A new class of quasistatic frictional contact problems governed by a variational–hemivariational inequality. (December 2019)

• Record Type: Journal Article
• Authors: Migórski, Stanisław; Gamorski, Piotr
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 583
• Page End: 602
• Publication Date: 2019-12
• Subjects: Variational–hemivariational inequality -- Clarke generalized gradient -- History-dependent operator -- Existence and uniqueness -- Coulomb law of dry friction; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.014
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A quasistatic nonsmooth frictional contact problem for a viscoelastic material is studied. The contact is modeled by a multivalued normal damped response condition with the Clarke generalized gradient of a locally Lipschitz superpotential and the friction is described by a version of the Coulomb law of dry friction with the friction bound depending on the regularized normal stress. The weak formulation of the contact problem is a history-dependent variational–hemivariational inequality coupled with an operator equation for the stress field. A result on the unique weak solvability to this coupled system is proved through a recent contribution on history-dependent subdifferential inclusions and a fixed point approach. Highlights: New model in contact mechanics. Multivalued contact conditions depending on each other. Existence and uniqueness of a local solution. Application of existence and uniqueness result to real world problems.