesired morphological discrepancies. Yet, techniques to incorporate these imperfect AM geometries into the numerical material characterization analysis are computationally demanding. In this contribution, an efficient imagetomaterialparallel Finite Cell Method is proposed. In this way, a flexible nongeometryconforming discretization facilitates mesh generation for very complex microstructures at hand and allows a direct analysis of the images stemming from CTscans. Numerical examples including a comparison to the experiments illustrate the potential of the proposed framework in the field of additive manufacturing product simulation.

Wassermann, B.; Korshunova, N.; Kollmannsberger, S.; Rank, E.; Elber, G. Finite Cell Method for functionally graded materials based on Vmodels and homogenized microstructures
Advanced Modeling and Simulation in Engineering Sciences  (7), pp. 49, 2020
DOI: 10.1186/s40323020001821  Status: Verlagsversion / published

Hug, L.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. A 3D benchmark problem for crack propagation in brittle fracture
Computer Methods in Applied Mechanics and Engineering, 2020  Status: Verlagsversion / published

Jomo, J.; de Prenter, F.; Elhaddad, M.; D'Angella, D.; Verhoosel, C.; Kollmannsberger, S.; Kirschke, J.; Nübel, V.; van Brummelen, H.; Rank, E. Robust and parallel scalable iterative solutions for largescale finite cell analyses
Finite Elements in Analysis and Design  Status: Accepted for publication, 2019
DOI: 10.1016/j.finel.2019.01.009

Paolini, A.; Kollmannsberger, S.; Rank, E.; Horger, T.; Wohlmuth, B. Show abstract A mortar formulation including viscoelastic layers for vibration analysis
Computational Mechanics 63 (1), pp. 2333, 2019
DOI: 10.1007/s0046601815829  Status: Verlagsversion / published
In order to reduce the transfer of sound and vibrations in structures such as timber buildings, thin elastomer layers can be embedded between their components. The influence of these elastomers on the response of the structures in the low frequency range can be determined accurately by using conforming hexahedral finite elements. Threedimensional mesh generation, however, is yet a nontrivial task and mesh refinements which may be necessary at the junctions can cause a high computational effort. One remedy is to mesh the components independently from each other and to couple them using the mortar method. Further, the hexahedral mesh for the thin elastomer layer itself can be avoided by integrating its elastic behavior into the mortar formulation. The present paper extends this mortar formulation to take damping into account such that frequency response analyses can be performed more accurately. Finally, the proposed method is verified by numerical examples.

Kollmannsberger, S.; Carraturo, M.; Reali, A.; Auricchio, F. Show abstract Accurate prediction of melt pool shapes in laser powder bed fusion by the nonlinear temperature equation including phase changes
Integrating Materials and Manufacturing Innovation, 2019
DOI: 10.1007/s40192019001329  Status: Verlagsversion / published
In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB201802 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity

Paolini, A.; Kollmannsberger, S.; Rank, E. Show abstract Additive manufacturing in construction: A review on processes, applications, and digital planning methods
Additive Manufacturing, 2019
DOI: 10.1016/j.addma.2019.100894  Status: Postprint / reviewed
The application of additive manufacturing (AM) in construction has been increasingly studied in recent years. Large robotic arm and gantrysystems have been created to print building parts using aggregatebased materials, metals, or polymers. Significant benefits of AM are the automation of the production process, a high degree of design freedom, and the resulting potential for optimization. However, the building components and 3Dprinting processes need to be modeled appropriately. In this paper, the current state of AM in construction is reviewed. AM processes and systems as well as their application in research and construction projects are presented. Moreover, digital methods for planning 3Dprinted building parts and AM processes are described.

Kollmannsberger, Stefan; D'Angella, Davide; Rank, Ernst; Garhuom, Wadhah; Hubrich, Simeon; Düster, Alexander; Stolfo, Paolo Di; Schröder, Andreas Show abstract Spline and hpbasis functions of higher differentiability in the finite cell method
GAMMMitteilungen 0 (0), pp. e202000004, 2019
DOI: 10.1002/gamm.202000004  Status: Verlagsversion / published
In this paper, the use of hpbasis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, Ck hpbasis functions based on classical Bsplines and a new approach for the construction of C1 hpbasis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C1 approach also includes varying polynomial degrees. The properties of the hpbasis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the Ck hpbasis functions based on Bsplines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.

Nagaraja, S.; Elhaddad, M.; Ambati, M.; Kollmannsberger, S.; De Lorenzis, L.; Rank, E. Show abstract Phasefield modeling of brittle fracture with multilevel hpFEM and the finite cell method
Computational Mechanics 63 (63), pp. 118, Springer, 2019
DOI: 10.1007/s0046601816497  Status: Postprint / reviewed
The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phasefield approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small lengthscale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phasefield profile. In the classical approach, phasefield models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phasefield models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multilevel hprefinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes nontrivial. We address this issue by integrating a twodimensional phasefield framework for brittle fracture with the finite cell method (FCM). The FCM based on highorder finite elements is a nongeometryconforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multilevel hprefinement and the FCM in the context of phasefield simulations.

Wassermann, B.; Kollmannsberger, S.; S., Yin; L., Kudela; E., Rank Show abstract Integrating CAD and Numerical Analysis: ’Dirty Geometry’ handling using the Finite Cell Method
Computer Methods in Applied Mechanics and Engineering, 2019  Status: Verlagsversion / published
This paper proposes a computational methodology for the integration of Computer Aided De sign (CAD) and the Finite Cell Method (FCM) for models with “dirty geometries”. FCM, being a ﬁctitious domain approach based on higher order ﬁnite elements, embeds the physical model into a ﬁctitious domain, which can be discretized without having to take into account the bound ary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an e ﬀ ective Point Membership Classiﬁcation algorithm that determines the insideoutside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also “dirty geometries”, i.e. imprecise or ﬂawed geometric models, a combination of a segmenttriangle intersection algorithm and a ﬂood ﬁll algorithm be ing insensitive to most CAD model ﬂaws is proposed to identify the a ﬃ liation of the integration points. The present method thus allows direct computations on geometrically and topologically ﬂawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.

Paolini, A.; Frischmann, F.; Kollmannsberger, S.; Rabold, A.; Horger, T.; Wohlmuth, B.; Rank, E. Show abstract BIM gestützte strukturdynamische Analyse mit Volumenelementen höherer Ordnung
Bauingenieur 93 (4), pp. 160166, 2018  Status: Verlagsversion / published
Building Information Modeling ermöglicht die automatisierte Erstellung von Simulationsmodellen und schafft somit eine wichtige Grundlage, Zeit und Kosten einzusparen sowie die Qualität der Planung von Gebäuden zu erhöhen. Die Art des Simulationsmodells hängt jedoch wesentlich von der konkreten Problemstellung ab. Für Schwingungsanalysen bei Massivholzkonstruktionen ist eine mechanisch korrekte Beschreibung der Stoßstellen zwischen den Bauteilen von großer Bedeutung. Dafür eignen sich Modelle aus hexaedrischen finiten Elementen erheblich besser als Schalenelemente. Ein konformes Hexaedernetz kann allerdings mit verfügbaren Netzgeneratoren nur bei bestimmten Gebäudegeometrien automatisch erzeugt werden und weist an Stoßstellen eine große Anzahl von Elementen auf, was zu einem hohen Rechenaufwand führen kann. Im vorliegenden Beitrag wird deshalb ein alternatives Verfahren vorgestellt, mit dem ein hexaedrisches Finite Elemente Modell automatisch aus einem Bauwerksinformationsmodell (BIM) abgeleitet werden kann. Die im BIM definierten Bauteile werden dabei getrennt voneinander vernetzt und deren Verbindungen zueinander mit Hilfe der MortarMethode abgebildet. Eine große Recheneffizienz wird durch die Verwendung von Ansatzfunktionen höherer Ordnung in Kombination mit einem relativ groben Netz erreicht. Nach der Beschreibung des Verfahrens wird seine Anwendbarkeit an einem mehrgeschossigen Massivholzgebäude demonstriert.

Kudela, L.; Frischmann, F.; Yossef, O.; Uzan, A.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. Imagebased mesh generation of tubular geometries under circular motion in refractive environments
Machine Vision and Applications, 2018  Status: Verlagsversion / published

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Zander, N.; Rank, E. Show abstract A hierarchical computational model for moving thermal loads and phase changes with applications to Selective Laser Melting
Computers & Mathematics with Applications 75 (5), pp. 14831497, 2018
DOI: 10.1016/j.camwa.2017.11.014  Status: Verlagsversion / published
Computational heat transfer analysis often involves moving fluxes which induce traveling fronts of phase change coupled to one or more field variables. Examples are the transient simulation of melting, welding or of additive manufacturing processes, where material changes its state and the controlling fields are temperature and structural deformation. One of the challenges for a numerical computation of these processes is their multiscale nature with a highly localized zone of phase transition which may travel over a large domain of a body. Here, a transient local adaptation of the approximation, with not only a refinement at the phase front, but also a derefinement in regions, where the front has past is of advantage because the derefinement can assure a bounded number of degrees of freedom which is independent from the traveling length of the front. We present a computational model of this process which involves three novelties: a) a very low number of degrees of freedom which yet yields a comparatively high accuracy. The number of degrees of freedom is, additionally, kept practically constant throughout the duration of the simulation. This is achieved by means of the multilevel hpfinite element method. Its exponential convergence is verified for the first time against a semianalytic, threedimensional transient linear thermal benchmark with a traveling source term which models a laser beam. b) A hierarchical treatment of the state variables. To this end, the state of the material is managed on a separate, octreelike grid. This material grid may refine or coarsen independently of the discretization used for the temperature field. This methodology is verified against an analytic benchmark of a melting bar computed in three dimensions in which phase changes of the material occur on a rapidly advancing front. c) The combination of these technologies to demonstrate its potential for the computational modeling of selective laser melting processes. To this end, the computational methodology is extended by the finite cell method which allows for accurate simulations in an embedded domain setting. This opens the new modeling possibility that neither a scan vectors no a layer of material needs to conform to the discretization of the finite element mesh but can form only a fraction within the discretization of the field and state variables.

Özcan, A.; Kollmannsberger, S.; Jomo, J; De Lorenzis, L.; Rank, E. Residual stresses in metal deposition modeling: discretizations of higher order
Computers and Mathematics with Applications, 2018  Status: Postprint / reviewed

D'Angella, D.; Kollmannsberger, S.; Rank, E.; Reali, A. Multilevel Bézier extraction for hierarchical local refinement of Isogeometric Analysis
Computer Methods in Applied Mechanics and Engineering, 2018  Status: Verlagsversion / published

Elhaddad, M.; Zander, N.; Bog, T.; Kudela, L.; Kollmannsberger, S.; Kirschke, J.S.; Baum, T.; Ruess, M.; Rank, E. Multilevel hpfinite cell method for embedded interface problems with application in biomechanics
International Journal for Numerical Methods in Biomedical Engineering 34 (4), pp. e2951, Wiley, 2017
DOI: 10.1002/cnm.2951  Status: Verlagsversion / published

Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, RP.; Rank, E. Parallelization of the multilevel hpadaptive finite cell method
Computers and Mathematics with Applications 74 (1), pp. 126142, Elsevier, 2017
DOI: 10.1016/j.camwa.2017.01.004  Status: Verlagsversion / published

Hubrich, S.; Di Stolfo, P.; Kudela, L.; Kollmannsberger, S.; Rank, E.; Schröder, A.; Düster, A. Numerical integration of discontinuous functions: moment fitting and smart octree
Computational Mechanics, pp. 119, Springer, 2017
DOI: 10.1007/s0046601714410  Status: Verlagsversion / published

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Show abstract Weak imposition of frictionless contact constraints on automatically recovered highorder, embedded interfaces using the finite cell method
Computational Mechanics, 2017  Status: Postprint / reviewed
The finite cell method (FCM) is a fictitious domain approach that greatly simplifies simulations involving complex structures. Recently, the FCM has been applied to contact problems. The current study continues in this field by extending the concept of weakly enforced boundary conditions to inequality constraints for frictionless contact. Furthermore, it formalizes an approach that automatically recovers highorder contact surfaces of (implicitly defined) embedded geometries by means of an extended Marching Cubes (MC) algorithm. To further improve the accuracy of the discretization, irregularities at the boundary of contact zones are treated with multilevel hprefinements. Numerical results and a systematic study of h, p and hprefinements show that the FCM can efficiently provide accurate results for problems involving contact.

Wassermann, B.; Kollmannsberger, S.; Bog, T.; Rank, E. Show abstract From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry
Computers & Mathematics with Applications, 2017
During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottleneck. Several approaches have been developed to overcome this timeconsuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically BSplines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (BRep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the models interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration) point lies inside or outside of the geometric model. This paper mainly discusses such pointinmembership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the pointinmembershiptest can be carried out effciently and robustly.

