First order rigidity transition and multiple stability regimes for random networks with internal stresses

By applying effective medium-style calculations to random spring networks, we demonstrate that internal stresses fundamentally alter the nature of the rigidity transition in disordered materials, changing it from continuous to first-order and increasing the mean coordination number z at which rigidity first occurs. Furthermore, we predict the existence of a novel stability regime at low z when the distribution of stresses is asymmetric. Means of verifying these predictions are suggested.