A SIMPLE-MODEL FOR STRESS FLUCTUATIONS IN PLASTICITY WITH APPLICATIONTO GRANULAR-MATERIALS

When granular material is modeled as a continuum, plastic constitutive behavior is often assumed. The use of plasticity amounts to replacing a complicated micromechanical system by its average behavior. Recent experiments have shown that, at least for small-scale systems, stress fluctuations may be of the same order, or even much larger, than avera ge stresses. In this paper a first generation of discrete models for s tress fluctuations is discussed. These models consist of many spring-s lider elements in parallel. The sliders all obey the same law for fric tional resistance, and this resistance varies with the position, but n ot the velocity, of the slider. The initial positions (and hence the i nitial frictional resistances) of the sliders are taken to be random. The usual elastoplastic response emerges as the ensemble average over all possible initial positions of the sliders. The stress response res ulting from any particular choice of initial conditions exhibits fluct uations similar to those in the experiments. It is shown that the magn itude of fluctuations is governed by two parameters, namely, the syste m size and the roughness, the latter defined as the ratio of particle contact length to particle size. In numerical simulations, it is obser ved that the roughness parameter controls the shape of the stress resp onse as a function of applied strain.