Time continuity in cohesive finite element modeling

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 implementations: 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 multiaxial 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.