A contact algorithm for voxel-based meshes using an implicit boundary representation
Numerical methods operating on structured grids have become popular since they offer good run time performance and are able to process directly voxel-based digital data from image recordings. Hence, the general framework of these fast solvers presupposes an unfitted boundary approximation avoiding complicated meshing of bodies. This allows an efficient handling with geometrical issues. Nevertheless, contacts between deformable solids are hard to deal with in the presence of this boundary representation. For this difficulty we suggest the usage of an implicit boundary representation combined with a modified saddle point formulation, resembling Nitsche's approach. Both ideas give an elegant approach for discretizing the contact terms and enable a simple contact detection. Moreover, we suggest an intermediate surface as new reference contact area which fits well into our proposed method. In the end we present numerical results and analyze the accuracy and convergence rate. Furthermore, we demonstrate the current application range of our approach for problems with multiple contacts. In this paper we focus only on frictionless contact with small deformations.