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Configurational‐force‐based structural updates and adaptive remeshing strategies
Author(s) -
Zimmermann Dominik,
Miehe Christian
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700171
Subject(s) - fracture mechanics , dissipation , normality , dual (grammatical number) , fracture (geology) , set (abstract data type) , mathematics , computer science , mathematical optimization , mechanics , structural engineering , physics , materials science , engineering , thermodynamics , art , statistics , literature , composite material , programming language
The application of configurational forces in h ‐adaptive strategies for fracture mechanics and inelasticity is investigated. Starting from a global Clausius‐Planck inequality, dual equilibrium conditions are derived by means of a Coleman‐type exploitation method. The remaining reduced dissipation inequality is used for the derivation of evolution equations for the internal variables. In fracture mechanics, crack loading conditions as well as a normality rule for the crack propagation are obtained. In the discrete setting, the crack propagation is governed by a configurational‐force‐driven update of the geometry model. The material balance equation is used to set up a h ‐adaptive refinement indicator. A relative global criterion is defined used for the decision on mesh refinement. In addition, a criterion on the element level is evaluated controlling the local refinement procedure. The capability of the proposed procedures is demonstrated by means of numerical examples. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)