Volume 21, Number 1, January-March 2015
|Page(s)||1 - 59|
|Published online||17 October 2014|
From an adhesive to a brittle delamination model in thermo-visco-elasticity∗,∗∗
1 DICATAM – Sezione di Matematica,
Università di Brescia, via Valotti
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
Revised: 3 November 2013
We address the analysis of a model for brittle delamination of two visco-elastic bodies, bonded along a prescribed surface. The model also encompasses thermal effects in the bulk. The related PDE system for the displacements, the absolute temperature, and the delamination variable has a highly nonlinear character. On the contact surface, it features frictionless Signorini conditions and a nonconvex, brittle constraint acting as a transmission condition for the displacements. We prove the existence of (weak/energetic) solutions to the associated Cauchy problem, by approximating it in two steps with suitably regularized problems. We perform the two consecutive passages to the limit via refined variational convergence techniques.
Mathematics Subject Classification: 35K85 / 47J20 / 49J45 / 49S05 / 74F07 / 74R10
Key words: Rate-independent evolution of adhesive contact / brittle delamination / Kelvin−Voigt viscoelasticity / nonlinear heat equation / Mosco-convergence / special functions of bounded variation / regularity of sets / lower density estimate
R.R. has been partially supported by MIUR-PRIN grants for the projects “Optimal mass transportation, geometric and functional inequalities and applications” and “Calculus of Variations”, and by GNAMPA ((Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni), of INdAM (Istituto Nazionale di Alta Matematica).
© EDP Sciences, SMAI 2014
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