# A nonsmooth optimization approach for hemivariational inequalities with applications in Contact Mechanics

## TL;DR

This paper develops a nonsmooth optimization framework for hemivariational inequalities, proving existence and uniqueness, and applies it to contact mechanics problems involving nonmonotone friction laws with computational validation.

## Contribution

It introduces a novel nonsmooth optimization approach for hemivariational inequalities and demonstrates its application to complex contact mechanics problems.

## Key findings

- Existence and uniqueness of solutions established.
- Numerical scheme effectively approximates solutions.
- Simulations validate the theoretical approach.

## Abstract

In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This contact is governed by a nonmonotone friction law with dependence on normal and tangential components of displacement. Finally, computational simulations are performed to illustrate obtained results.