Anisotropic shear response of 3D tesselated granular metamaterials

Prior studies have shown that the ensemble-averaged shear modulus of jammed sphere packings (with purely repulsive linear spring interactions) increases with pressure p, , where , in the large-system limit due to pressure-induced rearrangements. However, there are numerous applications for which it is desirable to design materials that can maintain their flexibility with small values of G even at high pressures. To design bulk materials with shear moduli G that decrease with increasing pressure, we construct tessellated 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 measure the shear moduli along different shear planes as a function of the shear angle for all configurations for small numbers of monodisperse, frictionless spheres confined within single voxels, as well as tessellated structures. We determine the circumstances under which the shear modulus for single voxels decreases versus increases with pressure and then design bulk tessellations with shear moduli that are able to lock-in the mechanical response of single voxels.