NONLINEAR ELASTICITY AND THERMODYNAMICS OF GRANULAR MATERIALS

Hernán A. Makse ()
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Hernán A. Makse: Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA

Advances in Complex Systems (ACS), 2001, vol. 04, issue 04, 491-501

Abstract: 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 bulkk, 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; theaffineassumption (which underlies the elastic formulation) is found to be valid forkbut to breakdown seriously for μ. This explains why the experimental and numerical values ofμ(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.

Keywords: Granular matter; nonlinear elasticity; thermodynamics; effective temperature (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219525901000425

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