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

¹ Dipartimento di Matematica – Laboratoire Lagrange, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy. elena.bonetti@unipv.it
² Centre de Mathématiques et de leurs Applications – Laboratoire Lagrange, École Normale Supérieure de Cachan, France. fremond@cmla.ens-cachan.fr

Received: 24 June 2009
Revised: 2 February 2010

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 +∞.