Analysis of a Contact Problem Modeled by Hemivariational Inequalities in Thermo-Piezoelectricity (Journal of Nonlinear Modeling and Analysis, 2025)
We study a quasistatic contact problem from both variational andnumerical perspectives, focusing on a thermo-piezoelectric body interactingwith an electrically and thermally rigid foundation. The contact is modeledwith a normal damped response and unilateral constraint for the velocity field,associated with a total slip-dependent version of Coulomb’s law of dry friction.The electrical and thermal conditions on the contact surface are describedby Clarke’s subdifferential boundary conditions. We formulate the problem’sweak form as a system combining a variational-hemivariational inequality withtwo hemivariational inequalities. Utilizing recent results in the theory of hemivariational inequalities, along with the fixed point method, we demonstratethe existence and uniqueness of the weak solution. Furthermore, we examinea fully discrete scheme for the problem employing the finite element method,and we establish error estimates for the approximate solutions.