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.

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

^{1}; Thomas, Marita

^{2}

@article{COCV_2015__21_1_1_0, author = {Rossi, Riccarda and Thomas, Marita}, title = {From an adhesive to a brittle delamination model in thermo-visco-elasticity}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1--59}, publisher = {EDP-Sciences}, volume = {21}, number = {1}, year = {2015}, doi = {10.1051/cocv/2014015}, zbl = {1323.35101}, mrnumber = {3348414}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014015/} }

TY - JOUR AU - Rossi, Riccarda AU - Thomas, Marita TI - From an adhesive to a brittle delamination model in thermo-visco-elasticity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1 EP - 59 VL - 21 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014015/ DO - 10.1051/cocv/2014015 LA - en ID - COCV_2015__21_1_1_0 ER -

%0 Journal Article %A Rossi, Riccarda %A Thomas, Marita %T From an adhesive to a brittle delamination model in thermo-visco-elasticity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1-59 %V 21 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014015/ %R 10.1051/cocv/2014015 %G en %F COCV_2015__21_1_1_0

Rossi, Riccarda; Thomas, Marita. From an adhesive to a brittle delamination model in thermo-visco-elasticity. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 1, pp. 1-59. doi : 10.1051/cocv/2014015. http://archive.numdam.org/articles/10.1051/cocv/2014015/

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