Time continuity in cohesive finite element modeling 1 Katerina D. Papoulia 2 Stephen A. Vavasis 3 June 1, 2002 Abstract We introduce the notion of time continuity for the analysis of cohesive zone interface finite element models. We focus on “initially rigid” models in which an interface is inactive until the traction across it reaches a critical level. We argue that methods in this class are time discontinuous, unless special provision is made for the opposite. Time discontinuity leads to pitfalls in numerical im- plementations: oscillatory behavior, non-convergence in time and dependence on nonphysical regularization parameters. These problems arise at least partly from the attempt to extend uniaxial traction-displacement relationships to multiax- ial loading. We also argue that any formulation of a time-continuous functional traction-displacement cohesive model entails encoding the value of the traction components at incipient softening into the model. We exhibit an example of such a model. Most of our numerical experiments concern explicit dynamics. Keywords: Cohesive interface finite elements, explicit dynamics, regularization 1 Cohesive zone modeling Cohesive zone modeling is one of the most widely used techniques for modeling fracture of brittle and quasibrittle materials. It is predicated on the fact that in quasibrittle fracture, a process zone forms ahead of the crack front, in which material softening takes place. In the spirit of Dugdale [6] and Barenblatt [2] cohesive zone modeling idealizes the process zone with a weak interface of thickness zero. A material point on this interface is initially undamaged, but when the traction across the interface reaches some critical level it starts losing cohesion, and gradually softens until a stress-free surface is created. In one dimension softening is manifested as a gradual drop in traction with increasing relative displacement. 1 Supported in part by NSF awards CMS-9973277 and ACI-0085969. 2 Assistant Professor, School of Civil and Environmental Engineering, 363 Hollister Hall, Cornell University, Ithaca, NY 14853, U.S.A., kp58@cornell.edu, phone 607-254-5441, fax 607-255-9004. 3 Professor, Department of Computer Science, Cornell University, Ithaca, NY 14853, U.S.A., vavasis@cs.cornell.edu. 1