Analysis of history-dependent hemivariational inequalities in dynamic contact problems with frictional and electrical effects

In this paper, we present a novel dynamic frictional contact model between a viscoelastic piezoelectric body with long-term memory and a conductive foundation. The contact is modeled with complex nonmonotone subdifferential boundary conditions determined by both mechanical memory operators and the electric potential. These conditions create a complicated system of nonlinear evolutionary inclusions of the subdifferential kind, which can only be investigated and solved using advanced mathematical techniques. To solve the well-posed problem, we develop a weak system that includes a second-order hemivariational inequality with a Volterra integral component for the displacement field and a history-dependent hemivariational inequality for the electric potential field.