Obtaining initially rigid cohesive finite element models that are temporally convergent q Chin-Hang Sam a , Katerina D. Papoulia b, * , Stephen A. Vavasis c a School of Civil and Environmental Engineering, 220 Hollister Hall, Cornell University, Ithaca, NY 14853, USA b School of Civil and Environmental Engineering, 363 Hollister Hall, Cornell University, Ithaca, NY 14853, USA c Department of Computer Science, 4130 Upson Hall, Cornell University, Ithaca, NY 14853, USA Received 11 March 2004; received in revised form 14 December 2004; accepted 30 December 2004 Available online 23 May 2005 Abstract Based on a time continuity condition proposed in our earlier work, we develop a fairly general framework, free of regularization issues, for producing initially rigid cohesive finite element models that are temporally convergent in an explicitdynamicssetting.Thesemodelsareadaptiveinthesensethataninterfaceisinactiveuntilthetractionacrossit reaches a critical level. We require that the traction across the interface be a continuous function of displacement, and therefore of time, i.e., the traction before and after activation should be the same. We demonstrate with examples that failure to satisfy this condition leads to non-optimal convergence or failure of convergence as the time step tends to zero.Wealsoinvestigatethepredictedcrackpathproducedbyatimecontinuousmodelversusadiscontinuousmodel inasimulationofalaboratoryexperiment.Thetime-continuousmodelproducescrackpathsthatarestablewithvari- ations of the time step and are close to laboratory measurements. Ó 2005 Published by Elsevier Ltd. 1. Introduction Fracture processes can generally be represented either as weak or strong discontinuities. Cohesive zone modeling, which was originally proposed by Dugdale [6], Barenblatt [2] and Rice [26], is in the latter category. In such a model, the separation of bulk material is resisted by cohesive forces, governed by the corresponding cohesive constitutive model. 0013-7944/$ - see front matter Ó 2005 Published by Elsevier Ltd. doi:10.1016/j.engfracmech.2004.12.008 q Supported in part by NSF award CMS-0239068. * Corresponding author. Tel.: +1 607 254 5441; fax: +1 607 255 9004. E-mail addresses: cs229@cornell.edu (C.-H. Sam), kp58@cornell.edu (K.D. Papoulia), vavasis@cs.cornell.edu (S.A. Vavasis). Engineering Fracture Mechanics 72 (2005) 2247–2267 www.elsevier.com/locate/engfracmech