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Phase Field Modeling of Crack Propagation at Large Strains with Application to Rubbery Polymers
Author(s) -
Schänzel Lisa,
Hofacker Martina,
Miehe Christian
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110206
Subject(s) - classification of discontinuities , phase field models , fracture mechanics , field (mathematics) , fracture (geology) , phase (matter) , complex fracture , displacement field , materials science , displacement (psychology) , mechanics , topology (electrical circuits) , composite material , structural engineering , mathematics , physics , mathematical analysis , engineering , finite element method , psychology , quantum mechanics , combinatorics , pure mathematics , psychotherapist
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities exhibits drawbacks in situations with complex crack topologies. This drawback is overcome by diffusive crack modeling based on the introduction of a fracture phase field characterizing via an auxiliary variable the crack topology. In the following we extend recent advances in phase‐field‐type fracture based on operator split techniques, suggested in Miehe et al. [1], to the modeling of crack propagation in geometrically large deforming solids e.g. rubber‐like materials. An extremely robust algorithmic treatment based on an operator split scheme is introduced consisting of three steps. Updating i) a local history‐field containing the maximum reference energy, ii) the fracture phase field, and iii) the displacement field. We demonstrate the performance of proposed phase field formulation for largely deforming solids by means of a representative numerical example. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)