Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

Weimin Han; Meir Shillor; Mircea Sofonea

doi:10.1016/S0377-0427(00)00707-X

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Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

Journal article

Open access

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Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

Weimin Han, Meir Shillor and Mircea Sofonea

Journal of computational and applied mathematics, Vol.137(2), pp.377-398

2001

DOI: 10.1016/S0377-0427(00)00707-X

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Abstract

We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulomb's law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions.

Coulomb's friction

Finite element method

Variational analysis

Numerical analysis

Normal compliance

Variational inequality

Mechanical damage

Viscoelastic material

Fully discrete scheme

Quasistatic frictional contact

Details

Title: Subtitle: Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage
Creators: Weimin Han - Department of Mathematics, University of Iowa, Iowa City, IA 52242-1410, USA
Meir Shillor - Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
Mircea Sofonea - Laboratoire de Théorie des Systèmes, Université de Perpignan, 66860 Perpignan, France
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.137(2), pp.377-398
DOI: 10.1016/S0377-0427(00)00707-X
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V
Language: English
Date published: 2001
Academic Unit: Mathematics
Record Identifier: 9983986091802771

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