Rate-Dependence of the Flow Stress in Amorphous Media: Effects of Disorder and Sample Preparation

We present results on the rate dependence of the flow stress in a realistic mesoscopic model of amorphous plasticity. In our model, the material is divided into adjacent, non-overlapping tiles and each tile is associated a continuous strain energy function, whereas transition between subsequent local minima corresponds to plastic deformation. Distances between subsequent minima are distributed in order to account for structural disorder. In contrast to previous studies, we find that a Herschel-Bulkley kind of rate dependence can only be recovered if the strain energy function is smooth. By tuning the sharpness of the potential at the barriers, we show that the rate dependence disappears as the potential becomes sharper. We show that the rate dependence is a consequence of the competition between the time scale of the barrier crossings and the time scale of the driving and these two have to be commensurate for rate dependence to take place.
Since amorphous plasticity is particularly sensitive to initial conditions, special care is taken to the sample preparation and the effect of quench rate is investigated. Results are compared both to molecular dynamics and to lattice model simulations.