INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2006; 67:1–16 Published online 18 January 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1598 Spatial convergence of crack nucleation using a cohesive finite-element model on a pinwheel-based mesh Katerina D. Papoulia 1, ∗, † , Stephen A. Vavasis 2, ‡ and Pritam Ganguly 3, § 1 School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, U.S.A. 2 Department of Computer Science, Cornell University, Ithaca, NY 14853, U.S.A. 3 Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, U.S.A. SUMMARY We consider the use of initially rigid cohesive interface models in a two-dimensional dynamic finite- element solution of a fracture process. Our focus is on convergence of finite-element solutions to a solution of the undiscretized medium as the mesh spacing x (and therefore time-step t ) tends to zero. We propose the use of pinwheel meshes, which possess the ‘isoperimetric property’ that for any curve C in the computational domain, there is an approximation to C using mesh edges that tends to C including a correct representation of its length, as the grid size tends to zero. We suggest that the isoperimetric property is a necessary condition for any possible spatial convergence proof in the general case that the crack path is not known in advance. Conversely, we establish that if the pinwheel mesh is used, the discrete interface first activated in the finite-element model will converge to the initial crack in the undiscretized medium. Finally, we carry out a mesh refinement experiment to check convergence of both nucleation and propagation. Our results indicate that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to other types of meshes. Copyright  2006 John Wiley & Sons, Ltd. KEY WORDS: cohesive zone modelling; finite element; convergence; crack nucleation; mesh dependence 1. RIGID COHESIVE MODELS Cohesive zone modelling, which was originally proposed by Dugdale [1], Barenblatt [2] and Rice [3], represents cracks as displacement discontinuities in a solid body. The separation of ∗ Correspondence to: Katerina D. Papoulia, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, U.S.A. † E-mail: kp58@cornell.edu ‡ E-mail: vavasis@cs.cornell.edu § E-mail: pg45@cornell.edu Contract/grant sponsor: NSF CAREER award; contract/grant number: CMS-0239068 Contract/grant sponsor: NSF; contract/grant number: CMS-0220327 Contract/grant sponsor: NSF; contract/grant number: CCF-0085969 Received 11 June 2005 Revised 4 October 2005 Copyright  2006 John Wiley & Sons, Ltd. Accepted 21 October 2005