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Mathematical Problems in Engineering
Volume 2014, Article ID 646514, 10 pages
Research Article

Stable Cracking Particles Method Based on Stabilized Nodal Integration and Updated Lagrangian Kernel

School of Mechanical Engineering, Jiangnan University, China

Received 27 November 2013; Revised 27 January 2014; Accepted 17 February 2014; Published 7 May 2014

Academic Editor: Goangseup Zi

Copyright © 2014 S. Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A stable cracking particles method (CPM) based on updated Lagrangian kernels is proposed. The idea of CPM is to model the crack topology by a set of cracked particles. Hence no representation of the crack surface is needed making the method useful for problems involving complex fracture patterns as they occur in dynamics and under fast loading conditions. For computational efficiency, nodal integration is exploited in the present paper. In order to avoid instabilities, a scheme is presented to stabilized the integration. Moreover, a set of simple cracking rules are proposed in order to prevent numerical fracture. The method is applied to two benchmark problems and shows good accuracy.