Internal states of model isotropic granular packings. III. Elastic properties

TL;DR

This paper investigates the elastic properties of simulated isotropic granular packings, revealing how coordination number and contact mechanics influence stiffness and elastic moduli, with implications for understanding granular material behavior.

Contribution

It provides a detailed numerical analysis of elastic moduli in granular packings, highlighting the role of coordination number and contact mechanics, and compares results with experimental data.

Findings

Elastic moduli are sensitive to coordination number, not just density.

Voigt and Reuss bounds accurately bracket bulk modulus but not shear modulus.

Shear modulus varies with force indeterminacy and load direction in fragile networks.

Abstract

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.