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

International Journal for Numerical Methods in Engineering - Tập 58 Số 12 - Trang 1873-1905 - 2003
Ted Belytschko1, Hao Chen1,2, Jingxiao Xu1, Goangseup Zi1
1Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.
2Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94550, U.S.A.

Tóm tắt

Abstract

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.

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International Journal for Numerical Methods in Engineering

Tập 58 Số 12

1873-1905

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