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A computational framework of three dimensional configurational‐force‐driven crack propagation
Author(s) -
Gürses Ercan,
Miehe Christian
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700620
Subject(s) - fracture mechanics , discontinuity (linguistics) , isotropy , stiffness , planarity testing , embedding , fracture (geology) , dissipation , brittleness , mechanics , structural engineering , computer science , materials science , mathematics , mathematical analysis , physics , engineering , quantum mechanics , combinatorics , artificial intelligence , composite material , thermodynamics
A variational formulation of quasi‐static brittle fracture is considered and a new finite‐element‐based computational framework is developed for propagation of cracks in three‐dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The evolving crack discontinuity is realized by the doubling of critical nodes and triangular interface facets of the tetrahedral mesh. The crucial step for the success of the procedure is its embedding into an r‐adaptive crack‐facet reorientation procedure based on configurational‐force‐based indicators in conjunction with crack front constraints. We further propose a staggered algorithm which minimizes the stored energy at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive definite subproblems with successively decreasing overall stiffness, providing a very robust algorithmic setting in the postcritical range. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)