ABSTRACT
Accompanying the impressive experimental investigations are a slew of analytical and numerical works (Coppersmith et al. 1996; Eloy and Clement 1997; Goldhirsch and Goldenberg 2002; Bouchaud et al. 2001). To ease the calculations, most of this work has been carried out using an underlying 2D lattice for the particle configuration. Yet, these results are also proving insightful to understand just how a particle assembly responds to a given force perturbation. In some cases, the principle assumption is the existence of well-defined ‘force chains’– extended particle structures that support the stress throughout the system (Bouchaud et al. 2001). However, as yet, the
definition of a force chain remains ambiguous and largely depends on artificial cut-offs introduced to identify the entities one is looking for. Another recent approach has led to the development of a microelasticity formulation (Goldhirsch and Goldenberg 2002). Upon coarse graining the contact forces over some spatial region of the order of the particle size, the propagating stresses can be calculated through the system. Subsequently, it has recently been proposed (Bouchaud et al. 2001; Goldhirsch and Goldenberg 2002) that on shorter length scales, of the order of tens of particle diameters, the system knows of its granularity such that the particulate nature of the packing is reflected in measured quantities such as stress response (hyperbolic). On larger length scales, when one can average over the discreteness of the constituent particles, the systems appears to respond more like an (elliptic) elastic medium. This is also related to the elastic-granular crossover in Lennard-Jones glasses (Tanguy et al. 2002; Leonforte et al. 2004).
