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A frictional contact problem for an electro-viscoelastic body. (English) Zbl 1139.74041

Summary: We study a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation. 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 law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for displacements and 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.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49J40 Variational inequalities
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