Journal of the
Korean Mathematical Society JKMS

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.

Keywords: Piezoelectric material, electro-viscoelastic, frictional contact, nonlocal Coulomb's law, adhesion, quasi-variational inequality, weak solution, fixed point theorem

MSC numbers: Primary 74H10, 74M15, 74F25, 49J40, 74M10