On some frictional contact problems with velocity condition for  elastic and visco-elastic materials

Khalid Addi; Oanh Chau; Daniel Goeleven

doi:10.3934/dcds.2011.31.1039

Article Contents

2011, Volume 31, Issue 4: 1039-1051. Doi: 10.3934/dcds.2011.31.1039

This issue Previous Article Finite-time Lyapunov stability analysis of evolution variational inequalities Next Article Planar quasilinear elliptic equations with right-hand side in $L(\log L)^{\delta}$

On some frictional contact problems with velocity condition for elastic and visco-elastic materials

1.
University of La Réunion, PIMENT EA4518, 97715 Saint-Denis Messag cedex 9 La Réunion

Received: September 30, 2009

Revised: April 30, 2010

Published: September 2011

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Abstract

We study the evolution of a class of quasistatic problems, which describe frictional contact between a body and a foundation. The constitutive law of the materials is elastic, or visco-elastic: with short or long memory, and the contact is modelled by a general subdifferential condition on the velocity. We derive weak formulations for the models and establish existence and uniqueness results. The proofs are based on evolution variational inequalities, in the framework of monotone operators and $fi$xed point methods. We show the approach of the viscoelastic solutions to the corresponding elastic solutions, when the viscosity tends to zero. Finally we also study the approach to short memory visco-elasticity when the long memory relaxation coefficients vanish.

Keywords:

Elastic material,
visco-elastic material,
long and short memory,
sub-differential contact condition,
quasistatic process,
fixed point,
variational inequality,
weak solution,
approaches to elasticity and short memory viscoelasticity.

Mathematics Subject Classification: Primary: 74M15, 74M10; Secondary: 34G25.

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