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Phase Field Modeling of Fracture in Plates and Shells
Author(s) -
Ulmer Heike,
Hofacker Martina,
Miehe Christian
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210076
Subject(s) - classification of discontinuities , fracture (geology) , complex fracture , phase field models , representation (politics) , field (mathematics) , fracture mechanics , phase (matter) , structural engineering , computer science , mechanics , materials science , engineering , physics , mathematics , mathematical analysis , composite material , quantum mechanics , politics , political science , pure mathematics , law
The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by a diffusive crack modeling , which is based on the introduction of a crack phase field. In this paper, we extend ideas recently outlined in [1, 2] towards the phase field modeling of fracture in dimension‐reduced continua with application to Kirchhoff plates and shells. The introduction of history fields, containing the maximum reference energy obtained in history, provides a very transparent representation of the coupled balance equations and allows the construction of an extremely robust operator split technique. The performance of the proposed models is demonstrated by means of representative numerical examples. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)