Bas, O.; DeJuanPardo, E.; Meinert, C.; D'Angella, D.; Baldwin, J.; Bray, L.; Wellard R.; Kollmannsberger, S.; Rank, E. Werner, C.; Klein, T.; Catelas I.; Hutmacher, D.W. Biofabricated soft network composites for cartilage tissue engineering
Biofabrication, Biofabrication, 2017
DOI: 10.1088/17585090/aa6b15  Status: Verlagsversion / published

Onur Bas; Davide D'Angella; Jeremy G. Baldwin; Nathan J. Castro; Felix M. Wunner; Navid T. Saidy; Stefan Kollmannsberger; Alessandro Reali; Ernst Rank; Elena M. DeJuanPardo; Dietmar W. Hutmacher Show abstract An integrated design, material and fabrication platform for engineering biomechanically and biologically functional soft tissues
ACS Appl. Mater. Interfaces, 2017
DOI: 10.1021/acsami.7b08617  Status: Verlagsversion / published
The development of advanced soft materials can be faciliated through bioinspired design methodologies. Translating the fibrereinforcement approach of nature, biologically functional soft network composites with enhanced compressive mechanical properties have been achieved. However, design and fabrication concepts addressing the mechanical requirements of tissues which are predominantly functioning under tensile loading (e.g., skin, tendon, ligament, muscle, etc.) are under studied in the current literature. In this communication, to our knowledge for the first time we describe and validate a design library combined with a innovative biomaterials & 3D printing platform which meets the requirements for tissue engineering applications subjected to tensile loads. Herein, we present a library of fibre elements to be used as building blocks for the development of tailored fibrous networks. These fibrous networks are then combined with a tunable interpenetrating polymer network (IPN) system that mimics highly flexible natural extracellular matrices (ECMs). Our holistic design allows the selection and fabrication of customised reinforcing fibre networks and matrices to match both complex tissuespecific biomechanical and biological properties. We mechanically validate our approach through an exemplary soft network composite model which is charactarized to be flexible yet ~125 times stronger (E = 3.19 MPa) and ~100 times tougher (WExt = ~2000 kJ m3) than its bare hydrogel counterpart.

Paolini, A.; Kollmannsberger, S.; Winter, C.; Buchschmid, M.; Müller, G.; Rabold, R.; Mecking, S.; Schanda, U.; Rank, E. Show abstract A high order finite element model for vibration analysis of cross laminated timber assemblies
Building Acoustics 24 (3), pp. 135158, 2017
DOI: 10.1177/1351010X17727126  Status: Verlagsversion / published
The vibration behavior of cross laminated timber (CLT) components in the low frequency range can be predicted with high accuracy by the finite element method. However, the modeling of assembled CLT components has been studied only scarcely. The threedimensional pversion of the finite element method, which is characterized by hierachical high order shape functions, is well suited to consider coupling and support conditions. Furthermore, a small number of degrees of freedom can be obtained in case of thinwalled structures by using pelements with high aspect ratios and anisotropic ansatz spaces. In this paper, a model for CLT assemblies made of volumetric high order finite elements is presented. Two representative types of connections are investigated, one with an elastomer between the CLT components and the other without. The model is validated and suitable ranges for the stiffness parameters of the finite elements which represent the junction are identified.

Zander, N.; Bog, T.; Elhaddad, M.; Frischmann, F.; Kollmannsberger, S.; Rank, E. The multilevel hpmethod for threedimensional problems: Dynamically changing highorder mesh refinement with arbitrary hanging nodes.
Computer Methods in Applied Mechanics and Engineering 310, pp. 252277, 2016
DOI: 10.1016/j.cma.2016.07.007

D'Angella, D.; Zander, N.; Kollmannsberger, S.; Frischmann, F.; Rank, E.; Schröder, A.; Reali, A. Show abstract MultiLevel hpAdaptivity and Explicit Error Estimation
Advanced Modeling and Simulation in Engineering Sciences, pp. 118, Springer, 2016
DOI: 10.1186/s4032301600855  Status: Verlagsversion / published
Recently, a multilevel hpversion of the Finite Element Method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hpapproximation capabilities. In the original paper, the refinement procedure made use of apriori knowledge of the solution. However, adaptive procedures can produce discretizations which are more effective than an intuitive choice of element sizes h and polynomial degree distributions p. This is particularly prominent when apriori knowledge of the solution is only vague or unavailable. The present contribution demonstrates that multilevel hpadaptive schemes can be efficiently driven by an explicit aposteriori error estimator. To this end, we adopt the classical residualbased error estimator. The main insight here is that its extension to multilevel hpFEM is possible by considering the refinedmost overlay elements as integration domains. We demonstrate on several two and threedimensional examples that exponential convergence rates can be obtained.

Kudela, László; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst Smart octrees: accurately integrating discontinuous functions in 3D
Computer Methods in Applied Mechanics and Engineering, 2016  Status: Verlagsversion / published

Di Stolfo, P.; Schröder, A.; Zander, N.; Kollmannsberger, S. Show abstract An easy treatment of hanging nodes in hpfinite elements
Finite Elements in Analysis and Design 121, pp. 101117, 2016
DOI: 10.1016/j.finel.2016.07.001  Status: Verlagsversion / published
We present an easy treatment of (multilevel) hanging nodes in hpfinite elements in two dimensions. Its simplicity is due to the fact that the connectivity matrices can directly be computed in a rowwise fashion. This is achieved by treating a global degree of freedom as a local degree of freedom on each element in an appropriate union of elements. This forms a type of support which is larger than the one used in the conventional approach and generalizes the recently presented multilevel hpmethod. Numerical experiments compare the new approach with respect to accuracy and the conditioning of the resulting linear system. We conclude that this new approach achieves nearly the same properties as the conventional approach in all investigated examples and provides an excellent tradeoff between implementational complexity and solvability.

Zander, N.; Ruess, M.; Bog, T.; Kollmannsberger, S.; Rank, E. MultiLevel hpAdaptivity for Cohesive Fracture Modelling
International Journal for Numerical Methods in Engineering 109 (3), pp. 17231755, 2016
DOI: 10.1002/nme.5340  Status: Verlagsversion / published

Kudela, L.; Zander, N.; Bog, T.; Kollmannsberger, S.; Rank, E. Show abstract Efficient and accurate numerical quadrature for immersed boundary methods
Advanced Modeling and Simulation in Engineering Sciences 2 (1), Springer International Publishing, 2015
DOI: 10.1186/s403230150031y  Status: Verlagsversion / published
One question in the context of immersed boundary or fictitious domain methods is how to compute discontinuous integrands in cut elements accurately. A frequently used method is to apply a composed Gaussian quadrature based on a spacetree subdivision. Although this approach works robustly on any geometry, the resulting integration mesh yields a low order representation of the boundary. If high order shape functions are employed to approximate the solution, this lack of geometric approximation power prevents exponential convergence in the asymptotic range. In this paper we present an algorithmic subdivision approach that aims to be as robust as the spacetree decomposition even for closetodegenerate cases—but remains geometrically accurate at the same time. Based on 2D numerical examples, we will show that optimal convergence rates can be obtained with a nearly optimal number of integration points.

Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst Show abstract MultiLevel hpAdaptivity: HighOrder Mesh Adaptivity without the Difficulties of Constraining Hanging Nodes
Computational Mechanics 55 (3), pp. 499ff., 2015
DOI: 10.1007/s004660141118x  Status: Verlagsversion / published
The implementation of hpadaptivity is challenging as hanging nodes, edges, and faces have to be constrained to ensure compatibility of the shape functions. For this reason, most hpcode frameworks restrict themselves to 1irregular meshes to ease the implementational effort. This work alleviates these difficulties by introducing a new formulation for highorder mesh adaptivity that provides full local hprefinement capabilities at a comparably small implementational effort. Its main idea is the extension of the hpd method such that it allows for highorder overlay meshes yielding a hierarchical, multilevel hpformulation of the Finite Element Method. This concept enables intuitive refinement and coarsening procedures, while linear independence and compatibility of the shape functions are guaranteed by construction. The proposed method is demonstrated to achieve exponential rates of convergence for problems with nonsmooth solutions, is used alongside the Finite Cell Method to simulate the heat flow around moving objects on a nonconforming background mesh and is combined with an energybased refinement indicator for automatic hpadaptivity.

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Show abstract Normal contact with high order finite elements and a fictitious contact material
Computers & Mathematics with Applications 70 (7), pp. 1370–1390, 2015
DOI: 10.1016/j.camwa.2015.04.020  Status: Verlagsversion / published
Contact problems in solid mechanics are traditionally solved using the hversion of the finite element method. The constraints are enforced along the surfaces of e.g. elastic bodies under consideration. Standard constraint algorithms include penalty methods, Lagrange multiplier methods and combinations thereof. For complex scenarios, a major part of the solution time is taken up by operations to identify points that come into contact. This paper presents a novel approach to model frictionless contact using high order finite elements. Here, we employ an especially designed material model that is inserted into two respectively three dimensional regions surrounding contacting bodies. Contact constraints are thus enforced on the same manifold as the accompanying structural problem. The application of the current material formulation leads to a regularization of the KarushKuhnTucker conditions. Our formulation can be classified as a barriertype method. Results are obtained for two and threedimensional prob lems, including a Hertzian contact problem. Comparisons to a commercial FEA package are provided. The proposed formulation works well for nonmatching discretizations on adjacent contact interfaces and handles selfcontact naturally. Since the nonpenetrating conditions are solved in a physically consistent man ner, there is no need for an explicit contact search.

Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Shadavakhsh, A.; Nübel, V.; Rank, E. Show abstract Finite Cell Method: High order structural dynamics for complex geometries
International Journal for Structural Stability and Dynamics 15 (7), pp. 125, 2015
DOI: 10.1142/S0219455415400180  Status: Verlagsversion / published
In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundaryvalue problem. Semidiscrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A onedimensional benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using stateoftheart commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

Kollmannsberger, S.; Özcan, A.; Baiges, J.; Ruess, M.; Rank, E.; Reali,A. Parameterfree, weak imposition of Dirichlet boundary conditions and coupling of trimmed and nonconforming patches
International Journal For Numerical Methods In Engineering, 2015
DOI: 10.1002/nme.4817

Sorger, C.; Frischmann, F.; Kollmannsberger, S.; Rank, E. Show abstract TUM.GeoFrame: Automated highorder hexahedral mesh generation for shelllike structures
Engineering with Computers 30 (1), pp. 4156, 2014
DOI: 10.1007/s0036601202848
This paper presents a fully automated highorder hexahedral mesh generation algorithm for shelllike structures based on enhanced sweeping methods. Traditional sweeping techniques create allhexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming highorder allhexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skewangled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a socalled interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.

Cai, Quanji; Kollmannsberger, Stefan; Sala, Esther; Antonio, Huerta; Rank, Ernst On the natural stabilization of convection dominated problems using high order BubnovGalerkin Finite Elements
Computers & Mathematics with Applications 66 (12), pp. 25452558, 2014
DOI: 10.1016/j.camwa.2013.09.009  Status: Verlagsversion / published

Rabold, A.; Schanda, U.; Kollmannsberger, S.; Rank, E. Schallschutz im mehrgeschossigen Holzbau  Luft und Trittschalldämmung von Trenndecken 
Bauingenieur 89, 2014  Status: Verlagsversion / published

Zander, N.; Bog, T; Elhaddad, M.; Espinoza, R.; Hu, H.; Joly, A.F.; Wu, C.; Zerbe, P.; Düster, A.; Kollmannsberger, S.; Parvizian, J.; Ruess, M.; Schillinger, D.; Rank, E. FCMLab: A Finite Cell Research Toolbox for MATLAB
Advances in Engineering Software 74, pp. 4963, 2014
DOI: 10.1016/j.advengsoft.2014.04.004  Status: Verlagsversion / published

Horger, T.; Kollmannsberger, S.; Frischmann, F.; Rank, E.; Wohlmuth, B. A new mortar formulation for modeling elastically bedded structures in vibroacoustics in 3D
Advanced Modeling And Simulation In Engineering Sciences 1 (18), 2014  Status: Postprint / reviewed

Yang, Z.; Ruess, M.; Kollmannsberger, S.; Düster, A.; Rank, E. An efficient integration technique for the voxelbased finite cell method
International Journal for Numerical Methods in Engineering 91 (5), pp. 457471, John Wiley & Sons, Ltd, 2012
DOI: 10.1002/nme.4269

Zander, N.; Kollmannsberger, S.; Ruess, M.; Yosibash, Z.; Rank, E. Show abstract The Finite Cell Method for linear thermoelasticity
Computers & Mathematics with Applications 64 (11), pp. 3527  3541, 2012
DOI: 10.1016/j.camwa.2012.09.002
The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of highorder Finite Elements. While previous publications concentrated on singlefield applications, this paper demonstrates that the advantages of the method carry over to the multiphysical context of linear thermoelasticity. The ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem. A second example shows that the Finite Cell Method correctly captures the thermoelastic state of a complex problem from engineering practice. Both examples additionally verify that, also for twofield problems, Dirichlet boundary conditions can be weakly imposed on nonconforming meshes by the proposed extension of Nitsche's Method. The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of highorder Finite Elements. While previous publications concentrated on singlefield applications, this paper demonstrates that the advantages of the method carry over to the multiphysical context of linear thermoelasticity. The ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem. A second example shows that the Finite Cell Method correctly captures the thermoelastic state of a complex problem from engineering practice. Both examples additionally verify that, also for twofield problems, Dirichlet boundary conditions can be weakly imposed on nonconforming meshes by the proposed extension of Nitsche's Method.

