ANALYSIS OF A FRICTIONAL CONTACT PROBLEM FOR VISCOELASTIC MATERIALS WITH LONG MEMORY

被引：11
作者：
Migorski, Stanislaw [1 ]
Ochal, Anna [1 ]
Sofonea, Mircea [2 ]
机构：
[1] Jagiellonian Univ, Fac Math & Comp Sci, Inst Comp Sci, PL-30348 Krakow, Poland
[2] Univ Perpignan, Phys Math Lab, F-66860 Perpignan, France
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 15卷 / 03期
关键词：
Viscoelastic material; Volterra integral term; frictional contact; Clarke subdifferential; operator inclusion; hemivariational inequality; weak solution; INEQUALITIES;
D O I：
10.3934/dcdsb.2011.15.687
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is time-dependent, the material behavior is described with a viscoelastic constitutive law with long memory and the contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is of the form of a hemivariational inequality with Volterra integral term for the displacement field. Then we prove existence and uniqueness results in the study of abstract inclusions as well as in the study of abstract hemivariational inequalities with Volterra integral term. The proofs are based on arguments on pseudomonotone operators, compactness and fixed point. We use the abstract results to prove the unique solvability of the frictional contact problem. Finally, we present examples of contact and frictional boundary conditions for which our results work.
引用
收藏
页码：687 / 705
页数：19
相关论文
共 50 条
[21]   ANALYSIS OF QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH SUBDIFFERENTIAL FORM, UNILATERAL CONDITION AND LONG-TERM MEMORY [J].
Ourahmoun, A. ;
Bouderah, B. ;
Serrar, T. .
INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2020, 18 (02) :161-171
[22]   Integrodifferential hemivariational inequalities with applications to viscoelastic frictional contact [J].
Migorski, Stanislaw ;
Ochal, Anna ;
Sofonea, Mircea .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (02) :271-290
[23]   Study of a viscoelastic frictional contact problem with adhesion [J].
Touzaline, Arezki .
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2011, 52 (02) :257-272
[24]   A quasistatic contact problem for viscoelastic materials with friction and damage [J].
Li, Yunxiang ;
Liu, Zhenhai .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (07) :2221-2229
[25]   Analysis of a dynamic contact problem for electro-viscoelastic cylinders [J].
Migorski, Stanislaw ;
Ochal, Anna ;
Sofonea, Mircea .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (05) :1221-1238
[26]   Analysis of a history-dependent frictional contact problem [J].
Sofonea, M. ;
Farcas, A. .
APPLICABLE ANALYSIS, 2014, 93 (02) :428-444
[27]   ANALYSIS OF A FRICTIONAL CONTACT PROBLEM WITH ADHESION [J].
Lerguet, Z. ;
Sofonea, M. ;
Drabla, S. .
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2008, 77 (02) :181-198
[28]   Modeling and analysis of a contact problem for a viscoelastic rod [J].
Bartosz, Krzysztof ;
Sofonea, Mircea .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2016, 67 (05)
[29]   A FRICTIONAL CONTACT PROBLEM FOR AN ELECTRO-VISCOELASTIC BODY [J].
Lerguet, Zhor ;
Shillor, Meir ;
Sofonea, Mircea .
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[30]   The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory [J].
Ammar Derbazi ;
Mohamed Dalah ;
Amar Megrous .
Applications of Mathematics, 2016, 61 :339-358
12345