Geodesic
From an adhesive to a brittle delamination model in thermo-visco-elasticity
Rossi, Riccarda1 ; Thomas, Marita2
1 DICATAM – Sezione di Matematica, Università di Brescia, via Valotti 9, 25133 Brescia, Italy.
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 1-59

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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.

DOI : 10.1051/cocv/2014015
Classification : 35K85, 47J20, 49J45, 49S05, 74F07, 74R10
Keywords: 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

Rossi, Riccarda 1 ; Thomas, Marita 2

1 DICATAM – Sezione di Matematica, Università di Brescia, via Valotti 9, 25133 Brescia, Italy.
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. 
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     title = {From an adhesive to a brittle delamination model in thermo-visco-elasticity},
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Rossi, Riccarda; Thomas, Marita. From an adhesive to a brittle delamination model in thermo-visco-elasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 1-59. doi: 10.1051/cocv/2014015

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