Contact Mechanics in Computational Homogenization

Abstract

Concerning homogenization, we consider in this contribution periodic boundary-interface value problems (BIVP) within representative volume elements (RVE), which contain porous materials consisting of possibly many separate objects. For instance, these RVEs are available from micro scans in voxel resolution. However, the occurrence of contact between deformable, solid objects requires advanced techniques of methods solving common elasticity problems. With regard to that, we will demonstrate the treatment of contact between each of those by means of an implicit boundary description, used for both surface reconstruction and contact detection. Furthermore, a new technique for solving contact problems is introduced which can be easily integrated as material law routine into so called fast solvers [1], performing on Cartesian grids and exploiting the fast Fourier transform (FFT). In the end, we will present numerical results for a standard problem from contact mechanics, obtained by this new approach.