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Analytical results on a model for damaging in domains and interfaces*

Published online by Cambridge University Press:  18 August 2010

Elena Bonetti  and
Michel Frémond
Elena Bonetti
Affiliation:
Dipartimento di Matematica – Laboratoire Lagrange, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy. elena.bonetti@unipv.it
Michel Frémond
Affiliation:
Centre de Mathématiques et de leurs Applications – Laboratoire Lagrange, École Normale Supérieure de Cachan, France. fremond@cmla.ens-cachan.fr
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Abstract

This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of a Schauder fixed point argument, combined with monotonicity and compactness tools. We also perform an asymptotic analysis of the solutions as the interfacial damage energy (between the body and the contact surface) goes to +∞.

Keywords

Damagecontactadhesionexistenceasymptotic analysis
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 955 - 974
Copyright
© EDP Sciences, SMAI, 2010

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