Stress in frictionless granular material: Adaptive network simulations

We present a minimalistic approach to simulations of force transmission thr ough granular systems. We start from a configuration containing cohesive (t ensile) contact forces and use an adaptive procedure to find the stable con figuration with no tensile contact forces. The procedure works by sequentia lly removing and adding individual contacts between adjacent beads, while t he bead positions are not modified. In a series of two-dimensional realizat ions, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent the ories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about 0.6 of the normal loading. The spati al distribution of contact forces shows strong concentration along "force c hains." The probability of contact forces of magnitude f shows an exponenti al falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.