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Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
Author(s) -
Belytschko Ted,
Chen Hao,
Xu Jingxiao,
Zi Goangseup
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.941
Subject(s) - classification of discontinuities , discontinuity (linguistics) , finite element method , extended finite element method , fracture mechanics , partial differential equation , dynamic problem , measure (data warehouse) , structural engineering , mathematical analysis , mathematics , mechanics , computer science , engineering , physics , algorithm , database
A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial differential equation loses hyperbolicity. The approach is limited to rate‐independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extended finite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks. Copyright © 2003 John Wiley & Sons, Ltd.