A VARIATIONAL-HEMIVARIATIONAL INEQUALITY IN CONTACT PROBLEM FOR LOCKING MATERIALS AND NONMONOTONE SLIP DEPENDENT FRICTION  

作　　者：Stanistnw MIGORSKI Justyna OGORZALY 

机构地区：[1]Chair of Optimization and Control,Jagiellonian University in KrakSw,ul.Lojasiewicza 6,30348 Krakdw,Poland [2]Faculty of Mathematics and Computer Science,Jagiellonian University in Krakow,ul.Lojasiewicza 6,30348 Krakow,Poland

出　　处：《Acta Mathematica Scientia》2017年第6期1639-1652,共14页数学物理学报（B辑英文版）

基　　金：supported by the National Science Center of Poland under the Maestro 3 Project No.DEC-2012/06/A/ST1/00262;the project Polonium“Mathematical and Numerical Analysis for Contact Problems with Friction”2014/15 between the Jagiellonian University and Universitde Perpignan Via Domitia

摘　　要：We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.

关 键 词：variational-hemivariational inequality Clarke subdifferential locking material unilateral constraint nonmonotone friction 

分 类 号：O1[理学—数学]