Quasistatic contact problem with unilateral constraint for elastic-viscoplastic materials

TL;DR

This paper proves the unique solvability of a variational-hemivariational inequality with history dependence and applies it to a quasistatic contact model involving elastic-viscoplastic materials with frictional contact, unilateral constraints, and memory effects.

Contribution

It establishes the existence and uniqueness of solutions for a complex contact problem with history-dependent operators, extending previous static results to dynamic models.

Findings

Proved unique solvability of the variational-hemivariational inequality.

Developed a mathematical model for elastic-viscoplastic contact with friction.

Applied the abstract result to a quasistatic contact problem with memory effects.

Abstract

This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static variational-hemivariational inequality and a fixed point argument. In the second part, we consider a mathematical model which describes quasistatic frictional contact between a deformable body and a rigid foundation. In the model the material behaviour is modelled by an elastic-viscoplastic constitutive law. The contact is described with a normal damped response, unilateral constraint and memory term. In the analysis of this model we use the abstract result from the first part of the paper.