2, ESPCI, Paris Tech, Paris, , France
We present results on the rate dependent flow stress in a coarse grained model of an amorphous material. In particular we study two variants of the model. Both are based on a non-convex local strain-energy function which contains quenched disorder. One variant consists of a piece-wise quadratic strain-energy function, the other variant consists of a smooth strain-energy function. Other groups have recently introduced rate-dependence into models with similar strain-energy functions via an explicit, but ad-hoc, time dependence in the local yielding rate. Here, instead, we simply suppose that the background material surrounding a yielding site acts as a visco-elastic material. We make no other assumptions about the local yielding rate in the shear zone, and it simply follows as a consequence of our model of the viscous background. With this prescription for the dynamics, we show that the smooth-potential version of the model — but not the cuspy-potential version — gives precise agreement with finer-scale particle based simulations for the rate dependence of: i) the flow stress, ii) the plastic correlation length, and iii) the diffusion coefficient. We conclude that correct modeling of both i) the smoothness of the strain-energy function and ii) the background viscosity and time-dependent yielding is necessary to get agreement with finer-scale particle-based models.