Pressure-dependent elastic moduli of granular assemblies

Conventional homogenization theories developed for a matrix-inclusion syste m cannot be used for deriving the pressure-dependent elastic behaviour of a granular material. This is caused by the lack of a proper description of t he high stress concentrations at the particle contacts. This paper discusse s a more suitable homogenization theory, which follows from micro-structura l considerations at the particle level. Accordingly, for an assembly of iso tropically distributed, equal-sized spherical particles, expressions for th e pressure-dependent shear modulus and the Poisson's ratio are derived. Thi s is done for the case of hydrostatic compression. The derivation of these equations is based on the so-called best-Jit hypothesis of the actual displ acement field in the granular assembly. The usefulness of the equation deri ved for the shear modulus is illustrated via a comparison with experiment r esults. Copyright (C) 2000 John Wiley & Sons, Ltd.