The recently introduced Finite Cell Method (FCM) is targeted at circumventing the complete mesh generation. Its main feature is the combination of high-order Legendre based finite elements by a fictitious domain approach, which allows the extension of the physical domain beyond its boundaries. It complements the weak formulation of the mechanical problem by an additional function α, which is 1 inside the physical domain and 0 outside. Thus, the boundary information is implicitly incorporated into the functional and does not need to be represented by the mesh. Since the extension of solution fields are smooth beyond the physical domain, FCM can preserve exponential convergence of conventionl p-FEM.

The FCM strategy is briefly illustrated in Figs. 2 through 4 by the simple benchmark problem of a perforated plate. Due to its fictitious domain capability, the plate can be discretized irrespective of the circular hole in the middle by just 4 Legendre elements (p=10). The accuracy of the method significantly depends on capturing the discontinuity of α along the physical boundary during numerical integration (α=0 inside the circular hole, α=1 in the plate). This is achieved by an adaptive partitioning with sub-cells, which each contain a grid of 10x10 Gauss points.

Up to now, FCM has been successfully applied in the linear elastic analysis of complex voxel-based structures, such as the proximal femur bone in Fig. 5. However, porous structures at higher load levels respond strongly nonlinear and can therefore not be described accurately by linearized theories. In the context of metal foams, these nonlinearities include most importantly local buckling of cell walls, plastification of parts of the physical domain and self-contact of cell walls during the loading process. The main target of the present project is the integration of nonlinear capabilities into the existing linear FCM approach, so that an elasto-plastic deformation process at finite strains can be realistically simulated for the aluminium foam example.