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

TLDR

The study develops a methodology that switches from a continuum to a discrete discontinuity when the governing PDE loses hyperbolicity, enabling dynamic crack propagation modeling. The approach employs XFEM to represent arbitrary discontinuities, uses a hyperbolicity indicator to determine crack speed and direction, is limited to rate‑independent materials, and includes a new technique for handling discontinuities that terminate within an element. Applying the method to several dynamic crack growth problems demonstrates its ability to capture phenomena such as crack branching. © 2003 John Wiley & Sons, Ltd.

Abstract

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.