Letters to Nature

Nature 435, 188-191 (12 May 2005) | doi:10.1038/nature03497; Received 8 August 2004; Accepted 21 February 2005

Friction enhances elasticity in granular solids

C. Goldenberg1,3 & I. Goldhirsch2

  1. School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences,
  2. Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
  3. Present address: Physique et Mécanique des Milieux Hétérogènes, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 5, France

Correspondence to: I. Goldhirsch2 Correspondence and requests for materials should be addressed to I.G. (Email: isaac@eng.tau.ac.il).

For years, engineers have used elastic and plastic models to describe the properties of granular solids, such as sand piles and grains in silos1, 2, 3. However, there are theoretical4, 5, 6 and experimental7, 8, 9, 10, 11, 12, 13, 14 results that challenge this approach. Specifically, it has been claimed4, 5, 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.


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