The linear and nonlinear elastic properties of granular media are analyzed within the context of effective medium theories. as well as with numerical molecular dynamic simulations, assuming the validity of the Hertz-Mindlin theory at the single contact level. There is a crucial distinction between force laws which are path independent, leading to a hyper-elastic effective medium theory, and those which are path dependent, for which the deformation history must be followed explicitly. The effective medium theories provide a reasonable description of existing experimental data, considered as a function of applied stress, but there are significant discrepancies. Numerical simulations resolve the question as to whether the problem Lies with the treatment of the individual grain-grain contact or with the effective medium approximation (ema). We find that the problem lies principally with the latter: The bulk modulus is well described by the ema but the shear modulus is not, principally because the ema does not correctly allow for the grains to relax from the affine motion assumed by the ema. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 12]
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