Computational contact mechanics based on implicit boundary representations for voxel-based meshes

Numerical methods for mechanical problems involving contact have developed significantly in the recent past. For the geometrical representation in these methods, a standard finite element mesh is very often the basis for the considered solids. In contrast to this practice, our work relies on structured meshes built of voxels, which considerably reduces the effort required to handle geometrical problems. Based on this voxel grid, we introduce implicit boundary representations by level sets as alternative to conventional finite element approximations. By adapting the description of boundary movements using level set functions, we show how a novel kind of contact surface makes it possible to elegantly enforce the contact conditions. In this context of regular grids and level sets, we apply level set methods and Nitsche's Method in order to detect the correct contact surface on colliding bodies. In the end, we demonstrate the potential of the proposed method with extensive numerical experiments.