WIAS Preprint No. 1638, (2011)

Quasistatic damage evolution with spatial BV-regularization


Authors

  • Thomas, Marita
    ORCID: 0000-0001-9172-014X

2010 Mathematics Subject Classification

  • 35K85 74R05 49J45 49S05 74R20

Keywords

  • Partial damage, damage evolution with spatial regularization, functions of bounded variation, energetic formulation, Gamma convergence of rate-independent systems

DOI

10.20347/WIAS.PREPRINT.1638

Abstract

An existence result for energetic solutions of rate-independent damage processes is established. We consider a body consisting of a physically linearly elastic material undergoing infinitesimally small deformations and partial damage. In [ThomasMielke10DamageZAMM] an existence result in the small strain setting was obtained under the assumption that the damage variable z satisfies z∈ W1,r(Ω) with r∈(1,∞) for Ω⊂Rd. We now cover the case r=1. The lack of compactness in W1,1(Ω) requires to do the analysis in BV(Ω). This setting allows it to consider damage variables with values in 0,1. We show that such a brittle damage model is obtained as the Γ-limit of functionals of Modica-Mortola type.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. S, 6 (2013) pp. 235--255.

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