On the solution of contact problems with adaptive polygonal meshing using the virtual element method

This work describes the application of the virtual element method (VEM) to contact problems between elastic bodies. The easiest approach to solve contact problems using a discretisation scheme is a node-to-node method where degrees of freedom from both bodies are directly linked by constraints that are enforced by a penalty or Lagrange multiplier method. This direct link, however, is only possible for matching meshes on both surfaces. For the case of non-matching meshes at the contact surfaces this work presents an adaptive meshing scheme that includes node insertion and remeshing with polygonal elements to create nodal pairs. Basis is the virtual element method (VEM) as a generalisation of the finite element method (FEM). It can handle arbitrarily shaped elements with an arbitrary number of nodes. The work shows advantages of this new discretisation scheme for treating contact in comparison to classical finite element approaches.