Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment.

*(English)*Zbl 1032.74662Summary: 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.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74A45 | Theories of fracture and damage |

##### Keywords:

finite element method; fracture mechanics; dynamic fracture; loss of hyperbolicity; cohesive crack model; extended finite element method
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\textit{T. Belytschko} et al., Int. J. Numer. Methods Eng. 58, No. 12, 1873--1905 (2003; Zbl 1032.74662)

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