Transitional negative stiffness and numerical modelling of failure of particulate material

We observed negative stiffness effect during the bond breakage in a simple 4 discs PFC 2D simulation. This negative stiffness effect only exists during the transitional time during which the model regains equilibrium. We subsequently call this negative stiffness effect - transitional negative stiffness effect. It can be shown the instability of geomaterials is reached when the (incremental) Poisson’s ratio reached value of 1(2D case). Hence we embarked on verifying the hypothesis that the peak load coincides with the critical incremental Poisson’s ratio. We demonstrate that the peak on the stress-strain curve corresponds to the incremental Poisson’s ratio reaching 1. This gives a confirmation that the transitional negative stiffness can be responsible for the global instability of particulate materials.