Mohamed Elhaddad, M.Sc. Research Assistant Room: 3159 Email: Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein! Tel: +49 89 289-23074 Fax: +49 89 289-25051

Research

 Numerical analysis of human vertebrae using the finite cell method

Publications



Submitted Preprints

Journal Papers

• 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 large-scale finite cell analyses
  Finite Elements in Analysis and Design - Status: Accepted for publication, 2019
  DOI: 10.1016/j.finel.2019.01.009
  
  
  
  
  
  
  
• Nagaraja, S.; Elhaddad, M.; Ambati, M.; Kollmannsberger, S.; De Lorenzis, L.; Rank, E. Show abstract Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method
  Computational Mechanics 63 (63), pp. 1-18, Springer, 2019
  DOI: 10.1007/s00466-018-1649-7 - Status: Postprint / reviewed
  
  
  
  The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field 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 length-scale 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 phase-field profile. In the classical approach, phase-field 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 phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement 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 non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming 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 multi-level hp-refinement and the FCM in the context of phase-field simulations.
  
  
  
• Elhaddad, M.; Zander, N.; Bog, T.; Kudela, L.; Kollmannsberger, S.; Kirschke, J.S.; Baum, T.; Ruess, M.; Rank, E. Multi-level hp-finite 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, R-P.; Rank, E. Parallelization of the multi-level hp-adaptive finite cell method
  Computers and Mathematics with Applications 74 (1), pp. 126-142, Elsevier, 2017
  DOI: 10.1016/j.camwa.2017.01.004 - Status: Verlagsversion / published
  
  
  
  
  
  
  
• Zander, N.; Bog, T.; Elhaddad, M.; Frischmann, F.; Kollmannsberger, S.; Rank, E. The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes.
  Computer Methods in Applied Mechanics and Engineering 310, pp. 252-277, 2016
  DOI: 10.1016/j.cma.2016.07.007
  
  
  
  
  
  
  
• 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. 1-25, 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/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A one-dimensional 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 state-of-the-art 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.
  
  
  
• 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. 49-63, 2014
  DOI: 10.1016/j.advengsoft.2014.04.004 - Status: Verlagsversion / published
  
  
  
  
  
  
  

Conference Talks

• Hug, L.; Elhaddad, M.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. A Phase-Field 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
  
  
  
  
  
  
  
• Nagaraja, S.; Elhaddad, M.; Ambati, M.; Kollmannsberger, S; De Lorenzis, L.; Rank E. Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method
  In: 6th European Conference on Computational Mechanics, Glasgow, United Kingdom, 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 multi-level hp-adaptive finite cell method
  In: 6th European Conference on Computational Mechanics, Glasgow, United Kingdom, 2018
  
  
  
  
  
  
  
• Elhaddad, M.; Kollmannsberger, S.; Valentinitsch, A.; Kirschke, J.S.; Ruess, M.; Rank, E. Micro-CT based finite cell analysis of vertebral bodies
  In: Engineering Mechanics Institute Conference 2017, San Diego, CA, USA, 2017
  
  
  
  
  
  
  
• Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, R-P.; Rank, E. A parallel approach for the multi-level hp-daptive finite cell method
  In: Siam Conference on Computational Science and Engineering 2017, SIAM, 2017
  
  
  
  
  
  
  
• Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, R-P.; Rank, E. Parallelization of the multi-level hp-adaptive finite cell method
  In: 5th European Seminar on Computing, Pilsen, Czech Republic, 2016
  
  
  
  
  
  
  
• Elhaddad, M.; Zander, N.; Jomo, J.; Kollmannsberger, S.; Kirschke, J. S.; Ruess, M.; Rank, E. Show abstract Adaptive discretizations for bone-implant 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 bone-implant systems. Patient-specific 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 voxel-based mesh, where a predefined number of voxels constitute one finite element in a grid that matches the voxel model. Alternatively, geometry-conforming 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 Computer-Aided-Design (CAD) models, and then incorporated in the finite element mesh. The adequate treatment of the bone-implant interface demands the spatial refinement of the finite element mesh at the interface for an accurate solution. For voxel-based 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, geometry-conforming finite elements need more pre-processing (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 CT-scan, 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 pre-processing effort. Furthermore, the hierarchical refinement scheme yields a higher accuracy at the bone-implant interface by adaptively refining the FCM grid.
  
  
  
• 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 patient-specific 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 peri-implant bone strains are of major interest. High forces are transmitted at the bone-implant 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 CT-data 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 bone-implant system, the adequate treatment of the bone-implant 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 bone-implant systems, the hierarchic refinement is used to resolve the bone-implant 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.; 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 p-extension. 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 octree-based 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 close-to-degenerate cases, but remains algorithmically simple at the same time. Several further recent developments of the FCM will be discussed. A new two- and three-dimensional 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 de-refinement. Finally, a re-interpretation 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.
  
  
  
• Rank, E.; Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Bauer, J.; Ruess, M. Show abstract Coupling scales and adaptive refinement for simulation of bone-fixation 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 bone-implant systems have been presented. In general, a geometric model of a bone is derived from qCT-data, 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 pre-stress 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 multi-scale method and demonstrate its feasibility for simulating bone-mechanics on the example of the fixation of a spinal segment.
  
  
  
• 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
  
  
  
  
  
  
  

Theses

• 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/boundary-value problem. Semi-discrete 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 state-of-the-art 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.
  
  
  
• Elhaddad, M. Level-set Geometry Description for the Finite Cell Method
  Honours project, Technische Universität München, 2013
  
  
  
  
  
  
  

Teaching

Courses

• Introduction to Programming in C++ (Winter Term 14/15, 15/16)
• Partial Differential Equations: An Algorithmic Approach (Winter Term 16/17, 17/18)

Supervised Theses

• Oztoprak, Oguz Enforcement of Boundary Conditions in FCM with Applications to Biomechanics
  
  
  
  
  
  
  
• Barzanooni, Reza Modeling of Flexible Wirings and Contact Interactions in Industrial Robots Using Geometrically Exact Beam Formulation
  Master's thesis, Technische Universität München, 2019
  
  
  
  
  
  
  
• Nagaraja, S. Phase-field modeling of brittle fracture with multi-level hp-FEM and the Finite Cell Method
  Master's thesis, Technische Universität München, 2017
  
  
  
  
  
  
  
• Gümüş, E. Finite Element Simulation of Anatomical Distortion due to Brain Tumor Growth
  Master's thesis, Technische Universität München, 2016
  
  
  
  
  
  
  
• Breu, T. Numerical Stabilization of badly cut cells for the Finite Cells Method using Gradient Jump Penalization
  Bachelor's thesis, Technische Universität München, 2016