Time domain boundary elements for dynamic contact problems
This work provides a novel numerical framework for dynamic contact problems, which is important for engineering applications involving wave propagation and contact mechanics.
The authors develop a time-domain boundary element method for solving unilateral dynamic contact problems for the wave equation, reducing it to a variational inequality and a saddle point formulation. Numerical experiments demonstrate stability and convergence for non-flat geometries.
This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using boundary elements in the time domain. As a model problem, also a variational inequality for the single layer operator is considered. A priori estimates are obtained for Galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area, where the existence of solutions to the continuous problem is known. Numerical experiments demonstrate the performance of the proposed mixed method. They indicate the stability and convergence beyond flat geometries.