Rank, E.; Ruess, M.; Kollmannsberger, S.; Schillinger, D.; Düster, A. Geometric modeling, isogeometric analysis and the finite cell method
Computer Methods in Applied Mechanics and Engineering 249252 (0), pp. 104  115, 2012
DOI: 10.1016/j.cma.2012.05.022

Yang, Zhengxiong; Kollmannsberger, Stefan; Düster, Alexander; Ruess, Martin; Garcia, Eduardo Grande; Burgkart, Rainer; Rank, Ernst Show abstract Nonstandard bone simulation: interactive numerical analysis by computational steering
Computing and Visualization in Science 14 (5), pp. 207–216, SpringerVerlag, 2011
DOI: 10.1007/s007910120175y
Numerous numerical methods have been developed in an effort to accurately predict stresses in bones. The largest group are variants of the hversion of the finite element method (hFEM), where low order Ansatz functions are used. By contrast, we3 investigate a combination of high order FEM and a fictitious domain approach, the finite cell method (FCM). While the FCM has been verified and validated in previous publications, this article proposes methods on how the FCM can be made computationally efficient to the extent that it can be used for patient specific, interactive bone simulations. This approach is called computational steering and allows to change input parameters like the position of an implant, material or loads and leads to an almost instantaneous change in the output (stress lines, deformations). This direct feedback gives the user an immediate impression of the impact of his actions to an extent which, otherwise, is hard to obtain by the use of classical non interactive computations. Specifically, we investigate an application to presurgical planning of a total hip replacement where it is desirable to select an optimal implant for a specific patient. Herein, optimal is meant in the sense that the expected postoperative stress distribution in the bone closely resembles that before the operation.

Rank, E.; Kollmannsberger, S.; Sorger, Ch.; Düster, A. Shell Finite Cell Method: A high order fictitious domain approach for thinwalled structures
Computer Methods in Applied Mechanics and Engineering 200 (4546), pp. 3200  3209, 2011
DOI: 10.1016/j.cma.2011.06.005

Rank, E.; Kollmannsberger, S.; Düster, A. High Order Finite Elements: Principles, Achievements, Open Questions
In: Topping, B.H.V.; Adam, J.M.; Pallares, F.J.; Bru, R.; Romero, M.L. (Eds): Computational Technology Reviews, SAXECOBURG Publications, 2010

Geller, S.; Kollmannsberger, S.; Bettah, M.El; Krafczyk, M.; Scholz, D.; Düster, A.; Rank, E. An Explicit Model for ThreeDimensional FluidStructure Interaction using LBM and pFEM
In: Bungartz, HansJoachim; Mehl, Miriam; Schäfer, Michael (Eds.), Fluid Structure Interaction II, 73, Springer Berlin Heidelberg, 2010, pp. 285325

Kollmannsberger, S.; Geller, S.; Düster, A.; Tölke, J.; Sorger, C.; Krafczyk, M.; Rank, E. Fixedgrid fluidstructure interaction in two dimensions based on a partitioned Lattice Boltzmann and pFEM approach
International Journal for Numerical Methods in Engineering 79 (7), pp. 817845, John Wiley & Sons, Ltd., 2009
DOI: 10.1002/nme.2581

Scholz, Dominik; Kollmannsberger, Stefan; Düster, Alexander; Rank, Ernst Thin Solids for FluidStructure Interaction
In: Bungartz, HansJoachim; Schäfer, Michael (Eds.), FluidStructure Interaction, 53, Springer Berlin Heidelberg, 2006, pp. 294335
Show all entries 
Conference Proceedings

D. D'Angella; L. Coradello; M. Carraturo; L. Kudela; S. Kollmannsberger; E. Rank; A. Reali Trimming and Local Refinement for Isogeometric Shells Analysis
In: HOFEIM2019, 2019

Korshunova N., Jomo J., Reznik D., Kollmannsberger S., Rank E. From CTScans to material characterization: mechanical behavior of microporous metal structures
In: HighOrder Finite Element and Isogeometric Methods, 2019

D’Angella, D.; Hughes, T.J.R.; Kollmannsberger, S.; Rank, E.; Reali, A. Reaction computations on trimmed locally refined meshes
In: Seventh International Conference on Isogeometric Analysis (IGA 2019), 2019

Korshunova, N., Jomo, J., Reznik, D., Kollmannsberger, S., Rank, E. Material characterization of additively manufactured complex steel components
In: Simulation for Additive Manufacturing (SimAM 2019), 2019

Hug, L.; Elhaddad, M.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. A PhaseField Model for Crack Propagation in 3D using the Finite Cell Method
In: International Conference on Computational Modeling of Fracture and Failure of Materials and Structures (CFRAC), 2019

Garhuom, W.,; Hug, L.; Di Stolfo, P.; Hubrich, S.; Radtke, L.; Düster, A.; Kollmannsberger, S.; Rank, E.; Schröder, S. The Finite Cell Method: New hptype discretizations and nonlinear applications
In: Modern Finite Element Technologies (MFET), 2019

Jomo J., Carraturo M., Hug. L, Kollmannsberger S., Mundani R. P., Rank E. Numerical simulation of coupled problems in the context of the parallel hpadaptive finite cell method
In: VIII International Conference on Coupled Problems in Science and Engineering, Sitges, Spain, 2019

Kollmannsberger, S.; Carraturo, M.; D'Angella, D.; Auricchio, F.; Reali, A.; Rank, E. Accurate prediction of melt pool shapes in laser powder bed fusion by the nonlinear temperature equation including phase changes
In: Simulation in Additive Manufacturing, Rovereto, Italy, 2019

Kollmannsberger, S.; Kudela, L.; Rank, E. Structural analysis of domains defined by point clouds
In: HighOrder Finite Element and Isogeometric Methods, Pavia, Italy, 2019

Kollmannsberger, S.; Carraturo, M.; Auricchio, F.; Reali, A.; Rank, E. Simulation of AM processes: Aspects of verification and validation
In: Additive Manufacturing: The process chain, from designers to endusers, Rovereto, Italy, 2019

Wassermann, Benjamin; Kollmannsberger, Stefan; Rank, Ernst; Elber, Gershon Simulation of functionally graded materials using VReps and the Isogeometric Finite Cell Method
In: Proc. of the IGA 2019 Conference, Munich, Germany, 2019

Di Stolfo, P.; Düster, A.; Kollmannsberger, S.; E., Rank; Schröder, A. Show abstract A posteriori error control for the finite cell method
In: Proceedings in Applied Mathematics \ Mechanics, Vienna, Austria, 2019  Status: Verlagsversion / published
The paper presents some concepts of the finite cell method and discusses a posteriori error control for this approach. The focus is on the application of the dual weighted residual approach (DWR), which enables the control of the error with respect to a userdefined quantity of interest. Since both the discretization error and the quadrature error are estimated, the application of the DWR approach provides an adaptive strategy which equilibrates the error contributions resulting from discretization and quadrature. The strategy consists in refining either the finite cell mesh or its associated quadrature mesh. Numerical experiments confirm the performance of the error control and the adaptive scheme for a nonlinear problem in 2D.

Jomo J., Korshunova N., Carraturo M., Kollmannsberger S., Mundani R. P., Rank E. A parallel immersed finite element framework for numerical computations of metal additive manufacturing processes and products
In: II International Conference on Simulation for Additive Manufacturing, Pavia, Italy, 2019

Kollmannsberger, S.; Kudela, L.; Rank, E. Structural analysis of domains defined by point clouds
In: Photogrammetric Image Analysis 2019, Munich, Germany, 2019

Onur Bas; Elena M. DeJuanPardo; Davide D'Angella; Stefan Kollmannsberger; Alessandro Reali; Ernst Rank; D. W. Hutmacher Rational design and fabrication of soft network composites for soft tissue engineering applications: a numerical modelbased approach
In: TERMIS 5th World Congress, Kyoto, Japan, 2018

Kudela, L.; Kollmannsberger, S.; Rank, E. An immersed boundary approach for the numerical analysis of objects represented by oriented point clouds
In: CompIMAGE’18 – Computational Modeling of Objects Presented in Images: Fundamentals, Methods, and Applications, 2018  Status: Postprint / reviewed

Paolini, A.; Winter, C.; Müller, G.; Kollmannsberger, S.; Rank, E. Show abstract Vergleich der h und pVersion der FEM zur Prognose des Körperschalls in Massivholzkonstruktionen
In: Fortschritte der Akustik, DAGA 2018, München, Deutschland, 2018
Bei der Planung eines Massivholzgebäudes sollte der Schallschutz sorgfältig berücksichtigt werden. Für die Bestimmung des Körperschalls in Massivholzkonstruktionen ist beispielsweise die Energieflussanalyse geeignet, die auf der Finiten Elemente Methode (FEM) basiert. Der Berechnungsaufwand kann jedoch insbesondere im hohen Frequenzbereich groß sein, weil eine feine Diskretisierung zur Berücksichtigung geringer Wellenlängen erforderlich ist. Im vorliegenden Beitrag wird deshalb der Einfluss verschiedener Diskretisierungsansätze auf den Aufwand von Körperschallprognosen im bauakustisch relevanten Bereich bis etwa 3000 Hz anhand eines repräsentativen DeckenWandanschlusses untersucht. Dabei werden zwei unterschiedliche Strategien zur Erhöhung der Genauigkeit der Lösung angewendet: hVerfeinerung und pVerfeinerung. Im Fall der hVerfeinerung wird das FiniteElementeNetz verfeinert, ohne den Polynomgrad der Ansatzfunktionen zu erhöhen. Im Fall der pVerfeinerung wird der Polynomgrad erhöht, während das Netz grob bleibt. Die Ergebnisse dieser Untersuchung zeigen, dass die Recheneffizienz im betrachteten Frequenzbereich durch die Verwendung von Ansatzfunktionen hoher Ordnung deutlich gesteigert werden kann.

Davide D'Angella; Stefan Kollmannsberger; Ernst Rank; Alessandro Reali Efficient Algorithms for the Extraction of (Truncated) Hierarchical B Splines
In: 3rd Conference on Isogeometric Analysis and Applications, 2018

Davide D'Angella; Luca Coradello; Massimo Carraturo; László Kudela; Stefan Kollmannsberger; Ernst Rank; Alessandro Reali Locally Refined Isogeometric Analysis of Trimmed Shells
In: The 13th World Congress in Computational Mechanics, 2018

Korshunova, N., Jomo, J., Reznik, D., Kollmannsberger, S., Düster, A., Rank, E. Show abstract From images to material characterization of additively manufactured microarchitectured structures
In: 13th World Congress in Computational Mechanics, 2018
Recent developments in additive manufacturing have provided a unique possibility to create complex structures with porosity on a micro and mesostructural levels. Such designs can outperform conventional materials in specific industrial applications, e.g. turbine blades with a transpiration cooling. However, the high flexibility of the input parameters for the 3D printers, such as the laser diameter, hatch distance etc., challenges a reliable estimation of the mechanical behaviour of the final parts. Moreover, a high variation of porosity in all of the material directions limits the application of analytical bounds based on the void fraction ratio. Numerical homogenization is an efficient and robust alternative to perform nondesctructive evaluation of the material characteristics based on high resolution 3D images of produced specimens. The conventional Finite Element Method applied to numerical homogenization leads to a labor intensive meshing procedure to extract the representative volume elements that makes it impractial from the industrial point of view. Furthermore, nonsymmetric microarchitectured structures make it difficult to apply correct boundary conditions for the solution of the microstructural boundary value problem. To address these issues, in the scope of the presented work the Finite Cell Method is employed in combination with the window method. A road map is presented for the automatized numerical computation of the homogenized elasticity tensor of additively manufactured steel structures using 3D images. The computational results are verified with the direct finitecell computation of a given produced specimen. Validation of the proposed model is performed comparing the numerical results with the results stemming from experimental tests.

Davide D'Angella; Luca Coradello; Massimo Carraturo; László Kudela; Stefan Kollmannsberger; Ernst Rank; Alessandro Reali Trimming and Local Refinement for Isogeometric Shells Analysis
In: 6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems) (ECCM 6) and the 7th European Conference on Computational Fluid Dynamics (ECFD 7), 2018

Kopp, P.; Korshunova, N.; Seidl, R.; Zander, N.; Kollmannsberger, S.; Rank, E. Finite Cell discretizations for Full Waveform Inversion
In: European Conference on Computational Mechanics, 2018

Kudela, L.; Almac, U.; Kollmannsberger, S.; Rank, E. Direct numerical analysis of historical structures represented by point clouds
In: EUROMED 2018: International Conference on Digital Heritage, Cyprus, 2018  Status: Postprint / reviewed

Kollmannsberger, S.; Carraturo, M.; D'Angella, D.; Auricchio, F.; Özcan, A.; Reali, A.; Rank, E. Show abstract Multilevel finite elements of highorder for the simulation of melt pool sizes and cooling rates in metal additive manufacturing
In: AM Bench conference, Geithersburg, Washington, USA, 2018
The presentation addresses the numerical modelling of the benchmark AMB201802 where we take upon the challenge of verifying the melt pool geometry (CHALAMB201802MP) and the cooling rate (CHALAMB201802CR). We employ a variant of the numerical model presented in [1] and extend it to hierarchical BSplines [2]. The principal idea is to use highorder refinements to resolve the region around the boundary of the weld pool with high accuracy. The numerical effort in parts of the domain remote to the laser impact are coarsened such that a computationally efficient model results.

