NONLINEAR ELASTICITY AND THERMODYNAMICS OF GRANULAR MATERIALS

The elastic properties of granular materials can be enormously nonlinear as compared with the properties of non-porous materials. Experiments on isotropic compression of a granular assembly of spheres show that the shear μ, and bulk k, moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz–Mindlin elasticity theory. Moreover, the ratio between the experimental bulk and shear moduli is found to be constant but with a value larger than the theoretical prediction. Numerical simulations resolve the question as to whether the problem lies with the treatment of the grain-grain contact or with the elastic framework. We find that the problem lies principally with the latter; the affine assumption (which underlies the elastic formulation) is found to be valid for k but to breakdown seriously for μ. This explains why the experimental and numerical values of μ(p) are much smaller than the elastic predictions. In this paper we review recent progress on the understanding of this problem based on microscopic simulations, elasticity theory and more innovative ideas such as jamming, fragility and thermodynamics of granular materials.