Particulated Granular Metamaterials*

Granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus <G> increases with pressure as P^0.5 in the large-system limit when particles are allowed to rearrange during isotropic compression.  In this work, we seek granular materials with shear moduli that decrease with increasing pressure even in the large-system limit. To do this, we design “particulated” granular metamaterials composed of multiple cubic “voxels” each containing jammed packings of a small number of spheres (N < 8).  As shown in previous studies, G typically decreases linearly with P for a single voxel containing a small number of spheres with a slope that depends on the angle of the shear. We show that the behavior of G versus P for granular metamaterials made up of a large number of voxels (each with N < 8) is controlled by the ratio of the particle-particle and particle-wall interactions. In particular, we are able to achieve large particulated granular metamaterials for which G decreases with increasing P.