Obtaining initially rigid cohesive finite element models that are temporally convergent

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 explicit dynamics setting. These models are adaptive in the sense that an interface is inactive until the traction across it 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. We also investigate the predicted crack path produced by a time continuous model versus a discontinuous model in a simulation of a laboratory experiment. The time-continuous model produces crack paths that are stable with variations of the time step and are close to laboratory measurements.