INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2004; 61:2316–2343 Published online 18 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1151 Cracking particles: a simplified meshfree method for arbitrary evolving cracks T. Rabczuk ‡ and T. Belytschko ∗, †, § Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208-311, U.S.A. SUMMARY A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack’s topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright  2004 John Wiley & Sons, Ltd. KEY WORDS: meshfree methods; cohesive crack model; dynamic fracture 1. INTRODUCTION The simulation of a large set of evolving cracks by finite element or meshfree methods still poses substantial difficulties. One of the most popular class of methods over the past decade has been what can be called interelement separation models, see References [1–4]. In these methods, cracks are only allowed to develop along existing interelement edges. This endows the method with comparative simplicity, but can result in an overestimate of the fracture energy when the actual crack paths are not coincident with element edges. Furthermore, it has been noted that the solutions sometimes depend significantly on mesh refinement, see Reference [5]. This sensitivity has been mollified by adding randomness to the ∗ Correspondence to: T. Belytschko, Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-311, U.S.A. † E-mail: tedbelytschko@northwestern.edu ‡ Post-Doctoral Research Fellow, Department of Mechanical Engineering. § Walter P. Murphy, Professor of Computational Mechanics. Contract/grant sponsor: Office of the Naval Research Contract/grant sponsor: Army Research Office Received 1 April 2004 Revised 4 May 2004 Copyright  2004 John Wiley & Sons, Ltd. Accepted 9 June 2004