Numerical solution of contact problems using level set methods on voxel discretizations

Fast solvers performing on a regular grid are often used for problems in elasticity, in order to avoid expensive mesh generations. However, if overlaps between solid materials occur without any interactions, these might deteriorate the results, especially for the stresses. Therefore, we want to present an approach for developing numerical methods for contact problems on a regular mesh with the help of signed distance data and multi-material voxels. In this contribution we will focus on problems in linear elastostatics with contact between several different bodies. Finally, we present the results from a numerical test for the two dimensional Hertz problem, solved on a triangular regular mesh.