Time domain boundary elements for elastodynamic contact

TL;DR

This paper introduces a boundary element method in the time domain for simulating elastodynamic contact problems, providing a stable and convergent approach validated through numerical experiments on various geometries and moving obstacles.

Contribution

It formulates the Signorini contact problem as a variational inequality using boundary elements in the time domain, offering a novel numerical solution approach.

Findings

Method is stable and convergent

Effective for flat and curved geometries

Handles moving obstacles successfully

Abstract

This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for the elastodynamic equations on the boundary, which is solved in a mixed formulation using boundary elements in the time domain. We obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments confirm the stability and convergence of the proposed method for the contact problem in flat and curved two-dimensional geometries, as well as for moving obstacles.