Adhesive contact problem for viscoplastic materials. (February 2020)

• Record Type: Journal Article
• Authors: Pączka, Dariusz
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Viscoplastic material -- Adhesion -- Friction -- Variational–hemivariational inequality -- Almost history-dependent operator -- Orlicz space; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.102982
• Languages: English
• ISSNs: 1468-1218

Abstract

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.