Packing Structure and Mechanical Properties of Granulates

Abstract

The stiffness tensor relating the stress and strain in the generalized Hooke's law can take various forms depending upon the symmetry of the mechanical properties of the granular material. This material symmetry is expected to be closely related to the packing structure of the granular material. In this paper, the microstructural continuum method is employed to study the relationship between the symmetry of mechanical properties and the packing structure for random granular packings. The distribution density functions characterizing the packing structure are represented by spherical harmonics expansion. Closed‐form solutions for the stiffness tensor are derived for anisotropic granular packings of equal spheres with linear interparticle contact interactions. The relation between the “fabric” parameters describing the density functions and the material symmetry are discussed. Bounds imposed by the condition of positive definiteness of strain energy on fabric parameters are also studied. Parametric study is performed to show the effect of packing structure and contact stiffness on the mechanical behavior of a packing.