Variational analysis for a quasistatic piezoelectric contact problem governed by a class of history-dependent quasi-variational-hemivariational inequalities

We introduce a mathematical model for the quasistatic Coulomb's frictional contact between a piezoelectric body and an electrically conductive rigid foundation. The model includes a linear electro-viscoelastic constitutive law with long-memory term. We represent certain contact and electrical boundary conditions on the contact surface through unilateral constraints. By formulating the weak form of the problem as a system that combines two variational-hemivariational inequalities, we demonstrate its equivalence to a single variational-hemivariational inequality. We then establish the existence and uniqueness of the solution using recent advances in the theory of variational-hemivariational inequalities. Finally, we analyze the continuous dependence of the solution on the input data.