Force heterogeneities in particle assemblies: from order to disorder.

The effect of increasing structural disorder on the distribution of contact forces P(f) inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a face-centered-cubic array, where all contact forces are identical, an increasing number of defects is introduced into the assembly, after which the system is then allowed to relax into a different mechanically stable state. Three distinct protocols for imposing disorder are compared. A quantitative measure of the disorder is obtained from distributions of the coordination number and three-particle contact angle. The distribution of normal contact forces show dramatic qualitative changes with increasing disorder. In the regime where the disorder is relatively weak, the pressure and the lowest normal mode frequency scale approximately linearly in the coordination number, with distance from the crystalline state. These results for P(f) are discussed in the context of jamming phenomena in glassy and granular materials.