Solvability of a coupled hemivariational system in anti planes hear

Abstract

In this research paper, we present some results on the solvability of the evolutionary system constituting two types of hemivariational inequalities in the study of a piezoelectric frictional contact problem with specific subdifferential boundary conditions. Here, the modeling of quasistatic contact processes is described with linear electro-viscoelastic behavior in the case of antiplane shear deformation, where the foundation is assumed conductive.  The novelty of this modeling is the dependence of the friction force on the total slip-rate with electrical effects, while the conductivity coefficient only depends on the total slip rate. We use a variational formula to express this friction model, which is a coupled system composed of two hemivariational inequalities, one of which is specific to the displacement field and the other is time-dependent for the electric potential field. Then, we show that this mathematical model has a unique weak solution, the proof is based on results of evolutionary and history-dependent inclusions under certain assumptions.