WIAS Preprint No. 2259, (2016)

From adhesive to brittle delamination in visco-elastodynamics



Authors

  • Rossi, Riccarda
  • Thomas, Marita

2010 Mathematics Subject Classification

  • 49J53 49J45 74H20 74C05 74C10 74M15 74R10

Keywords

  • adhesive contact, brittle delamination, Kelvin-Voigt visco-elasticity, inertia, non-smooth brittle constraint, coupled rate-dependent/rate-independent evolution, energetic solutions

Abstract

In this paper we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvability concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit.

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