VARIATIONAL ANALYSIS OF A FRICTIONAL CONTACT PROBLEM WITH WEAR AND DAMAGE

Mohammed Salah Mesai Aoun,Abdelaziz Azeb Ahmed,Mohamed Selmani

doi:10.3846/mma.2021.11942

Mohammed Salah Mesai Aoun, Abdelaziz Azeb Ahmed + Show 1 more

Open Access

https://doi.org/10.3846/mma.2021.11942

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Abstract

We study a quasistatic problem describing the contact with friction and wear between a piezoelectric body and a moving foundation. The material is modeled by an electro-viscoelastic constitutive law with long memory and damage. The wear of the contact surface due to friction is taken into account and is described by the differential Archard condition. The contact is modeled with the normal compliance condition and the associated law of dry friction. We present a variational formulation of the problem and establish, under a smallness assumption on the data, the existence and uniqueness of the weak solution. The proof is based on arguments of parabolic evolutionary inequations, elliptic variational inequalities and Banach fixed point.

Highlights

The piezoelectric effect is characterized by the coupling between the mechanical and electrical behavior of the materials
There are very few mathematical results concerning contact problems involving piezoelectric materials and there is a need to extend the results on models for contact with deformable bodies which include coupling between mechanical and electrical properties
For works concerned with the frictional contact problems for electro-viscoelastic materials with long memory, we refer to [15, 16] and the references therein

Summary

Introduction

The piezoelectric effect is characterized by the coupling between the mechanical and electrical behavior of the materials. There are very few mathematical results concerning contact problems involving piezoelectric materials and there is a need to extend the results on models for contact with deformable bodies which include coupling between mechanical and electrical properties. In the present paper we consider a mathematical model for the process of a frictional contact problem with normal compliance and wear for an electro-viscoelastic material with long memory, damage and a moving conductive foundation. A mathematical models which describe the equilibrium of an elastic or a viscoelastic body in frictional contact with a moving foundation were considered in [24, 25, 26] In all these papers, the damage function β is restricted to have values between zero and one. It is based on arguments of classical results for elliptic variational inequalities, on parabolic inequalities and fixed point arguments

Notation and preliminaries

Mechanical and variational formulations

Existence and uniqueness result