2024 , Volume 29, № 6, p.52-75

The focus of this paper is on a mathematical model that depicts the state equilibrium of a piezoelectric structure in contact with a conductive foundation, taking into account the presence of friction. The constitutive law governing the electro-elastic behavior of the system is considered to be non-linear, while the contact is modelled using Signorini’s modified contact conditions. These conditions are supplemented by a non-local Coulomb friction law and an electrical conductivity condition that has been regularized. A weak formulation of the model is presented as a coupled system that relates the displacement and electric potential fields. The weak solution is shown to be both unique and existent through the invoke of Banach fixed-point theorem and arguments of abstract elliptic quasi-variational inequalities. Additionally, we explore the problem’s finite element approximation and derive estimate of its associated error. In conclusion, an iterative method is introduced to solve the finite element system resulting from the analysis, and the convergence analysis of the method is considered under appropriate conditions.