Thermo-Electro-Elastic Friction Problem with Modified Signorini Contact Conditions

Abstract

The purpose of this paper is to investigate a frictional contact problem between a thermo-piezoelectric body and an obstacle (such as a foundation). The thermo-piezoelectric constitutive law is assumed to be nonlinear. Modified Signorini’s contact conditions are used to describe the contact, and these are adjusted to account for temperature-dependent unilateral conditions, which are associated with a nonlocal Coulomb friction law. The problem is formulated as a coupled system of displacement field, electric potential, and temperature, which is solved using a variational approach. The existence of a weak solution is established through the utilization of elliptic quasi-variational inequalities, strongly monotone operators, and the fixed point method. Finally, an iterative method is suggested to solve the coupled system, and a convergence analysis is established under appropriate conditions.