Tunable anisotropy in 3D tessellated granular materials

In jammed packings of granular materials, particle rearrangements frequently occur in response to applied stress or strain, which lead to homogenization of the elastic moduli. To design jammed packings with robust, anisotropic elastic moduli, we constructed tessellated granular materials, consisting of multiple connected particle-filled voxels. We employ discrete element method simulations to calculate the linear elastic response of particle-filled single voxels and bulk tessellations. We focus on two coordinate-invariant measures of anisotropy,  and , which describe shear and compressive anisotropy, respectively. For single particle-filled voxels, both measures of anisotropy scale with , where p is the pressure and N is the number of particles, and can be tuned over more than two orders of magnitude. We show that bulk tessellations can possess an anisotropy up to 100 times that of crystalline materials. We also show that the non-affine response of the tessellations increases with heterogenous patterns of voxels, which provides an additional mechanism to tune the mechanical response.