Abstract
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumptions, we deliver the weak formulation of the contact model, which is an elliptic system with Lagrange multipliers, and which consists of a hemivariational inequality and a variational inequality. Then, we prove the solvability of the contact problem. Finally, employing the notion of H-convergence of nonlinear elasticity tensors, we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator, body forces, and surface tractions.
Highlights
The aim of this paper is to investigate a mathematical model described by a system consisting of a hemivariational inequality and a variational inequality in reflexive Banach spaces
Such systems appear as weak formulations of various static contact problems in the theory of elasticity and are motivated by a menagerie of friction and contact boundary conditions
We will analyze a new nonlinear frictional contact problem which is described by a nonlinear elastic constitutive law and mixed boundary conditions
Summary
The aim of this paper is to investigate a mathematical model described by a system consisting of a hemivariational inequality and a variational inequality in reflexive Banach spaces Such systems appear as weak formulations of various static contact problems in the theory of elasticity and are motivated by a menagerie of friction and contact boundary conditions. The structure of the paper is as follows: in Section 2, a complicated frictional elastic contact problem is introduced and studied for which we prove the theorem of the existence of solutions for the contact problem under consideration; Section 3 deals with the convergence of solutions to the model under the H-convergence of nonlinear elasticity tensors, perturbations in the body forces, and surface tractions
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