Friction enhances elasticity in granular solids

For years, engineers have used elastic and plastic models to describe the properties of granular solids, such as sand piles and grains in silos(1-3). However, there are theoretical(4-6) and experimental(7-14) results that challenge this approach. Specifically, it has been claimed(4-6) that stress in granular solids propagates in a manner described by wave-like ( hyperbolic) equations, rather than the elliptic equations of static elasticity. Here we report numerical simulations of the response of a two-dimensional granular slab to an external load, revealing that both approaches are valid - albeit on different length scales. For small systems that can be considered mesoscopic on the scale of the grains, a hyperbolic-like, strongly anisotropic response is expected. However, in large systems ( those typically considered by engineers), the response is closer to that predicted by traditional isotropic elasticity models. Static friction, often ignored in simple models, plays a key role: it increases the elastic range and renders the response more isotropic, even beyond this range.