Space-time boundary elements for frictional contact in elastodynamics

This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincar\'e-Steklov operator. The variational inequality is solved in a mixed formulation using boundary elements in space and time. In the model problem of unilateral Tresca friction contact with a rigid obstacle we obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments in two space dimensions demonstrate the stability, energy conservation and convergence of the proposed method for contact problems involving concrete and steel in the linearly elastic regime. They address both unilateral and two-sided dynamic contact with Tresca or Coulomb friction.