History-dependent variational-hemivariational inequalities in contact mechanics

被引：66

作者：

Migorski, Stanislaw ^{[1
]}

Ochal, Anna ^{[1
]}

Sofonea, Mircea ^{[2
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[2] Univ Perpignan Via Domitia, Lab Math & Phys, F-66860 Perpignan, France

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 22卷

关键词：

Variational-hemivariational inequality; Clarke subdifferential; History-dependent operator; Viscoelastic material; Frictionless contact; GENERALIZED-GRADIENTS; UNILATERAL PROBLEMS; MEDIA;

D O I：

10.1016/j.nonrwa.2014.09.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an abstract class of variational-hemivariational inequalities which arise in the study of a large number of mathematical models of contact. The novelty consists in the structure of the inequalities which involve two history-dependent operators and two non-differentiable functionals, a convex and a nonconvex one. For these inequalities we provide an existence and uniqueness result of the solution. The proof is based on arguments of surjectivity for pseudomonotone operators and fixed point. Then, we consider a viscoelastic problem in which the contact is frictionless and is modeled with a new boundary condition which describes both the instantaneous and the memory effects of the foundation. We prove that this problem leads to a history-dependent variational-hemivariational inequality in which the unknown is the displacement field. We apply our abstract result in order to prove the unique weak solvability of this viscoelastic contact problem. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：604 / 618

页数：15

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