Tessellated granular metamaterials with tunable elastic moduli

Abstract

Most granular packings possess shear moduli (G) that increase with the applied external pressure, and bulk moduli (B) that increase or remain constant with pressure. This paper presents “tessellated” granular metamaterials for which both G and the ratio G/B decrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to G and B are the particle–particle and particle–cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing G as we increase the pressure difference between the inside and outside of the tessellation, leading to G/B≪1 at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure.