A survey of numerical methods for hemivariational inequalities with applications to Contact Mechanics

TL;DR

This paper surveys numerical methods for hemivariational inequalities, focusing on contact mechanics applications, comparing three computational approaches, and providing theoretical and numerical insights into solving nonsmooth problems.

Contribution

It introduces a unified framework for solving hemivariational inequalities and compares multiple numerical methods in the context of contact mechanics.

Findings

The augmented Lagrangian method performs best among the three methods.

Numerical schemes effectively approximate solutions to nonsmooth contact problems.

Theoretical results guarantee existence and uniqueness of solutions.

Abstract

In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This problem leads to a hemivariational inequality which we solve numerically. Finally, we compare three computational methods of solving contact mechanical problems: direct optimization method, augmented Lagrangian method and primal-dual active set strategy.