On convergence of the penalty method for a static unilateral contact problem with nonlocal friction in electro-elasticity

Abstract

In this paper, we consider the penalty method to solve the unilateral contact with friction between an electro-elastic body and a conductive foundation. Mathematical properties, such as the existence of a solution to the penalty problem and its convergence to the solution of the original problem, are reported. Then, we present a finite elements approximation for the penalised problem and prove its convergence. Finally, we propose an iterative method to solve the resulting finite element system and establish its convergence.

Numerical approximation of a frictional contact problem in elasto‐plasticity based on the penalty approach

“…The proof of this theorem will be carried out in several steps. It is based on fixed point arguments similar to those used in []. We suppose in the sequel that the assumptions of Theorem are fulfilled.…”

“…In [], Chapter 5, Section 5.2, various results in the analysis of contact problems with Tresca's friction law and Coulomb's law without slip‐dependent coefficient of friction, for elastic materials, where the contact is modeled with various contact conditions, also, a penalty approach has been presented. In [], a penalization method to solve the frictional contact problem between a nonlinear electro‐elastic body and an electrically conductive foundation was presented. In the present paper, we use the same numerical approach in [].…”

“…In [], a penalization method to solve the frictional contact problem between a nonlinear electro‐elastic body and an electrically conductive foundation was presented. In the present paper, we use the same numerical approach in [].…”

The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

“…We recall that in the last few decades, tremendous popularity has been achieved by the investigation of a class of nonlinear unilateral elliptic problem due to their fundamental role in describing several phenomena, such as the study of fluid filtration in porous media, constrained heating, elastoplasticity, optimal control, financial mathematics and others; for those studies, there are large numbers of mathematical articles; see [1][2][3][4] for more details.…”

Hemivariational inequalities modeling electro-elastic unilateral frictional contact problem

“…The literature on this topic is still growing and we mention only recent references. The static adhesive contact problems for electro-elastic materials were studied in [6] under the assumption that the foundation is insulated, and in [7][8][9][10][11][12] under the assumption that the foundation is electrically conductive. In all aforementioned papers the contact problems were modeled by variational inequalities.…”