Space-time boundary elements for frictional contact in elastodynamics

TL;DR

This paper introduces a boundary element method for simulating dynamic frictional contact in elastodynamics, demonstrating stability and convergence through numerical experiments involving Tresca and Coulomb friction.

Contribution

It formulates a variational inequality approach using boundary elements in space and time for dynamic contact problems, providing new theoretical estimates and numerical validation.

Findings

Method is stable and energy-conserving in simulations.

Converges reliably for contact problems with Tresca and Coulomb friction.

Applicable to elastic bodies in two-dimensional models.

Abstract

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.