Nagaraja, S.; Elhaddad, M.; Ambati, M.; Kollmannsberger, S; De Lorenzis, L.; Rank E. Phasefield modeling of brittle fracture with multilevel hpFEM and the finite cell method
In: 6th European Conference on Computational Mechanics, Glasgow, United Kingdom, 2018

Paolini, A.; Kollmannsberger, S.; Rank, E. Additive Manufacturing in Construction: An Overview
In: LOC Center Day, Munich, Germany, 2018

de Prenter, F.; Jomo, J.; Elhaddad, M.; D'Angella, D.; Kollmannsberger, S.; Verhoosel, C.; van Brummelen, H.; Rank, E. Preconditioned iterative solvers for the multilevel hpadaptive finite cell method
In: 6th European Conference on Computational Mechanics, Glasgow, United Kingdom, 2018

Jomo, J.; Patel, N.; Kudela, L.; Kopp, P.; Ertl, C.; Kollmannsberger, S.; Allalen, M.; Mundani, RP.; Rank, E. Enabling efficient numerical simulations using the finite cell method on massively parallel systems
In: Environmental Informatics Techniques and Trends, Adjunct Proceedings of the 32nd EnviroInfo conference, Garching, Germany, 2018

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; D'Angella, D.; Zander, N.; Auricchio, A.; Reali, A.; Rank, E. Verification of a multilevel model for the simulation of AM processes
In: 89. Annual Meeting of the International Assosication of Applied Mathematics and Mechanics, Munich, Germany, 2018

Kollmannsberger, S.; Kaufmann, S.; Paolini, A.; Rank, E. Additive Manufacturing in Construction
In: Annual Meeting of the LOC, Munich, Germany, 2018

Kollmannsberger, S.; Özcan, A.; D'Angella, D.; Carraturo, M.; Kopp, P.; Zander, N.; Reali, A.; Auricchio, F.; Rank, E. Show abstract Computational Modelling of Metal Additive Manufacturing
In: European Conference on Computational Mechanics, Glasgow, UK, 2018
The numerical simulation of metal additive manufacturing bears numerous computational challenges. It is a thermomechanically coupled process in which material coefficients depend nonlinearly on the state of the material and the temperature. The energy input is highly localized which leads to strong temperature gradients and rapid changes of state in the material on growing computational domains. The large span of the involved spatial and the temporal scales call for highly efficient computational techniques. It is well known that hpfinite elements yield very accurate results for problems with strong gradients or even singular solutions. hpfinite elements are, therefore, an ideal candidate for the simulation of metal additive manufacturing. In this contribution, we present a computational framework which was specifically designed to resolve moving singularities and sharp fronts. Its core employs the multilevel hpmethod for the resolution of strong gradients in the solution field. This is complemented by a spatially hierarchic management of material coefficients in the spirit of the finite cell method. We will discuss the computation of the metal additive manufacturing process and evaluate accuracy and efficiency of the presented computational approach by comparison to benchmark solutions.

Carraturo, M.; Kollmannsberger, S.; Rank, E.; Auricchio, F.; Reali, A. Thermal simulation of Additive Manufacturing Processes using immersed multilevel isogeometric analysis
In: 10th European Solid Mechanics Conference, Bolognia, Italy, 2018

Carraturo, M.; Özcan, A.; D'Angella, D; Kollmannsberger, S.; Rank, E.; Auricchio, F.; Reali, A. Thermal Simulations of Additive Manufacturing Processes using Multilevel Isogeometric Analysis
In: World Congress of Computational Mechnaics, New York, USA, 2018

Wassermann, Benjamin; Kollmannsberger, Stefan; Rank, Ernst Direct Simulation of ‘dirty’ geometries using the Finite Cell Method
In: 6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems) (ECCM 6) and the 7th European Conference on Computational Fluid Dynamics (ECFD 7), Glasgow, UK, 2018

Wassermann, B.; Kollmannsberger, S.; E., Rank 'Dirty geometry' and splinebased numerical analysis
In: IGA 2018: Integrating Design and Analysis, Austin, USA, 2018

Elhaddad, M.; Kollmannsberger, S.; Valentinitsch, A.; Kirschke, J.S.; Ruess, M.; Rank, E. MicroCT based finite cell analysis of vertebral bodies
In: Engineering Mechanics Institute Conference 2017, San Diego, CA, USA, 2017

Özcan A.; Kollmannsberger S.; Jomo J.; Rank E. Thermoelastoplastic simulation of selective laser melting processes with multilevel hpadaptive finite cell method
In: XIV International Conference on Computational Plasticity , 2017

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Egger, J.; Schröder, A.; Rank, E. A multilevel model for the simulation of AM processes
In: Simulation for Additive Manufacturing, 2017  Status: Preprint / submitted

Paolini, A.; Frischmann, F.; Kollmannsberger, S.; Rabold, A.; Mecking, S.; Schanda, U.; Rank, E. Show abstract Abbildung von Elastomeren in FEModellen von Holzbaukonstruktionen
In: Fortschritte der Akustik, DAGA 2017, Kiel, Deutschland, 2017
Elastomere werden wegen ihrer viskoelastischen Eigenschaften in Holzbauverbindungen eingesetzt, um die Übertragung von Körperschall zwischen Bauteilen zu vermindern. Ihre Wirkung auf das Schwingungsverhalten von Holzbaukonstruktionen im niederfrequenten Bereich kann mit der Finiten Elemente Methode prognostiziert werden. Zur Erzielung aussagekräftiger und genauer Ergebnisse müssen geeignete Materialparameter für die finiten Elemente bestimmt werden, welche die Elastomere unter Verwendung eines viskoelastischen Materialmodells darstellen. Eine Möglichkeit, bei der keine weiteren experimentellen Untersuchungen durchzuführen sind, ist die Berechnung des komplexen Elastizitätsmoduls aus den Datenblattangaben des ElastomerHerstellers für eine festgelegte Querdehnzahl. Allerdings ist die Querdehnzahl nicht genau bekannt. Zudem werden bei diesem Verfahren vereinfachende Annahmen getroffen. Beispielsweise werden zusätzliche Aspekte des Aufbaus von Holzbauverbindungen wie die Verschraubung nicht berücksichtigt. Im vorliegenden Beitrag wird ein FEModell eines DeckenWandanschlusses, der eine Elastomerschicht enthält, hinsichtlich des Einflusses der Materialparameter des Elastomers auf dessen Eigenfrequenzen untersucht. Ferner werden die Berechnungsergebnisse mit den Messergebnissen einer Betriebsschwinganalyse verglichen. Hierdurch ist eine Verifikation der Modellannahmen und die Angabe eines geeigneten Wertebereichs der Querdehnzahl für den untersuchten Elastomertyp möglich.

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Kopp, P.; Jomo, J.; Rank, E. Additive Manufacturing
In: Advanced School on Immersed Methods, Eindhoven, Netherlands, 2017

Davide D'Angella; Onur Bas; Dietmar W. Hutmacher; Stefan Kollmannsberger; Alessandro Reali; Ernst Rank Simulation of Hydrogel Reinforced by 3D Printed Fibres
In: Simulation for Additive Manufacturing, 2017

D'Angella, D.; Kollmannsberger, S.; Rank, E.; Reali, A. The multilevel Bézier extraction
In: International Conference on Computational Plasticity, 2017

D'Angella, D.; Kollmannsberger, S.; Rank, E.; Reali, A. IGA Based on Extraction of (Truncated) Hierarchical BSplines
In: International Conference on Isogeometric Analysis, 2017

Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, RP.; Rank, E. A parallel approach for the multilevel hpdaptive finite cell method
In: Siam Conference on Computational Science and Engineering 2017, SIAM, 2017

Korshunova, N.; Reznik, D.; Kollmannsberger, R.; Rank, E. Show abstract Numerical simulation of material parameters of additively manufactured porous metal parts
In: 1st ECCOMAS Thematic Conference on Simulation for Additive Manufacturing, 2017
Selective Laser Melting is a wellknown variant of additive manufacturing. It offers the possibility to design porous, latticetype structures with desired mesoscale structure properties by varying the hatch distance and the laser scan direction. The porosity of such materials may be exploited e.g. in the design of nextgeneration gas turbine blades using transpiration cooling. However, the mechanical properties of these new type of materials must be estimated carefully prior to the built process to assure the quality of the finished parts. However, for these structures, analytical homogenization strategies fail as the characteristic mesostructural length scale (i.e. the diameter of the solidified melt pool) becomes comparable to the macroscopic one. Numerical homogenization techniques in combination with the Finite Element (FE) Method provide an efficient alternative to the conventional approach. A difficulty of FE analysis is its necessity to resolve the topologically complex graded lattice structures in a boundary conforming manner  a procedure which is not easily automatable in a robust manner. To address this issue, we utilize the Finite Cell Method for the numerical homogenization of the mesostructure and employ the window method to determine the effective material properties. We will demonstrate by various examples that the combination of these two approaches is an efficient technique and present a road map of an automatized numerical determination of the elastic mechanical properties of graded lattice structures.

Prenter F. d., Verhoosel C., Jomo J., Kollmannsberger S., van Brummelen H., Rank E. Preconditioned iterative solvers for finite cell discretizations
In: eXtended Discretization MethodS XDMS 2017, 2017

Kopp, P.; Zander, N; Kollmannsberger, S.; Rank, E; Calo V. M. Multilevelhp adaptive Finite Cell Method for the NavierStokes equations using a residualbased Variational Multiscale Method
In: International Conference on Finite Elements in Flow Problems, Rome, Italy, 2017

B., Wassermann; S., Kollmannsberger; L., Kudela; E., Rank; Y., Shuohui Show abstract Direct simulation of geometrical models using the Finite Cell Method
In: Proceedings of CAD'17, Okayama, Japan, 2017  Status: Verlagsversion / published
A typical task of an engineer – be it in civil, mechanical, aeronautical engineering and many other fields – is to design and develop new objects, which fulfill certain physical requirements, generally described by partial differential equations, e.g. for structural problems, heat transfer, fluid dynamics, etc. The realization of an optimal design naturally requires an iteration between geometric design, typically carried out by Computer Aided Design and numerical simulations, such as the Finite Element Method. Unfortunately, CAD models are not directly compatible with a numerical simulation, and thus need to be translated into a simulation suitable format, e.g. a mesh. This transition process is considered to be the bottleneck in the design process and has initiated the development of several new simulation techniques, which allow working directly on the CAD model. The most prominent approach is Isogeometric Analysis which relies on the idea of using the same type of functions for the description of the geometry and for the numerical approximation. Whereas IGA is best suited for dimensionally reduced models, such as shells, immersed boundary or fictitious domain methods fit better to general solids, particularly those which are described by Boundary Representation or by Constructive Solid Geometry.

Carraturo, M.; Özcan, A.; Kollmannsberger, S.; Rank, E. Reduced Order Model for Selective Laser Melting Processes using the Finite Cell Method
In: 1st ECCOMAS Conference on the Simulation of Additive Manufacturing, Garching, Germany, 2017

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Egger, J.; Schröder, A.; Rank, E. A multilevel model for the simulation of AM processes
In: 1st ECCOMAS Conference on the Simulation of Additive Manufacturing, Garching, Germany, 2017

Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, RP.; Rank, E. Parallelization of the multilevel hpadaptive finite cell method
In: 5th European Seminar on Computing, Pilsen, Czech Republic, 2016

Özcan, A.; Kollmannsberger, S.; Jomo, J.; Rank, E. Numerical Simulation of Selective Laser Melting Processes with MultiLevel hpAdaptive Finite Cell Method
In: 10th International Conference on Advanced Computational Engineering and Experimenting, Split, Croatia, 2016

Elhaddad, M.; Zander, N.; Jomo, J.; Kollmannsberger, S.; Kirschke, J. S.; Ruess, M.; Rank, E. Show abstract Adaptive discretizations for boneimplant systems using the finite cell method
In: Engineering Mechanics Institute Conference 2016, Nashville, TN, USA, 2016
In recent years, the finite element method has been increasingly used to study the biomechanics of boneimplant systems. Patientspecific models need to consider the individual geometry for every case. Typically, geometric models of the bone are reconstructed from medical images  most commonly CT scans . Following segmentation, a finite element mesh has to be generated. This can be a simple voxelbased mesh, where a predefined number of voxels constitute one finite element in a grid that matches the voxel model. Alternatively, geometryconforming meshing procedures can be used to generate an unstructured mesh. To this end, the surface points are extracted from the voxel model and converted to a solid model, which is then meshed into an unstructured grid. Similarly, the geometry of the implant is usually reconstructed from medical images, or provided by ComputerAidedDesign (CAD) models, and then incorporated in the finite element mesh. The adequate treatment of the boneimplant interface demands the spatial refinement of the finite element mesh at the interface for an accurate solution. For voxelbased finite elements, a very fine resolution is already necessary to resolve the implant's geometry. This leads to an extremely high number of degrees of freedom, as the whole grid has to be refined. On the other hand, geometryconforming finite elements need more preprocessing (converting the bone's voxel model to a solid model), and complex meshing procedures to resolve geometries of the bone and the implant with graded refinement of the mesh towards the interface. In this contribution, we will use the finite cell method (FCM) in conjunction with a hierarchical refinement scheme to model a vertebral fixation system. The FCM discretization completely circumvents the mesh generation procedure, as the geometry is resolved on the integration level. Here, the flexibility of FCM in dealing with different types of geometric representations is demonstrated: the bone's geometry is represented by the voxel model from a CTscan, whereas the implant's geometry is directly described by a CAD solid model. Both representations are directly used in the FCM framework, thereby substantially reducing the preprocessing effort. Furthermore, the hierarchical refinement scheme yields a higher accuracy at the boneimplant interface by adaptively refining the FCM grid.

