Theoretical and Experimental Study of Regular Packings of Granules

Abstract

The mechanical behavior of granular material is greatly influenced by packing geometry. A stress‐strain theory for small deformations of granular media made of equal‐sized particles arranged systematically is developed based on micro‐mechanical considerations. Stress, treated as a continuum field variable, is defined for a representative cell of the packing instead of an infinitesimally small point as in continuum materials. The overall macroscopic stress‐strain relationship is derived from the use of principle of energy conservation. The force‐deformation relationship at the contact between two particles is assumed to follow Mindlin's theory. However, this assumption is not a restriction of the proposed stress‐strain theory. The derived stress‐strain relationship is compared to experimental results and the existing solutions.