Curvilinear virtual elements for contact mechanics

The virtual element method (VEM) for curved edges with applications to contact mechanics is outlined within this work. VEM allows the use of non-matching meshes at interfaces with the advantage that these can be mapped to a simple node-to-node contact formulation. To account for exact approximation of complex geometries at interfaces, we developed a VEM technology for contact that considers curved edges. A number of numerical examples illustrate the robustness and accuracy of this discretization technique. The results are very promising and underline the advantages of the new VEM formulation for contact between two elastic bodies in the presence of curved interfaces.