Contact forces and angles in disordered materials
Disordered materials, such as window glass, powders, gels, concentrated emulsions, differ tremendously in their microscopic detail, there is increasing evidence that they belong to a more general phenomenon known as jamming. The response of disordered materials to applied stresses is a particularly interesting but difficult problem with broad applications in many fields. Using confocal microscopy, we performed systematic and detailed measurements of inter-drop contact forces inside three-dimensional piles of frictionless liquid droplets. We found chain-like structures of contact forces called force chains and measured long-range correlations of the directions and magnitudes of large forces. These correlations arise from the tendency of two largest forces on a droplet to oppose one another. Furthermore, we found that piles whose height was comparable to the length of force chains exhibited greater strain hardening than did tall piles. Thus, we established a connection between the microscopic force network and the elastic response of meso- or macroscopic disordered materials. A statistical model that incorporates the force-balance constraint and that assumes random orientation of contacts, confirmed the tendency of two large forces on a grain to oppose each other, which leads to the formation of force chains in disordered materials. This model also provided direct insight into other issues, such as the role of friction, the effects of stress anisotropy, the difference between two-dimensional materials and three-dimensional materials. The numerical results obtained from the model are qualitatively consistent with earlier simulations and experiments.
0794: Materials science