Why Effective Medium Theory Fails in Granular Materials

TL;DR

This paper investigates why effective medium theory (EMT) fails to accurately predict the shear modulus in granular materials under pressure, revealing the breakdown of the affine assumption for shear but not bulk modulus.

Contribution

The study demonstrates that EMT can match pressure dependence of moduli if contact number increase is included, but the affine assumption fails for shear modulus, explaining discrepancies.

Findings

EMT describes bulk modulus pressure dependence when contact number increase is considered.

Affine assumption holds for bulk modulus but breaks down for shear modulus.

Experimental and numerical shear moduli are smaller than EMT predictions due to assumption failure.

Abstract

Experimentally it is known that the bulk modulus, K, and shear modulus, \mu, of a granular assembly of elastic spheres increase with pressure, p, faster than the p^1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p. Most important, the affine assumption (which underlies EMT), is found to be valid for K(p) but breakdown seriously for \mu(p). This explains why the experimental and numerical values of \mu(p) are much smaller than the EMT predictions.