A quasistatic electro-elastic contact problem with normal compliance, friction and adhesion

• Main Authors: Nadhir Chougui, Salah Drabla
• Format: Article
• Language: English
• Published: Texas State University 2014-12-01
• Series: Electronic Journal of Differential Equations
• Subjects: Piezoelectric material; electro-elastic; frictional contact; Coulomb's law; adhesion; normal compliance; quasi-variational inequality; weak solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2014/257/abstr.html

In this article we consider a mathematical model which describes the contact between a piezoelectric body and a deformable foundation. The constitutive law is assumed linear electro-elastic and the process is quasistatic. The contact is adhesive and frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of dry friction. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a coupled system for the displacements, the electric potential and the bonding field. Under a smallness assumption on the coefficient of friction, we prove an existence result of the weak solution of the model. The proofs are based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.