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Phase field simulation of thermomechanical fracture
Author(s) -
Kuhn Charlotte,
Müller Ralf
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910070
Subject(s) - discretization , cracking , discontinuity (linguistics) , phase field models , fracture mechanics , finite element method , displacement field , energy minimization , brittleness , mechanics , brittle fracture , phase (matter) , materials science , structural engineering , mathematics , fracture (geology) , mathematical analysis , engineering , physics , composite material , quantum mechanics
In Francfort and Marigo's variational free‐discontinuity formulation of brittle fracture [1] cracking is regarded as an energy minimization process, where the total energy is minimized with respect to any admissible crack set and displacement field. No additional criterion is needed to determine crack paths, branching of cracks and crack initiations. However, a direct discretization of the model is faced with significant technical problems, as it involves minimizations in a set of possibly discontinuous functions. A regularized version of the model has been introduced by Bourdin [2] and based on this, we use the concept of a continuum phase field model to simulate cracking processes. Cracks are indicated by the order parameter of the phase field model and cracking can be regarded as a phase transition problem. Additionally, introducing the heat equation into the model, it is capable to also take account of crack propagation due to thermal stresses. In the numerical implementation, crack parameter as well as temperature are treated as additional degrees of freedom and the coupled field equations are solved using the finite element method together with an implicit time integration scheme. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)