Failure in rate-independent granular materials as a bifurcation toward a dynamic regime

This paper investigates the issue of failure in rate-independent granular material specimens under a novel line of reasoning. The mechanism of failure is related to an increase in kinetic energy. Based on energy conservation, expressed in an incremental form, kinetic energy is shown to be related to the so-called second-order work and a boundary integral involving the external loading directed to the system. Thus, the existence of an outburst in kinetic energy is related to a competition between the second-order work and this boundary integral. Elementary examples are discussed, providing a clear interpretation of the standard laboratory tests (drained, undrained and proportional strain triaxial paths). These theoretical findings are then confirmed based on numerical simulations using a discrete element method. Finally, this approach is assessed in boundary value problems.