MPM simulation of dynamic material failure with a decohesion constitutive model

An initiation criterion is developed for a discrete constitutive equation model of material failure. The decohesion constitutive model is combined with elasticity and implemented in the numerical material-point method. The complete numerical proceedure is used to study spall failure in brittle materials. A one-dimensional analytical solution for a bar subjected to a sinusoidal pulse is derived and used to verify the numerical method. The sinusoidal pulse leads to a finite region of the bar undergoing failure, rather than a single plane, as occurs with a square or triangular wave pulse. This observation may be related to experimental findings of multiple spall planes for impacted bars. The numerical method is not restricted to one-dimensional problems, thus we further study the additional features that arise for an impacted bar assuming that the bar deforms under plane stress conditions. Reflections of stress waves from the lateral surfaces of the bar result in the appearance of curved and secondary spall surfaces.