Primal-dual algorithm for quasi-static contact problem with Coulomb's friction

TL;DR

This paper introduces an accelerated primal-dual algorithm for efficiently solving quasi-static contact problems with Coulomb friction, outperforming traditional Newton methods in speed and simplicity.

Contribution

It proposes a novel primal-dual method tailored for second-order cone complementarity problems in contact mechanics, offering ease of implementation and improved performance.

Findings

Outperforms regularized Newton methods in numerical experiments

Easy to implement with basic vector and matrix operations

Effective for quasi-static contact problems with Coulomb friction

Abstract

This paper presents a fast first-order method for solving the quasi-static contact problem with the Coulomb friction. It is known that this problem can be formulated as a second-order cone linear complementarity problem, for which regularized or semi-smooth Newton methods are widely used. As an alternative approach, this paper develops a method based on an accelerated primal-dual algorithm. The proposed method is easy to implement, as most of computation consists of additions and multiplications of vectors and matrices. Numerical experiments demonstrate that this method outperforms a regularized and smoothed Newton method for the second-order cone complementarity problem.