Damage of nonlinearly elastic materials at small strain : existence and regularity results

Loading...
Thumbnail Image
Date
2009
Volume
1397
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Link to publishers version
Abstract

Literaturverz. S. 31 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.

Description
Keywords
Damage evolution with spatial regularization, partial damage, rateindependent systems, energetic formulation via energy functional and dissipation distance, energetic solutions, convexity of energy functional, temporal Lipschitz- and Hölder-continuity of solutions
Citation
Thomas, M., & Mielke, A. (2009). Damage of nonlinearly elastic materials at small strain : existence and regularity results (Vol. 1397). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
Collections
License
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.