Quasistatic Frictional Wear in Electro-Elasto-Viscoplastic Materials with Unilateral Constraints

Laldja Benziane; Sihem  Smata; Nemira  Lebri; Fares  Yazid

doi:10.5269/bspm.77634

Laldja Benziane University of Farhet Abbas Setif 1, Algeria
Sihem Smata
Nemira Lebri
Fares Yazid

Abstract

We investigate a mathematical model for wear-induced quasistatic frictional contact between a
moving foundation and a piezoelectric body. Archard’s law governs the evolution of the wear function. Taking
damage effects into account, the electro-elasto-viscoplastic constitutive law is used. In order to account
for foundation wear, the model takes into consideration both a regularized Coulomb’s law of dry friction
and a normal compliance condition with unilateral constraints. A parabolic inclusion with homogeneous
Neumann boundary conditions describes the evolution of damage. We provide a variational formulation for
the model, which is represented as a system that includes the wear field, damage field, electric potential field,
and displacement field. Arguments based on differential equations, elliptic variational inequalities, parabolic
inequalities, and the Banach fixed point theorem have been used to demonstrate the existence and uniqueness
of a result.

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