Analysis and Optimal Control of a Frictional Contact Problem with Normal Damped Response and a Semiconductor Piezoelectric Material

Abstract

This article examines a quasistatic contact problem with friction involving a piezoelectric material and a semi-conductive foundation. The material’s behavior is captured by an electroviscoelastic constitutive model. Contact interactions are modeled using a classical normal damped response condition along with a frictional law. We examine the variational framework associated with our model and demonstrate the uniqueness of the solution in the weak sense. Furthermore, we establish the existence of optimal solutions for two categories of optimal control and inverse problems, specifically within the context of the piezo-viscoelastic contact issue being analyzed.