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Keywords:

  • Damage evolution with spatial regularization;
  • partial damage;
  • rate-independent systems;
  • energetic solutions;
  • convexity of energy functional;
  • temporal Lipschitz- and Hölder-continuity.

Abstract

This paper discusses an existence result for energetic solutions of rate-independent damage processes and the temporal regularity of the solution. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [16] concerning the properties of the stored elastic energy density as well as the suitable Sobolev space for the damage variable: While previous work assumes that the damage variable z satisfies z in W1, r(Ω) with r > d for Ω ⊂ ℝd, we can handle the case r > 1 by a new technique for the construction of joint recovery sequences. Moreover, this work generalizes the temporal regularity results to physically nonlinearly elastic materials by analyzing Lipschitz- and Hölder-continuity of solutions with respect to time.