A frictional contact problem for an electro-viscoelastic body

Abstract

A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.

Description

Keywords

Piezoelectric, Frictional contact, Normal compliance, Fixed point, Variational inequality

Citation

Lerguet Z., Shillor M., and Sofonea M. (2007). A frictional contact problem for an electro-viscoelastic body. Electronic Journal of Differential Equations, 2007(170), 1-16.