Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Crack growth with non-interpenetration: A simplified proof for the pure Neumann problem

Pages: 1219 - 1231, Volume 31, Issue 4, December 2011      doi:10.3934/dcds.2011.31.1219

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Gianni Dal Maso - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)
Giuliano Lazzaroni - SISSA, via Bonomea 265, 34136 Trieste, Italy (email)

Abstract: We present a recent existence result concerning the quasistatic evolution of cracks in hyperelastic brittle materials, in the framework of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in [9].

Keywords:  Variational models, energy minimization, free-discontinuity problems, polyconvexity, quasistatic evolution, rate-independent processes, brittle fracture, crack propagation, Griffith's criterion, finite elasticity, non-interpenetration.
Mathematics Subject Classification:  35R35, 74R10, 74B20, 49J45, 49Q20, 35A35.

Received: December 2009;      Revised: December 2010;      Available Online: September 2011.