Existence results for unilateral contact problem with friction of thermo-electro-elasticity

摘要

This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation.The behavior of the material is modeled with a thermo-electro-elastic constitutive law.The contact is described by Signorini's conditions and Tresca's friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is derived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem.