A quasistatic frictional contact problem with damage involving viscoelastic materials with short memory. (November 2016)

• Record Type: Journal Article
• Authors: Li, Yunxiang; Migórski, Stanisław; Han, Jiangfeng
• Is Part Of: Mathematics and mechanics of solids. Volume 21:Number 10(2016)
• Page Start: 1167
• Page End: 1183
• Publication Date: 2016-11
• Subjects: Hemivariational inequality -- viscoelastic -- quasistatic -- frictional contact -- damage -- evolutionary inclusion -- weak solution; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286514558657
• Languages: English
• ISSNs: 1081-2865

Abstract

We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be quasistatic and the material behaviour is described by a viscoelastic constitutive law with damage. The friction and contact are modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the velocity and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of time-dependent stationary inclusions and a fixed point theorem.