Element‐local level set method for three‐dimensional dynamic crack growth

TLDR

The paper presents an approximate level set method for three‑dimensional crack propagation. The method defines each cracked element’s discontinuity surface with element‑local level sets generated by least‑squares fitting to satisfy fracture directionality and continuity, refines consistency iteratively, and treats the discrete discontinuity using a phantom node technique—a simplified XFEM—combining ELLS and phantom node approaches to solve dynamic fracture problems. Numerical examples for three‑dimensional dynamic crack propagation demonstrate the method’s effectiveness and robustness. © 2009 John Wiley & Sons, Ltd.

Abstract

Abstract An approximate level set method for three‐dimensional crack propagation is presented. In this method, the discontinuity surface in each cracked element is defined by element‐local level sets (ELLSs). The local level sets are generated by a fitting procedure that meets the fracture directionality and its continuity with the adjacent element crack surfaces in a least‐square sense. A simple iterative procedure is introduced to improve the consistency of the generated element crack surface with those of the adjacent cracked elements. The discrete discontinuity is treated by the phantom node method which is a simplified version of the extended finite element method (XFEM). The ELLS method and the phantom node technology are combined for the solution of dynamic fracture problems. Numerical examples for three‐dimensional dynamic crack propagation are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.