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Damage of nonlinearly elastic materials at small strain – Existence and regularity results –
Author(s) -
Thomas M.,
Mielke A.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900243
Subject(s) - generalization , lipschitz continuity , sobolev space , work (physics) , variable (mathematics) , space (punctuation) , mathematical analysis , mathematics , elastic energy , joint (building) , physics , computer science , structural engineering , thermodynamics , engineering , operating system
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 W 1 , r(Ω) with r > d for Ω ⊂ 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.