WIAS Preprint No. 1397, (2009)

Damage of nonlinearly elastic materials at small strain --- Existence and regularity results



Authors

  • Thomas, Marita
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 35K85 49S05 74C15 74R20

Keywords

  • Damage evolution with spatial regularization, partial damage, rate-independent systems, energetic formulation via energy functional and dissipation distance, energetic solutions, convexity of energy functional, temporal Lipschitz- and Hölder-continuity of solutions

Abstract

In this paper an existence result for energetic solutions of rate-independent damage processes is established and the temporal regularity of the solution is discussed. We consider a body consisting of a physically nonlinearly elastic material undergoing small deformations and partial damage. The present work is a generalization of [Mielke-Roubicek 2006] 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 ∈ W^1,r (Omega) with r>d for Omega ⊂ R^d, 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.

Appeared in

  • ZAMM Z. Angew. Math. Mech., 90 (2010) pp. 88--112.

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