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A novel treatment of crack boundary conditions in phase field models of fracture
Author(s) -
Strobl Michael,
Seelig Thomas
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510068
Subject(s) - isotropy , stiffness , materials science , field (mathematics) , mechanics , phase (matter) , fracture (geology) , phase field models , scalar (mathematics) , boundary value problem , orientation (vector space) , stress field , scalar field , crack tip opening displacement , fracture mechanics , crack closure , structural engineering , geometry , physics , composite material , classical mechanics , mathematics , mathematical analysis , engineering , finite element method , optics , quantum mechanics , pure mathematics
In the phase field approach for fracture an additional scalar field is introduced in order to describe the state of the material between intact and fully broken. So far, for the loading dependent degradation of stiffness (damage) either the volumetric‐deviatoric split of strain [1, 2] or the spectral decomposition [3, 4] is used. In contrast to such an isotropic degradation of stiffness, the fully broken state represents a crack with a particular orientation. Both aforementioned approaches do not take the crack orientation into account. This may lead to the violation of the crack boundary conditions. In order to satisfy these conditions the phase field approach is modified here by taking the orientation of the crack into account. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)