From shear bands to earthquakes in a model granular material with contact aging

We perform molecular dynamics simulations of homogeneous athermal systems of poly-disperse soft discs under shear. For purely repulsive interactions between particles, and under a confining external pressure, a monotonous flow curve (strain rate vs. stress) starting at a critical yield stress is obtained, with deformation distributing uniformly in the system, on average. Then we add a short range attractive contribution to the interaction potential that increases its intensity as particles remain in contact for a progressively longer time, mimicking an aging effect in the system. In this case the flow curve acquires a reentrant behavior, namely, a region where shear stress decreases with increasing strain. Within this region the deformation is seen to localize in a shear band with a well defined width that decreases as the global strain rate does. At very low strain rates the shear band becomes very thin and deformation acquires a prominent stick-slip behavior. This regime can be described as the system possessing a fault in which deformation occurs with an earthquake-resembling phenomenology. In this way the system we are analyzing connects a regime of uniform deformation at large strain rates, a localized deformation regime in the form of shear bands at intermediate stain rates, and seismic phenomena at very low strain rate. The unifying ingredient of this phenomenology is the existence of a reentrant flow curve, originating in the aging mechanisms present in the model. Accumulated strain (left) and particle snapshot (right) of a system under an applied simple shear along the x direction. Particles are coloured according to their value of the "aging function". Note the spatial localization of the deformation.