Davide D'Angella; Nils Zander; Stefan Kollmannsberger; Felix Frischmann; Andreas Schröder; Ernst Rank; Alessandro Reali Explicit Error Estimation and MultiLevel hpAdaptivity
In: Seventh International Workshop on HighOrder Finite Element and Isogeometric Methods, Jerusalem, Israel, 2016

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Weak imposition of contact constraints on automatically recovered high order embedded interfaces
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Zander, N.; Rank, E. A highorder accurate computational framework for the simulation of SLM processes
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016

Kudela, L.; Zander, N.; Kollmannsberger, S.; Rank, E. Smart Octrees: numerical quadrature for immersed boundary methods in three dimensions
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016

Zander, N.; D'Angella, D.; Bog, T.; Kollmannsberger, S.; Ruess, M.; Rank, E. Multilevel hpFEM: dynamic discretizations with arbitrary hanging nodes for solid mechanics
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016

Wassermann, B.; Bog, T.; Kollmannsberger, S.; Rank, E. Show abstract A DESIGNTHROUGHANALYSIS APPROACH USING THE FINITE CELL METHOD (ECCOMAS CONGRESS 2016)
In: ECCOMAS Congress 2016, Crete Island, Greece, 2016  Status: Postprint / reviewed
Modern 3D ComputerAidedDesign (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (BRep), where only the objects surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that BRep models are not necessarily watertight. These dirty geometries cause major difficulties in computational analysis because even basic geometric operations such as pointinmembership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to BRep models, CSG models are intrinsically watertight. To run a finite element simulation on a watertight CSG model, two alternatives are possible: (i) it can either be converted to a BRepmodel to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a designthrough analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable pointinmembership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the pointinmembership test as a sequence of CSGoperations, and discuss advantages and limitations on complex models of relevance in mechanical engineering.

Kopp, P.; Zander, N.; Kollmannsberger, S.; Rank, E. Multilevel hpadaptivity and the finite cell method for fluid problems
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016

Paolini, A.; Frischmann, F.; Kollmannsberger, S.; Rank, E.; Mecking, S.; Winter, C.; Buchschmid, M.; Müller, G. Show abstract Parameteridentifikation von BrettsperrholzElementen mittels Bayesscher Optimierung
In: Fortschritte der Akustik, DAGA 2016, Aachen, Deutschland, 2016
Die Finite Elemente Methode ist im Bereich niedriger Frequenzen ein leistungsstarkes Werkzeug zur schwingungstechnischen Analyse von Konstruktionen aus BrettsperrholzElementen. Die Berechnungsergebnisse hängen allerdings stark von den Werten der Materialparameter ab. Im vorliegenden Beitrag werden diese deshalb mit Hilfe eines Optimierungsverfahrens festgelegt. Das untersuchte Bauteil ist ein im Holzmassivbau üblicher DeckenWandanschluss. Dieser wurde messtechnisch untersucht und mit finiten Elementen hoher Ordnung simuliert. Die zu minimierende Zielfunktion wird durch den quadratischen Mittelwert (RMSWert) der prozentualen Abweichungen der berechneten Eigenfrequenzen beschrieben. Ihr Verlauf und ihre Ableitung sind jedoch nicht bekannt und ihre Werte können nur mit großem Aufwand an einzelnen Stellen ermittelt werden. Außerdem ist die Anzahl der Parameter wegen des orthotropen Materialverhaltens von Holz und der mit zusätzlichen Parametern zu berücksichtigenden Verbindungsstellen hoch. Da auch Aspekte des Aufbaus von BrettsperrholzElementen, wie z.B. die Verleimung, durch die Materialparameter abgebildet werden sollen, muss innerhalb großer Wertebereiche gesucht werden. Aufgrund dieser Umstände wird die Bayessche Optimierung verwendet. Dabei wird das globale Minimum durch schrittweise Auswertung der Zielfunktion bestimmt, wobei die jeweils folgende Stelle auf Grundlage der bereits bekannten Funktionswerte berechnet wird. Hierdurch konnte ein RMSWert von unter 5 erzielt werden.

Zander, Nils; Tino, Bog; Kollmannsberger, Stefan; Ruess, Martin; Schillinger, Dominik; Rank, Ernst Multilevel hpadaptivity for transient discretizations of complex domains
In: Engineering Mechanics Institute Conference, Stanford, USA, 2015

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Small and large deformation contact simulation using the finite cell method
In: European Solid Mechanics Conference 2015 (ESMC2015), Madrid, Spain, 2015

Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Bauer, J.; Ruess, M.; Rank, E. Show abstract Loading simulation of spinal vertebrae using the finite cell method
In: VI International Conference on Computational Bioengineering, Barcelona, Spain, 2015
Osteoporosis compromises bone strength, increasing the risk of vertebral fractures with severe health consequences. The development of an accurate and reliable patientspecific vertebral model would be of major clinical relevance, for both the prognosis of fractures and the investigation of implant systems. In the case of spinal fusion, the periimplant bone strains are of major interest. High forces are transmitted at the boneimplant interface and screw loosening is the major cause of surgical failure. In recent years, the finite element method has been increasingly applied to predict the biomechanical response of vertebrae. In general, quantitative CTdata is used to retrieve the geometric model and the inhomogeneous material properties. A finite element mesh is then generated for the numerical simulation. For the finite element analysis of a boneimplant system, the adequate treatment of the boneimplant interface demands the adaptive refinement of the finite element mesh for an accurate solution. In this contribution, the finite cell method (FCM), a high order embedded domain approach, is applied to simulate the biomechanical behavior of human vertebrae. The recently developed multi level hierarchical refinement is used to enrich the FCM, allowing to resolve the highly inhomogeneous material properties of vertebrae. For the simulation of boneimplant systems, the hierarchic refinement is used to resolve the boneimplant interface appropriately. The feasibility of using FCM for predicting the biomechanical response of human vertebrae is demonstrated with numerical examples on both intact and fused vertebral segments. Furthermore, the inherent hierarchical nature of the FCM strongly supports verification and validation.

Rank, E.; Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Bauer, J.; Ruess, M. Show abstract Coupling scales and adaptive refinement for simulation of bonefixation interfaces using the Finite Cell Method
In: VI International Conference on Coupled Problems in Science and Engineering, Venice, Italy, 2015
In recent years many studies on the numerical simulation of boneimplant systems have been presented. In general, a geometric model of a bone is derived from qCTdata, including its highly inhomogeneous material properties. Bone and implant are then meshed and simulated by finite elements. In the case of a fixation the zone of the bone close to the screw is of major interest. High forces are transmitted here and screw loosening is the major cause of surgical failure. As the scale of interest for this interface region may be several orders of magnitude smaller than that of the bone, an adaptive refinement of the finite element mesh is mandatory for an accurate solution. Whereas this is already quite demanding in cases of a single simulation, it becomes prohibitively expensive if a sequence of many simulations in order to optimize type, position and prestress of an instrumentation shall be performed.In this paper we will extend the recently developed Finite Cell Method, a high order embedded domain approach by a hierarchical refinement strategy in the regions of interest. Whereas the concept of the FCM completely relieves from the need to generate a finite element mesh, the hierarchical refinement yields an accuracy and a scale resolution which could not obtained by classical finite elements methods. We will discuss the basic properties of this adapted multiscale method and demonstrate its feasibility for simulating bonemechanics on the example of the fixation of a spinal segment.

Rank, E.; Bog, T.; Elhaddad, M.; Kollmannsberger, S.; L., Kudela; Zander, N. Show abstract The Finite Cell Method: Some Principles and Recent Progress
In: 13th U.S. National Congress on Computational Mechanics, San Diego, California, USA, 2015
The finite cell method (FCM) is a combination of a fictitious domain approach with finite elements of high order. The physical domain is embedded into an easy to mesh bigger computational domain. Finite cell meshes are then generated ignoring boundaries of the physical domain and result in rectangular ‘cells’ as support for the higher order shape functions. The geometry of the problem is only considered during the integration of the cell matrices. To this end an indicator function is introduced being equal to 1 inside the physical domain. Outside it is set (in order to avoid conditioning problems) to a very small value. The contribution of the fictitious domain is thus penalized, shifting the effort of meshing towards the numerical integration of the cell matrices. Combining these ingredients, an exponential rate of convergence can be observed for smooth problems, when performing a pextension. Since the quality and efficiency of the finite cell approximation strongly depends on the numerical integration scheme, this presentation will first discuss a new algorithmic subdivision approach, extending the conventional octreebased integration with the ability of resolving ‘kinks’ or corners of the physical domain. In combination with the blending function method, this algorithm yields a nearly exact decomposition of the cut cells. Our approach is able to resolve closetodegenerate cases, but remains algorithmically simple at the same time. Several further recent developments of the FCM will be discussed. A new two and threedimensional hierarchical refinement strategy yields exponential rate of convergence in energy norm even for singular problems, and its simple algorithmic structure allows an easy extension to transient problems with local refinement and derefinement. Finally, a reinterpretation of the fictitious domain in the sense of a ‘third material’ opens the way for a modified contact formulation without the necessity of contact search.

Özcan, A.; Kollmannsberger, S; Rank, E High order embedded domain methods: thermomechanical simulation of additive manufacturing processes
In: Extended Discretization Methods Conference 2015, Ferrara, Italy, 2015

Joulaian, Meysam; Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Rank, Ernst; Düster, Alexander Show abstract A highorder enrichment strategy for the finite cell method
PAMM 15 (1), pp. 207208, 2015
DOI: 10.1002/pamm.201510094
Abstract Thanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth – and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a highorder implicit representation of the material interface. (© 2015 WileyVCH Verlag GmbH & Co. KGaA, Weinheim)

Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst A contact formulation based on high order fictitious domain methods
In: 11th. World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014

Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst A formulation for frictionless contact using a material model and high order finite elements
In: Sixth International Workshop on HighOrder Finite Element and Isogeometric Methods, Frauenchiemsee Island, Germany, 2014

Nübel, V.; Shadavakhsh, A.; Elhaddad, M.; Zander, N.; Kollmannsberger, S. Dynamic analysis of high loaded components, discretized by fictitious domain methods
In: 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014

Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst MultiLevel hpAdaptivity: HighOrder Mesh Adaptivity without the Difficulties of Constraining Hanging Nodes
In: Sixth International Workshop on HighOrder Finite Element and Isogeometric Methods, Frauenchiemsee Island, Germany, 2014

Frischmann, F.; Kollmannsberger, S.; Rabold, A.; Rank, E. Show abstract High order Finite Elements for midfrequency vibroacoustics
In: Proc. IX Int. Conf. On Struct. Dynamics, Porto, Portugal, 2014
The quantification of vibroacoustic properties in multifloor timber buildings is currently still based on measurements and computational models are rarely used in practice. One reason surely is a lack of validated and robust numeric schemes for vibroacoustic simulations covering midrange frequencies which can be integrated smoothly into the planning process of multifloor timber buildings. To this end, we lay out a pipeline for the prediction of midfrequency vibroacoustic behavior of laminated timber constructions by modal analysis using threedimensional highorder finite elements. The integration into the planning process is achieved by deriving the computational model from IFCbased building information models.

Rabold, A.; Kollmannsberger, S.; Rank, E. Vibroakustik im Planungsprozess für Holzbauten, Teil 1: Luft und Trittschallberechnung auf Basis der Finite Elemente Methode
In: DAGA, 2014

Seidl, R.; Wille, H.; Fichtner, A.; Kollmannsberger, S.; Rank, E. Show abstract Monitoring healing processes in bones using the adjoint method
In: AEWG56, Salt Lake City, USA, 2014
One goal of nondestructive testing procedures is the identification of changes of interior details of a structure over time. More general, the deviation of the present state of a structure from a measured or simulated model state has to be identified. These and similar problems occur in different areas of natural sciences, engineering and technology, where geophysics, biomechanical engineering and Structural Health Monitoring are only a few examples. Over the last decade newly developed numerical methods in geophysics allow to identify the interior of the earth in much more detail than ever before [1]. Their dramatic progress is based on smart combinations of detailed seismic measurements, advanced mathematical approaches and efficient algorithms for high performance computing [2]. We present our attempts to transfer and further develop these methods to problems in biomechanics with the goal to monitor healing processes of fractured bone. To this end we investigate the socalled adjoint method, using a numerical bone model which stems from a CT scan of the damaged bone, an acoustic simulation based on this model and synthetic measurements obtained during the healing process. Because the wave equation is symmetric in time, the propagation of sound is timereversible [3]. Therefore, the differences of simulated and generated signals at the receiver locations can be timereversed and played backward into the model. Within the backward simulation sensors become sources and the wave fronts focus on the location of differences in the bone density, being the origin of the difference in the signals. Using the results of this simulation, we construct a sensitivity kernel highlighting the regions of maximal change of material parameters. We illustrate the potential of this approach on numerical experiments with a synthetic model and show that it could open the possibility to reduce cost and radiation exposure by reducing the number of necessary CT scans without compromising the quality of monitoring of the healing process.

