From an adhesive to a brittle delamination model in thermo-visco-elasticity
- Rossi, Riccarda
- Thomas, Marita
2010 Mathematics Subject Classification
- 35K85 74R10 47J20 49J45 49S05 74F07
- Rate-independent evolution of adhesive contact, brittle delamination, Kelvin-Voigt visco-elasticity, nonlinear heat equation, Mosco-convergence, functions of bounded variation
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.
- ESAIM Control Optim. Calc. Var., 21 (2015) pp. 1--59.