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 |