Zander, N.; Bog, T..; Kollmannsberger, S.; Schillinger, D.; Rank, E. HighOrder hpFEM: High Order Mesh Adaptivity without the difficulties of Hanging Nodes
In: 11th. World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014

Kollmannsberger, S.; Reali, A.; Özcan, A.; Ruess, M.; Baiges, J.; Rank, E. Show abstract Parameter free weak boundary and coupling conditions for IGA
In: Proc. III SouthEast European Conf. On Computational Mechanics, Kos, Greece, 2013
Weak Dirichlettype boundary conditions are especially important in embedded domain methods such as the Finite Cell Method. Well suited are Nitschetype methods which have been extended to problems of linear elasticity or fluid dynamics. In principle, they consist of two parts. The first part is negative and stems from an suitable Lagrange multiplier. The second part is positive and stems from the minimization of the difference between the primal solution at the boundary minus the imposed values. It is penalty like in nature but acts as a stabilization and ensures coercivity of the system matrix. This penalty part contains a free penalty parameter, which has to be chosen apriori. Alternatively, the necessary stabilization parameter may also be computed by solving an auxiliary eigenvalue problem. Recently, an attractive alternative was presented in the context of low order methods. It utilizes the same idea of identified Lagrange multipliers as in Nitsche's method, but replaces the penalty terms using the condition that the multiplier is the normal trace of the flux of the unknown in a least squares sense. We will present an analysis on the performance on this new type of conditions for the Finite Cell Method in the context of pFEM and Isogeometric Analysis. Further, we have utilized this method to derive a new formulation for parameterfree coupling of trimmed NURBS. We will show some preliminary results for coupled problems in one and two dimensions for Poisson's equation and for linear elasticity.

Frischmann, F.; Kollmannsberger, S.; Rabold, A. PräProzessor Framework für BIMgekoppelte vibroakustische Simulationen im Holzbau
In: Proc. of Forum Bauinformatik, Munich, Germany, 2013

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. The Finite Cell Method for Contact Problems in Solid Mechanics
In: 3rd International Conference on Computational Contact Mechanics (ICCCM 2013), Lecce, Italy, 2013

Özcan, A.; Ruess, M.; Schillinger, D.; Kollmannsberger, S.; Reali, A.; Rank, E. Weak Coupling of Trimmed Patches in Isogeometric Analysis and the Finite Cell Method
In: 5th German Association for Computational Mechanics (GACM), Hamburg, Germany, 2013

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. The Finite Cell Method for Contact Problems in Solid Mechanics
In: 6th EUROPEAN CONGRESS ON COMPUTATIONAL METHODS IN APPLIED SCIENCES AND ENGINEERING (ECCOMAS), 2012

Zander, N.; Erbts, P.; Kollmannsberger, S.; Düster, A.; Rank, E. Show abstract The Finite Cell Method for Transient, Nonlinear Heat Conduction
In: European Seminar on Computing, Pilsen, Czech Republic, 2012
Since the early years of computational engineering, the classical Finite Element Method (FEM) has become the stateoftheart approach to solve initial boundary value problems numerically. Although major enhancements allowed for highly sophisticated simulations, the idea to geometrically resolve the physical domain on the discretization level remained unchanged. In cases of complex geometries, this intrinsic need for a conform mesh is still a burden in todays engineering practice. The recently introduced Finite Cell Method (FCM) overcomes this problem by combining the benefits of highorder Finite Elements (pFEM) with the idea of fictitious domains. The approach embeds the possibly complex physical domain phys in a fictitious domain ?fict and solves the problem on their simply shaped union. The localization factor ? allows to recover the original geometry on the integration level. Recent research results confirm the excellent applicability of this new method in the fields of nonlinear continuum mechanics, topology optimization, thinwalled structures, bone mechanics and advectiondiffusion problems. Also the methods potential for multiphysical problems has been demonstrated in the context of linear thermoelasticity. In the present work, the Finite Cell Method is employed to solve the transient, nonlinear heat equation on nonconforming meshes. In particular, the weak enforcement of Dirichlet boundary conditions is addressed. The results of a conventional pFEM simulation serve as reference and the convergence characteristics of both approaches are compared.

Rank, E.; Kollmannsberger, S.; Schillinger, D.; Sorger, C.; Zander, N. Show abstract Geometric models, numerical analysis and computational steering in structural engineering
In: International Conference on Computing in Civil and Building Engineering, 2012
This paper intends to encourage a discussion on the geometrical and topological description of 3D computational models, and on the embedding of these models into the engineering design process. In the first part, we will report on the development of a mesh generator which tries to overcome some of the present problems of FEM meshers for thinwalled structures and is capable of generating hexahedral meshes for thin, curved geometries as they often appear in civil and mechanical engineering. The second part of the presentation will focus on the recently proposed Finite Cell Method (FCM), a fictitious domain approach, where even very complex geometries of the physical domain can be taken into account without any mesh generation. This new numerical method can be embedded in a computational steering environment for interactive computation, yielding an analysis and design environment, which is far more flexible and intuitive than classical finite elements in civil engineering.

Kollmannsberger, S.; Zander, N.; Monavari, M.; Ruess, M.; Düster, A.; Rank, E. The Finite Cell Method for imaged based modeling of heterogeneous materials
In: ECCOMAS, 2012

Kollmannsberger, S.; Knezevic, J.; Ruess, M.; Mundani, R.P.; Düster, A.; Rank, E. Show abstract Segmentation free computational steering for bone mechanics
In: WCCM, 2012
Numerous numerical methods have been developed in an effort to accurately predict stresses in bones. The largest group is the Finite Element Method, where both, low and high order Ansatz functions may be used. By contrast, we investigate the Finite Cell Method (FCM) and its application to computational steering. The FCM is an embedded domain approach for high order finite elements and allows for a direct use of CT data without the need for segmentation of the bone or mesh generation of its computer image. While the Finite Cell Method has been verified and validated in previous publications, this presentation demonstrates methods on how the FCM can be made computationally efficient to the extent that it can be used for patient specific, interactive bone simulations. This approach is called computational steering and allows to change input parameters such as the position of an implant, material or loads which in turn leads to an almost instantaneous change in the output (stress lines, deformations). This direct feedback gives the user an immediate impression of the impact of his actions to an extent which, otherwise, is hard to obtain by the use of classical non interactive computations.

Cai, Q.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The finite cell method for spatially varying dispersions in coupled multispecies reactive transprot problems
In: Proc. of Coupled Problems 2011: Computational Methods for Coupled Problems in Science and Engineering, 2011
Colloidal transport and dynamics in porous media can be well described by multispecies reactive transport equations where the governing equations are coupled by firstorder reactions. The solution of this type of coupled equations causes considerable computational effort. Additional difficulty is caused by the spatial inhomogeneity of species in porous media which calls for spatially varying dispersion coefficients. In such a setting, analytic solutions are only available for special cases. In the forthcoming paper, we will firstly present a spatial discretization of the problem by the finite cell method, which is an embedded domain approach using a high order finite element method, where the time domain is discretized by finite differences. We will demonstrate the efficiency and stability of this approach and discuss further advantages. Secondly, we will present different methods to solve the coupled problem where the coupling stems from the reactive terms. Here, we will compare different conventional fixedpoint iteration methods with a decoupling scheme utilized for the derivation of analytical solutions. The basic idea is to decompose the multiple reactive species by introducing auxiliary variables. The decoupling scheme can be carried over to our numerical framework, i.e. our inhouse code AdhoC, which results in the computational time speedup in the order of one magnitude. We will verify all presented numerical schemes by comparison to analytic solutions or benchmark problems and discuss their efficiency. We will conclude the final paper with a practical application.

Cai, Q.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The finite cell method for solute transport problems in porous media
In: Proceedings of the International Conference on Finite Elements in Flow Problems, 2011
Simulating a solute transport problem in a heterogeneous porous media requires considerable computational effort especially when refined boundary conforming meshes become necessary. The finite cell method, which combines a fictitious domain approach and the high order finite element method, was recently developed for solid mechanics and allows a trivial mesh generation regardless of the possibly complicated geometry. In this contribution, the finite cell method is generalized to solute transport problems in fluid mechanics. The nonsmooth problem occurs due to discontinuous material coefficients, i.e. porosity, within the cell being cut by the boundary of the original domain. This problem can be resolved by generating nonuniform subcells based on the adaptive integration scheme or by increasing the number of integration points on the cell level. As a validation of our approach, a benchmark problem is solved for a single component solute transport problem. Additionally, the method is extended to multicomponent reactive transport problems. A comparison of the convergence rate between the classical finite element method and the finite cell method will be given.

Schlaffer, M.; Geier, M.; Kollmannsberger, S.; Rank, E. Show abstract Nonreflecting free field boundary conditions for the lattice Boltzmann method
In: 2011, ICMMES, 2011
We present boundary conditions for the lattice Boltzmann method which suppress the reflection of sound waves. The partial density of a sound wave is approximated by lowpass filtering, an unknown population of the distribution function on the boundary node is set by adapting the momentum correspondingly to the wave resistance of the pressure wave. The results of an implementation in 1D are compared to the corresponding free field simulation showing good agreement for inviscid flows. An implementation of both velocity and pressure boundary conditions for the 2D case is shown. The suppression of waves approaching the boundary is hereby independent of the incident angle.

Wille, H.; Kollmannsberger, S.; Rank, E.; Yosibash, Z. Show abstract Incorporating Material Uncertainties into the Simulation of Human Femurs
In: CBU 2011 proceedings, 2011
Over the past years, the "Symposium on Computational Biomechanics in Ulm" (formerly known as "Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics, and Related Fields") has established itself as an internationally recognized event for sharing knowledge in computational methods (especially the Finite Element Method) applied to Biomechanics, Biomedical Engineering and Biomedicine and also for discussing current research trends in this area. The "17th International Symposium on Computational Biomechanics in Ulm" (CBU 2011) has again covered a broad range of exciting research topics including (but not limited to) computerized methods in orthopedics, dentistry and orthodontics. The CBU 2011 proceedings contain the keynote lecture as well as the papers presented at the symposium. All papers included in the proceedings went through an internal review process of the CBU 2011 organizing committee.

Sorger, C.; Kollmannsberger, S.; Rank, E. Show abstract Visual DoMesh: Hexahedral meshing for thin curved solid structures
In: ICCCBE, 2011
Thin walled structures are classically computed by dimensionally reduced models. During the last few years, there has been an increasing need to model thin structures as solids with hexahedral elements. Hexahedral elements generally provide more accurate solutions than the dimensionally reduced models and are well suited e.g. for the definition of anisotropic materials or the solution of nonlinear material behaviour. For these problems a difficulty is to create conforming meshes of hexahedral elements for arbitrarily curved thin walled structures. We will present a new algorithm for generating conforming meshes of hexahedral elements on bounded threedimensional surfaces. After first detecting all intersecting reference surfaces the geometry is manipulated such that the boundaries of the original surfaces are reshaped and referenced boundary edges are defined. On these rebounded surfaces a triangulation algorithm based on a domain subdivision approach is applied. Quadrilaterals are then formed by applying an automatic conversion algorithm. The generation of hexahedral elements is achieved by an offset mapping technique, thereby allowing for a varying thickness of the resulting mesh [1]. The interfaces at intersecting surfaces are formed to patches of regular hexahedral elements and conform to the boundaries of the mesh created on the manipulated surfaces geometries achieved in the first step.The principal contribution is a new meshing technique able to automatically generate conforming hexahedral elements directly from dimensionally reduced, arbitrarily curved thin walled structures without the necessity to model complex thin but solid structures in detail with a CAD tool. The proposed method also offers the advantage of avoiding expensive intersection and projection calculations commonly associated with hexahedral element generation.

S. Kollmannsberger, A. Düster, E. Rank, S. Geller, M. Krafczyk Modelling fluidstructure interaction with high order solids and Lattice Boltzmann
In: Proceedings of The Tenth International Conference on Computational Structures Technology, 2010

E. Rank, S. Kollmannsberger, A. Düster High Order Finite Elements: Principles, Achievements, Open Questions
In: Proceedings of The Tenth International Conference on Computational Structures Technology, 2010

Schillinger, D.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The finite cell method for geometrically nonlinear problems of solid mechanics
IOP Series: Materials Science and Engineering 10 (1), pp. 012170, 2010
The Finite Cell Method (FCM), which combines the fictitious domain concept with highorder pFEM, permits the effective solution of problems with very complex geometry, since it circumvents the computationally expensive mesh generation and guarantees exponential convergence rates for smooth problems. The present contribution deals with the coupling of the FCM approach, which has been applied so far only to linear elasticity, with established nonlinear finite element technology. First, it is shown that the standard pFEM based FCM converges poorly in a nonlinear formulation, since the presence of discontinuities leads to oscillatory solution fields. It is then demonstrated that the essential ideas of FCM, i.e. exponential convergence at virtually no meshing cost, can be achieved in the geometrically nonlinear setting, if highorder Legendre shape functions are replaced by a hierarchically enriched Bspline patch.

Sorger, C.; Kollmannsberger, S.; Rank, E. Show abstract A mixed model with highorder tetrahedral and hexahedral elements for the mortar element method
In: Proc. of the 19th International Meshing Roundtable, Sandia National Laboratories, USA, 2010
In this paper we present a model to create curved hexahedral and tetrahedral elements for the discretization of mixed structures arising in many engineering disciplines. To this end the recursive domain division is utilized for the generation of triangular and quadrilateral meshes for freeform surfaces. Hexahedral elements are formed by a projection approach which extrudes quadrilateral elements generated on reference surfaces with respect to predefined mathematical rules. The generation of tetrahedral elements is performed by the advancing front algorithm as implemented in Netgen. To make the model computable by finite element software, the Mortar method is employed at the interfaces of the tetrahedral and hexahedral elements. Quasiregional mapping is applied to represent curved high order solid elements. A series of examples concludes this work.

