×

Variational analysis of an electro-viscoelastic contact problem with friction and adhesion. (English) Zbl 1332.74023

Summary: We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini’s conditions and a version of Coulomb’s law of dry friction in which the adhesion of contact surfaces is taken into account. 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 system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach’s fixed point theorem.

MSC:

74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74M15 Contact in solid mechanics
74F25 Chemical and reactive effects in solid mechanics
49J40 Variational inequalities
74M10 Friction in solid mechanics