Analysis of a quasistatic thermo‐electro‐viscoelastic contact problem modeled by variational‐hemivariational and hemivariational inequalities

We study, from both variational and numerical perspectives, a quasistatic contact problem involving a thermo‐electro‐viscoelastic body and an electrically and thermally conductive rigid foundation. The contact is modeled by the Signorini's unilateral contact condition for the velocity field. Both the electrical and thermal conductivity conditions on the contact surface are described using the Clarke subdifferential boundary. We derive the weak formulation of the problem as a system coupling a variational‐hemivariational inequality and two hemivariational inequalities. We utilize recent results from the theory of variational‐hemivariational inequalities to establish the existence and uniqueness of the weak solution of the model. Finally, we study a fully discrete scheme for the problem using the Euler scheme and the finite element method. Under additional solution regularity assumptions, we derive error estimates for the approximate solutions.