Adhesive contact problem for viscoplastic materials

Dariusz Pączka

Abstract

We examine a mathematical model that describes a quasistatic adhesive contact between a viscoplastic body and deformable foundation. The material′s behaviour is described by the rate-type constitutive law which involves functions with a non-polynomial growth. The contact is modelled by the normal compliance condition with limited penetration and adhesion, a subdifferential friction condition also depending on adhesion, and the evolution of bonding field is governed by an ordinary differential equation. We present the variational formulation of this problem which is a system of an almost history-dependent variational-hemivariational inequality for the displacement field and an ordinary differential equation for the bonding field. The results on existence and uniqueness of solution to an abstract almost history-dependent inclusion and variational-hemivariational inequality in the reflexive Orlicz-Sobolev space are proved and applied to the adhesive contact problem.
Author Dariusz Pączka (FMIS / DODE)
Dariusz Pączka,,
- Department of Ordinary Differential Equations
Journal seriesNonlinear Analysis-Real World Applications, [Nonlinear Analysis: Real World Applications], ISSN 1468-1218
Issue year2020
Vol51
Pages102982-103005
Publication size in sheets1.15
Keywords in Polishmateriał lepkoplastyczny, adhezja, tarcie, nierówność wariacyjno-hemiwariacyjna, operator zależny prawie od historii, przestrzeń Orlicza
Keywords in EnglishViscoplastic material, adhesion, friction, variational-hemivariational inequality, almost history-dependent operator, Orlicz space
ASJC Classification2700 General Medicine; 2000 General Economics, Econometrics and Finance; 2200 General Engineering; 2603 Analysis; 2604 Applied Mathematics; 2605 Computational Mathematics
Abstract in PolishW pracy zbadano quasistatyczne zagadnienie adhezji materiałów lepkoplastycznych o niestandardowych (niewielomianowych) warunkach wzrostu i koercytywności. Udowodniono istnienie i jednoznaczność rozwiązania badanego problemu z wykorzystaniem rezultatów dla ewolucyjnych inkluzji subróżniczkowych cząstkowych oraz nierówności wariacyjno-hemiwariacyjnych z operatorem prawie zależnym od historii w przestrzeniach refleksywnych Orlicza-Sobolewa na skończonym przedziale czasowym.
DOIDOI:10.1016/j.nonrwa.2019.102982
URL https://www.sciencedirect.com/science/article/pii/S1468121819306121
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 26-06-2020, ArticleFromJournal
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.5; WoS Impact Factor: 2018 = 2.085 (2) - 2018=2.267 (5)
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