Cai, Q.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The High Order Finite Element Method for Steady Convectiondiffusionreaction Problems
In: ECCOMAS, 2010
A wide class of mass transfer problems is governed by the combined effect of convection, diffusion and reaction (CDR) processes. The finite element method using the standard Bubnov Galerkin method based on linear elements is widely applied for diffusiondominated problems where the method produces accurate results. However, at high P'eclet numbers of transport problems, where the convection process dominates, this scheme gives rise to numerical oscillations in the solution which do not coincide with the physical phenomena. As a remedy, the high order finite element method is applied for CDR problems in this paper. Two numerical examples are taken as test cases to illustrate the capability of the high order finite element method of suppressing residual oscillations. An error convergence study is also presented to show the different characteristics of the convergence of hrefinement and prefinement.

S. Kollmannsberger, S. Geller, A. Düster, J. Tölke, M. Krafczyk, E. Rank FluidStructure Interaction based on Lattice Boltzmann and pFEM: Verification and Validation
In: Proceedings of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS), Ischia Island, Italy, 2009

Papaioannou, I.; Heidkamp, H.; Düster, A.; Kollmannsberger, S.; Rank, E.; Katz, C. The subset simulation applied to the reliability analysis of a nonlinear geotechnical finite element model
In: Proceedings of the 7th International Probabilistic Workshop, 2009

Kollmannsberger, S.; Geller, S.; Duester, A.; Toelke, J.; Krafczyk, M.; Rank, E. Show abstract FluidStructure interaction based on Lattice Boltzmann and pFEM: Verification and Validation
In: Coupled Problems 2009: Computational Methods for Coupled Problems in Science and Engineering, June 0810, 2009, 2009
Over the last decade the Lattice Boltzmann Method (LBM) has matured as an efficient method for solving the NavierStokes equations. The p?version of the Finite Element Method (p?FEM) has proved to be highly efficient for a variety of problems in the field of structural mechanics. Our goal is to investigate the validity and efficiency of coupling the two completely different numerical methods to simulate transient bidirectional FluidStructure Interaction (FSI) problems with very large structural deflections.

Kollmannsberger, S.; Duester, A.; Rank, E. Show abstract Force Transfer for High Order Finite Element Methods using Intersected Meshes
In: 11th International Symposium on Emerging Technology in Fluids, Structures, and FluidStructure Interactions, within the ASME Pressure Vessel and Piping Conference, July 2226, 2007, 2007
High order Finite Element Methods have been shown to be an efficient approach for computing the behavior of fluids and structures alike. However the coupling of such methods in a framework for a partitioned fluidstructure interaction is still in its early stages. A difficulty hereby is a conservative transfer of the loads from the fluid to the solid and an appropriate transfer of the structural displacements back to the boundary of the fluid. This contribution describes the coupling of a high order finite element structural code to the commercial finite volume fluid solver CFX and focuses on the transfer of the loads. For this purpose, the fluid mesh and the structural mesh are intersected. The force acting on the solid is then computed by a composed integration scheme performed on the intersected mesh. The approach can be interpreted as a projection method taking into account the discretization on both sides, i.e. fluid and solid. Numerical examples will demonstrate the basic properties of this new type of data transfer.

Kollmannsberger, S.; Scholz, D.; Duester, A.; Rank, E. Show abstract FSI Based on Bidirectional Coupling of High Order Solids to a LatticeBoltzmann Method
In: 10th International Symposium on Emerging Technology in Fluids, Structures, and FluidStructure Interactions, within the ASME Pressure Vessel and Piping Conference, July 2327, 2006, Vancouver, Canada, 2006
Currently, a joint effort is made by German research groups to establish a benchmark for a bidirectional FluidStructureInteraction problem: a geometrically nonlinear vibrating structure being agitated by a laminar flow of an incompressible Newtonian fluid. Among other approaches, a partitioned solution procedure has been developed in this framework using a high order FEM code for the structural side of the solution coupled to a LatticeBoltzmann solver discretizing the fluid. The explicit coupling of these two completely different types of discretizations gives promising results also in terms of an efficient calculation. This paper briefly introduces the benchmark, presents the procedure used and gives some results obtained by the application of the method.

Geller, S.; Toelke, J.; Krafczyk, M.; Kollmannsberger, S.; Duester, A.; Rank, E. Show abstract A coupling algorithm for high order solids and lattice Boltzmann fluid solvers
In: Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS 2006, P. Wesseling, E. Onate and J. Periaux, editors, 2006
In this paper the implementation of the bidirectional coupling approach for the partitioned Lattice Boltzmann (LB) fluid flow and Finite Element (pFEM) structural mechanics solver will be discussed. Earlier research on a benchmark configuration showed that the explicit coupling algorithm of the two methods was prone to instabilities for some configurations. For this purpose an implicit coupling algorithm was designed and is presented in this paper.
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Other

Özcan, A.; Kollmannsberger, S; Rank, E. The Finite Cell Method for the Simulation of Additive Manufacturing, Technische Universität München, 2016

Bog, T.; Frisch, J.; Hager, G.; Kollmannsberger, S; Rank, E.; Zander, N. Performance Engineering in Aktion, Technische Universität München, 2014

Geller, S.; Janssen, C.; Krafczyk, M.; Kollmannsberger, S.; Rank, E. Show abstract Lattice Boltzmann method for fluidstructure interaction phenomena
In: The Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, 2011
In the recent years we investigated the validity and efficiency of coupling high order finite elements schemes for mechanics with the Lattice Boltzmann Method. The results on two dimensional and three dimensional benchmark configurations are very promising and show that an explicit coupling scheme is able to produce results which agree with reference solutions. The solid part was computed by the structural solver AdhoC and the fluid part by the parallel solver VirtualFluids, which is based on adaptive hierarchical grids and component technology. The applicability of the setup to problems in civil engineering such as the fully three dimensional, turbulent computation of a bridge in a storm will be pointed out. Further coupling to a rigid body dynamics engine (PhysicsEnginepe) leads to the possiblity to compute interaction problems with a huge number of particles. The parallel simulation of the coupled problem is the base for the simulation of a geothermic drilling project where the particles, cut by drilling, influence the fluid behaviour. A free surface Lattice Boltzmann approach coupled with rigid body motions shows further potential and demonstrates the broad applicability of the developed algorithms.

Schillinger, D.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The Finite Cell Method for Geometrically Nonlinear Problems of Solid Mechanics
In: Proceedings of the WCCM 2010, 2010
The Finite Cell Method (FCM), which combines the fictitious domain concept with highorder pFEM, permits the effective solution of problems with very complex geometry, since it circumvents the computationally expensive mesh generation and guarantees exponential convergence rates for smooth problems. The present contribution deals with the coupling of the FCM approach, which has been applied so far only to linear elasticity, with established nonlinear finite element technology. First, it is shown that the standard pFEM based FCM converges poorly in a nonlinear formulation, since the presence of discontinuities leads to oscillatory solution fields. It is then demonstrated that the essential ideas of FCM, i.e. exponential convergence at virtually no meshing cost, can be achieved in the geometrically nonlinear setting, if highorder Legendre shape functions are replaced by a hierarchically enriched Bspline patch.

Schillinger, D.; Kollmannsberger, S.; Mundani, R.P.; Rank, E. Show abstract The Hierarchical BSpline Version of the Finite Cell Method for Geometrically Nonlinear Problems of Solid Mechanics
In: Proceedings of the ECCM 2010, 2010
The Finite Cell Method (FCM), which combines the fictitious domain concept with highorder pFEM, permits the effective solution of problems with very complex geometry, since it circumvents the computationally expensive mesh generation and guarantees exponential convergence rates for smooth problems. The present contribution deals with the coupling of the FCM approach, which has been applied so far only to linear elasticity, with established nonlinear finite element technology. First, it is shown that the standard pFEM based FCM converges poorly in a nonlinear formulation, since the presence of discontinuities leads to oscillatory solution fields. It is then demonstrated that the essential ideas of FCM, i.e. exponential convergence at virtually no meshing cost, can be achieved in the geometrically nonlinear setting, if highorder Legendre shape functions are replaced by a hierarchically enriched Bspline patch.

Schlaffer, M.; Geier, M.; Kollmannsberger, S.; Rank, E. Show abstract Nonreflecting inflowoutflow boundary conditions for lattice Boltzmann methods using an intrinsically adapted acoustic impedance by separation of sound pressure levels
In: 2010, ICMMES, 2010
The lattice Boltzmann method, being a weakly compressible method for solving the Navier Stokes equations, seems to be well suited for simulation of aeroacoustics [1]. This application requires an acoustical free field boundary condition, possibly implemented by a nonreflective boundary. Apart from this issue, the lattice Boltzmann method is known to suffer from spurious pressure waves, usually evolving from poor initialization. These spurious pressure waves would naturally leave the simulation domain when hitting a nonreflective boundary. Unfortunately, the development of nonreflective boundary conditions for the lattice Boltzmann method has proven to be difficult. Current approaches are using sponge layers, lowpass filtering or, most promising, solution of onedimensional Euler equations at the boundary [2]. However, the latter suffers from flow nonnormal to the boundary surface, showing reflective behavior especially in corners of the intersecting boundary surfaces. Here we present a different approach. The sound pressure level is detected via lowpass filtering. The flow through the boundary is split up into a hydrostatic part and a part emerging from the pressure wave rho_s. The well known impedance condition for nonreflection arising from the wave equation p_s / c_s = rho_s · c_s is then matched by the isothermal gas law. An impedance matching velocity boundary condition and an impedance matching pressure boundary condition for arbitrary flow directions are shown in the presentation.

Sorger, C.; Kollmannsberger, S. Show abstract Refaktorisierung des NetzGenerators DoMesh
In: Forum Bauinformatik, 2008
Es werden die grundlegenden VernetzungsKonzepte des Netzgenerators DoMesh beschrieben und die Nachteile des Anfang der 90er Jahre aufgesetzten ProgrammCodes erläutert. Die Ziele der zwei Jahre andauernden Refaktorisierung werden aufgezählt und die grundlegende Vorgehensweise sowie konkrete Maßnahmen der CodeWiederbelebung beschrieben. Eine Zusammenfassung mit einem VernetzungsBeispiel schließen diese Arbeit ab.

Kollmannsberger, S.; Geller, S.; Duester, A.; Rank, E. Show abstract Fixed Grid and ALEtype FluidStructure Interaction with Elements of High Order
In: International Workshop on FluidStructure Interaction,Theory, Numerics and Applications, 2008
In fluidstructure interaction the structure is usually computed by the Finite Element Method. We utilize a high order structural FEMformulation suited for geometrically nonlinear computations ensuring exponential convergence rates in the strain energy for smooth problems Within the authors work for the "Forschergruppe 493" supported by the Deutsche Forschungsgemeinschaft, structural pFEM was coupled to several different fluid solvers. Among these are the Finite Volume Method in an Arbitrary LagrangeEulerian formulation, the Lattice Boltzmann Method and a Spectral Finite Element Method. Every couplingsetup was validated against numerical and/or experimental benchmarks. The fluidformulations used are completely different in their nature and implementation. One focus of this contribution is to describe the exchange of the variables on the interface between these formulations. Recognizing the workshop character of the symposium, we try to communicate the experience we gained with the methods in their current implementation w.r.t. fluidstructure interaction with large displacements. We will demonstrate some advantages and limits of each setting by means of examples.

Kollmannsberger, S.; Duester, A.; Rank, E.; Geller, S.; Toelke, J.; Krafczyk, M. Show abstract Adapted interface meshes for fluidstructure interaction with Lattice Boltzmann methods and pFEM
In: 2nd GACM Colloquium on Computational Mechanics (Abstracts), 2007
Both, Finite Element methods of higher order and Lattice Boltzmann methods have been shown to be an efficient approach for computing the behavior of structures and fluids respectively. In an effort to combine the advantages of these methods, a framework for a partitioned fluidstructure interaction with large deflections has recently been developed by the authors. A difficulty hereby is a conservative transfer of the loads from the fluid onto the structure. In a first approach, the forces were transferred onto the structural surface by means of a interface mesh whose corner nodes coincide with the Gaussian integration points of the structure. The LBM solver then interpolated its boundary forces onto this mesh and the structural high order FEM solver integrated the values at the corner nodes directly by means of a Gaussian integration. A disadvantage in this approach is that the mesh density and thus the resolution of the fluid forces as seen from the structural point of view is dependent on the structural Gaussian points. This contribution will introduce a force conservative transfer of the fluid boundary loads onto the structure by means of a composed integration. For this type of integration a surface mesh is still needed but it may be chosen independently of the discretization of the structure. An ideal mesh, taking into account the discretization of the fluidlattice, is an equidistant mesh and can be considered as a discretization adaptor between the large FEM elements and the very fine finitedifference discretization of the Lattice Boltzmann equation. The method will be discussed, its conservativity will be demonstrated, and the results will be compared to FSIBenchmarks.

Kollmannsberger, S.; Duester, A.; Rank, E.; Geller, S.; Toelke, J.; Krafczyk, M. Show abstract Thin solids in fluidstructure interaction
In: International Workshop on HighOrder Finite Element Methods (Poster Session), 2007
In this contribution the use of hexahedral elements for the structural simulation in a fluid structure interaction framework is presented, resulting in a consistent kinematic and geometric description of the solid. In order to compensate the additional numerical effort of the threedimensional approach, an anisotropic padaptive method for linear elastodynamic problems is proposed, resulting in a clearly higher efficiency and higher convergence rates than uniform pextensions. Special emphasis is placed on the accurate transfer of loads considering the fluid discretization for computation of the surface load integrals. For a coupling with a cartesian grid based Lattice Boltzmann code it was found that oscillations in the interface tractions may excite higher structural modes possibly leading to a nonstable coupling behavior. A first remedy to this problem was a linear modal analysis of the structure, thus allowing to control the number of modes to be considered without disregarding bidirectional fluid structure interactions. Preliminary results are presented for the FSI benchmark configuration proposed in this book.

