ABSTRACT
The time honored practice of the engineering community is to employ elasticity to describe granular bulk properties at low loads, and elasto-plastic theories to model yield and (quasi-static) flow. Perhaps surprisingly, in some experiments [depending on the method of preparation (Vanel et al. 1999)] the pressure on the floor under sand piles was found to possess a local minimum under the apex (Smid & Novosad 1981; Brockbank et al. 1997), while (isotropic) elasticity implies that the pressure is maximal there. Other experiments (Drescher & de Josselin de Jong 1972; Geng et al. 2001; Geng et al. 2003) revealed the existence of directed chains of particle contacts (“force chains”) along which the contact forces were stronger than average. These and additional experiments (Mueggenburg et al. 2002; Moukarzel et al. 2004; Da Silva & Rajchenbach 2000) were interpreted as evidence against elastic theories of granular matter. Models (Wittmer et al. 1996; Bouchaud et al. 2001; Tkachenko & Witten 1999) in which the forces propagate, like waves, along force chains, were proposed, giving predictions that were in good agreement with experiment. The basic equations in these theories are hyperbolic, in contrast with the elliptic nature of static elasticity. It is shown below that the recent results do not contradict the engineering approaches, since they apply to relatively small-sized (“mesoscopic”) granular systems (typically, the subject of studies by physicists), whereas the systems of interest to
engineers are usually large, in which case the “old” approaches may very well be justified.
