Damage of nonlinearly elastic materials at small strain --- Existence and regularity results
Authors
- Thomas, Marita
ORCID: 0000-0001-9172-014X - 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
DOI
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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