WIAS Preprint No. 1692, (2012)

From an adhesive to a brittle delamination model in thermo-visco-elasticity



Authors

  • Rossi, Riccarda
  • Thomas, Marita

2010 Mathematics Subject Classification

  • 35K85 74R10 47J20 49J45 49S05 74F07

Keywords

  • Rate-independent evolution of adhesive contact, brittle delamination, Kelvin-Voigt visco-elasticity, nonlinear heat equation, Mosco-convergence, functions of bounded variation

Abstract

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.

Appeared in

  • ESAIM Control Optim. Calc. Var., 21 (2015) pp. 1--59.

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