Mechanical response of particulated granular materials

Numerous prior studies have shown that the ensemble-averaged shear modulus of jammed packings of spherical particles increases with pressure p, ~p^β, where β=0.5 in the large-system limit. The growth of with increasing pressure is caused by pressure-induced particle rearrangements that lead to an increasing number of interparticle contacts. However, there are numerous applications for which it is desirable to design materials that can maintain their flexibility with small values of G, but possess large values of the bulk modulus B at high pressures. To design bulk materials with small values of G/B, we construct “particulated” granular metamaterials, which possess small numbers of grains confined within undercoordinated physical boundaries (or voxels) that are then connected to form a bulk structure. In this work, we employ discrete element method simulations to identify and measure the elastic moduli of all configurations for small numbers of monodisperse, frictionless spheres confined within single voxels with arbitrary shapes. We then relate the elastic moduli of the particle-filled single voxels to those for bulk systems composed of regular arrangements of the particle-filled single voxels. We show that since the particles are prevented from rearranging, we can design bulk particulated tessellations with small values of G/B < 10^-3 even at large external pressures.