A dynamic contact problem for elastic–viscoplastic materials with normal damped response and damage. Issue 11 (1st November 2016)

• Record Type: Journal Article
• Authors: Li, Yunxiang
• Is Part Of: Applicable analysis. Volume 95:Issue 11(2016)
• Page Start: 2485
• Page End: 2500
• Publication Date: 2016-11-01
• Subjects: Hemivariational inequality -- elastic–viscoplastic -- frictional contact -- damage -- weak solution; 74M15 -- 49J40 -- 47J20 -- 35Q74 -- 35J85; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1094797
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be dynamic and the material behavior is described by a elastic–viscoplastic constitutive law with damage. The frictional contact is modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the displacement 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 hyperbolic hemivariational inequality, a classical existence, and uniqueness result on parabolic inequalities and a fixed point argument.