Kollmannsberger, S. Show abstract FluidStrukturInteraktion mit Bezug auf das Bauwesen
In: Progress in Bauinformatik. Forum Bauinformatik 2005, 2005
Es wird aufgezeigt, wo FluidStrukturInteraktion im Bauwesen in Betracht gezogen werden muss. Numerische Vorgehensweisen werden erläutert, noch offene Fragen angeschnitten. Ein einfaches Koppelverfahren wird beschrieben und auf ein Beispiel angewendet.
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Teaching
I am involved in
 Master Program "Computational Mechanics"
 Bachelor's Programm "Computational Science and Engineering"
 Doctoral Seminars
in various mandatory and elective courses. For current organizational details of which course is given when check out TUMOnline. Corresponding course material is available online in Moodle. A concise overview is given on our page on education.
Supervised Theses

Ghiringhelli, Elisa Show abstract Proper Generalized Decomposition Applied to Selective Laser Melting Processing
Master's thesis, Technische Universität München, 2019
Selective Laser Melting (SLM) is a 3D printing technique very spreadly used in several engineering fields such as biomedicine, aerospace, and electronics. SLM is based on the use of a highpower laser which melts metal powder to create the desired object. In this work, we focus on the control of the intensity of the moving laser beam with respect to the temperature distribution on the powder layer. The idea is that, depending on the path, the intensity can be reduced in some areas, still hot from the previous passing, saving up energy costs. To solve this problem, a reduced order modeling technique is introduced. In particular, we exploit the Proper Generalized Decomposition on both a stationary and a transient configuration. This method constitutes an efficient tool to deal with parametric settings, providing accurate approximations while containing the wellknown curse of dimensionality.

MarotLassauzaie, Marc Show abstract Geometrieheilung mittels Finiter Zellen Methode
Bachelor's thesis, Technische Universität München, 2018
In this thesis we present a method for repairing dirty geometries by constructing and solving a Poisson equation over the domain.To preserve the sharp features at the boundary surface, homogeneous Dirichlet boundary conditions are set onto the surface of the original awed geometry. Additionally, a positive body load on the inside of the geometry and a negative body load on the outside of the geometry are set. The solution of the Poisson problem provides an implicit geometry description in the form of a signed scalar field, whose zero isosurface forms the reconstructed boundary. This algorithm is capable of accurately reproducing the original geometry, alltough additional research may still improve the results. The method was tested on two different numerical examples in order to evaluate its potential for practical applications.

Landesberger, Julian Optimization of Laser Bem Intensity Profiles for Additive Manufacturing
Master's thesis, Technische Universität München, 2018

Filomeno, Giovanni MatrixFree Conjugate Gradient for the Finite Cell Method
Master's thesis, Technische Universität München, 2017

Nagaraja, S. Phasefield modeling of brittle fracture with multilevel hpFEM and the Finite Cell Method
Master's thesis, Technische Universität München, 2017

Xujia, Zhu Show abstract Formulation and implementation of triangular shell elements for metal forming problems
Bachelor's thesis, Technische Universität München, 2017
Industry Cooperation with ESI, content is confidential

Egger, J. Show abstract FiniteCellSimulation of Conductive Heat Transfer during Additive Manufacturing Processes
Bachelor's thesis, Technische Universität München, 2017
Additive manufacturing (AM) is a promising technique for producing complex and customized structures: Components are synthesized layer by layer without molding tools out of a formless material. Simulating the production process is more complicated due to several factors that do not occur in conventional manufacturing. Adding a new layer leads to a larger physical domain, causing a artificial energy input within the simulation. This thesis uses the FiniteCellMethod (FCM) to simulate an additive manufacturing process in 1D and examine the problem at hand. FCM is an extension of the pversion of the FiniteElementMethod (FEM), which resolves the geometry on the integration level. Furthermore, the Thetamethod for executing the time integration is adapted by adding a predictor and corrector step to conserve energy. This universally applicable method leads to a very accurate approximation of the temperature distribution, while energy is conserved and computational requirements are low.

Kopp, P Multilevel hpFEM and the Finite Cell Method for the NavierStokes equations using a Variational Multiscale Formulation
Master's thesis, Technische Universität München, 2017

Pezzoli, Dario Topological analysis, healing and defeaturing of tessellated models
Master's thesis, Technische Universität München, 2016

Carraturo, Massimo Reduced Order Method for Selective Laser Melting Processes using the Finite Cell Method
Master's thesis, Technische Universität München, 2016

Korshunova, Nina Partitioned hpd approach for multiscale transient heat problems
Master's thesis, Technische Universität München, 2016

Coradello, Luca Implementation of a highorder KirchhoffLove shell: a comparison of IGA and pFEM
Master's thesis, Technische Universität München, 2016

Hosseini, S. B. Show abstract Implementation and analysis of error estimates for hp MITC finite elements of ReissnerMindlin plates
Master's thesis, Technische Universität München, 2016
This thesis concerns a priori and a posteriori error estimates of hp MITC finite elements for ReissnerMindlin plates. First, we recall the theory for the Reissner Mindlin plate model, starting from the principle of virtual work resulting in the strong form of the partial differential equations and boundary conditions. Second, we derive the standard form finite element method for the ReissnerMindlin plate problem. After a concise discussion in regard to the socalled shear locking effect, the nonstandard MITC finite element method is presented. Third, a priori and a posteriori error analysis are reviewed briefly, and the convergence results as well as error estimators for the MITC plate elements are introduced. Eventually, the MITC finite element method for ReissnerMindlin plates is implemented into a highorder finite element solver with C++ programming language. The method is verified by conducting an a priori error analysis using hp refinements. Thereafter, the a posteriori error estimators of the standard and MITC finite element method are implemented into the solver, and the behaviour of the estimators and their contribution to the global error estimator are studied. The provided results are in accordance with the theory. The a priori error estimators show the advantage of the MITC finite element over the standard finite element method in the terms of stability and convergence rate in the presence of the shear locking effect with thin plates. The corresponding convergence rates of the a posteriori estimators guarantee a basis for efficient adaptive refinements. Moreover, estimators are found capable of detecting a boundary layer in the case of a free boundary plate. Hence, it might be possible to use them for hprefinement.

D'Angella, D. Show abstract A Posteriori Error Estimator for the MultiLevel hpFinite Element Method
Master's thesis, Technische Universität München, 2015
This works aims to investigate the applicability of residualbased error estimators to two variants of the Finite Element Method: the multilevel Finite Element Method and the Finite Cell's Method (FCM). The study is performed both theoretically and numerically, showing excellent results for the MultiLevel Finite Element Method in the context of Poisson's and linear elastic problems. Furthermore, the analysis carried out in the context of the FCM furnishes a starting point for further developments and investigations on how to estimate the error in case of a nonconforming discretization.

Wich, Moritz Topologische Optimierung mit der Methode der Finiten Zellen für 2D und 3D Objekte in FCMLab
Bachelor's thesis, Technische Universität München, 2014

Balafas, Georgios Polyhedral Mesh Generation for CFDAnalysis of Complex Structures
Master's thesis, Technische Universität München, 2014

Elhaddad, M. Show abstract Transient Analysis with the Finite Cell Method
Master's thesis, Technische Universität München, 2014
In the thesis at hand, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundaryvalue problem. Semidiscrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A simple benchmark problem is solved using FCM, illustrating the method's abiltiy to solve problems of linear elastodynamics with high convergence rates. Finally, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to a solution obtained using stateoftheart commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics.

Zander, Nils Show abstract The Finite Cell Method for Linear Thermoelasticity
Master's thesis, Technische Universität München, 2011
This thesis presents an approach to approximate the phenomena of linear thermoelasticity numerically in the framework of the Finite Cell Method (FCM). For this purpose, the governing equations of the thermal, elastic and linear thermoelastic system are derived in their strong and weak formulation. In particular, it is outlined how Dirichlet boundary conditions of the three problems can be imposed in the weak sense. In the second part of this work, the constrained weak field equations are discretized in space utilizing the ideas of the Finite Cell Method. The performance of this approach is demonstrated through different examples.

Wille, Hagen A Stochastic Material Relationship for the Simulation of Human Femurs
Master's thesis, Technische Universität München, 2010

Xi, D. Show abstract Enhancement of AdhoC for padaptive FluidStructure Interaction
Master's thesis, Technische Universität München, 2008
AdhoC4 is a program of the Chair for Computation in Engineering to compute the static or dynamic behavior of structures. It is based on the pversion of the finite element method, where hierarchic shape functions are employed. The implementation of the anisotropic padaptive method for linear elastostatic analysis of thinwalled and massive structures presented in the Doctoral Thesis of D. Scholz [7] capitalizes on the hierarch y of the shape functions and was recasted in this Thesis such that the adaptive Version of AdhoC4 can be used in stationary FluidStructure Interaction (FSI) problems. It was, therefore, necessary to modify and improve the exist ing code. The original padaptive version was run by a script which restarted AdhoC4 at each adaption step. In the framework of FSI, however, the padaptive version of AdhoC4 needs to run as one process, without nterruption and without memory leakage. This Thesis describes the theory and implementational work needed to achieve these goals and assesses the performance of the resulting new version of AdhoC4. Moreover, the efficiency and suitability of the padaptive version of AdhoC4 with respect to FSI problems are discussed.

Sorger, C. Show abstract Revision concept and refactoring process for the mesh generator DoMesh
Master's thesis, Technische Universität München, 2007
The meshgenerator DoMesh is a tool for the generation of freeform surfacesmeshes and has its roots in a research project from the 1980ies. The algorithm became part of the research work at the Lehrstuhl für Bauinformatik  TU München and was implemented in the commercial engineering software SOFiSTiK. The unstructured and continuous implementation of the software led to a point, where the limits of the programstructure were reached and the code became enormously intricate. Under these circumstances, no further enhancement was possible such that it was necessary to revive the code within a refactoring process. Up to now large parts of the coderenewal are accomplished and a new DoMesh version, which is to eliminate the major drawbacks of the original code, has been developed. This presentation will introduce the basic ideas of meshgeneration in DoMesh and highlight the drawbacks of the old code. The targets of reengineering DoMesh are presented and the concepts with witch they were accomplished will be explained. The basic functionality of the newly developed code will be demonstrated along with a selection of more complex examples.

Zgür, G. Show abstract On MpCCI as a coupling library for FluidStructure Interaction with CFX
Master's thesis, Technische Universität München, 2006
On MPCCI as a coupling library for FluidStructure Interaction with CFX. One major simplification made when calculating physical behaviour is to take one field into account. While this may often be sufficient, some engineering problems require to consider two or more fields. For a flexible structure submerged in a fluid, the interaction of the fluid with the structure may be the driving mechanism characterising its behaviour. For the individual disciplines sophisticated solvers exists. Different solution methods for various flow problems have been developed. Various numerical methods and code implementations have been used to increase the quality of the results. In order to find a common basis of comparison, a set of benchmark problems have been defined. In view of the results of previous numerical tests a commercial robust fluid solver ANSYSCFX was chosen. MpCCI is a communication library to which ANSYSCFX provides an interface. Goal of this thesis was to assess this interface such that a structural solver could be connected to this interface. Therefore, the major steps had to be followed. First to assess the fluid solver by calculating a cylinder submerged in a fluid benchmark. Second to write a dummy structural code providing an interface to MpCCI and finally to couple the both codes such that an algorithmic coupling was possible.

Yang, Z. Show abstract Deterministic and probabilistic optimization of head up displays in automobile design using rodeo
Master's thesis, Technische Universität München, 2006
The focus of this thesis is the optimization of head up displays (HUD) used in a new generation of automobiles. The occurrence of optical deficiency caused by deformations of the concave mirrors which are fixed to the cabinet can not be avoided completely due to manufacturing tolerances. In order to minimize the image distortions, a multimirror visualization system is built up to simulate the imaging process and to assess the quality of the image for a given geometry. With this model at hand, the optimization of the geometry of the mirrors is performed with the help of a probabilistic approach using polynomial chaos as implemented in RODEO (Robust Design Optimizer), a nonlinear solver of SIEMENS.

Turkanovic, H. Show abstract Untersuchung des dynamischen Verhaltens von geometrisch linearen/nichtlinearen Balken und Platten mit pFE
Master's thesis, Technische Universität München, 2005
In der Diplomarbeit werden analytische Lösungen für die freien und fremderregten Balken und Plattenschwingungen vorgestellt und anschließend mit den Ergebnissen der pFEM Methode in AdhoC verglichen. Ziel ist die Verifizierung von AdhoC. Polynomgrad und Zeitschrittstudien werden sowohl im linearen als auch nichtlinearen Bereich präsentiert und das Konvergenzverhalten der AdhoCErgebnisse dargestellt.
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Industrial Cooperations
 Mesh Generator Domesh, core package within "sofimsh" of SOFiSTiK
 Various other projects, all concerned with computational mechanics, together with numerous partners including Siemens, BMW and Hilti.