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.

本文的目的是研究弹性中非线性静摩擦接触问题的数学模型，其混合边界条件由 Signorini 单边无摩擦接触条件、非单调多值接触和次微分形式的摩擦定律的组合描述。首先，在适当的假设下，我们提供了接触模型的弱公式，它是一个带有拉格朗日乘子的椭圆系统，由一个半变分不等式和一个变分不等式组成。然后，我们证明了接触问题的可解性。最后，使用H的概念-非线性弹性张量的收敛，我们提供了在弹性算子、体力和表面牵引力中出现的扰动下解的收敛结果。