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Computation of crack propagation in 3‐dimensional anisotropic solids
Author(s) -
Steigemann Martin,
SpecoviusNeugebauer Maria
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410077
Subject(s) - isotropy , anisotropy , fracture mechanics , computation , quadratic equation , plane (geometry) , work (physics) , mechanics , materials science , crack closure , energy (signal processing) , geometry , physics , mathematics , composite material , optics , thermodynamics , algorithm , quantum mechanics
This contribution presents ideas, how crack propagation in three‐dimensional solids composed of anisotropic materials can be predicted using the Griffith energy principle. Since the work of Irwin the change of potential energy caused by a straight elongation of a crack in an isotropic two‐dimensional homogeneous structure can be expressed in quadratic terms of the stress intensities at the crack tip. This result was generalized in the last decades using methods of asymptotic analysis by many authors [1] to more complicated geometries, to anisotropic and inhomogeneous materials. With the energy release rate at hand, quasi‐static scenarios of crack propagation can be simulated for plane problems [2], but this is still a complicated task for three‐dimensional problems [3]. We show an idea how the change of energy caused by propagation of a crack surface in a fully three‐dimensional solid of nearly arbitrary shape can be computed in anisotropic materials. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)