Particulated Granular Metamaterials

Granular materials have fascinating mechanical properties near the onset of jamming. For example, the elastic moduli depend strongly on the direction of the applied strain and they change abruptly when the grains rearrange, which occurs frequently in large systems near jamming onset. These features often make it difficult to control the mechanical properties of jammed granular materials. Here, we describe “particulated” granular materials---small numbers of grains confined within under-constrained trusses that are connected together into large frameworks---that allow us to design granular materials with specific mechanical properties. In this work, we focus on generating materials that can withstand large isotropic compression, but are extremely compliant under shear, i.e. they possess small values for the ratio of the shear modulus to the bulk modulus, G/B.  Our initial studies are in two dimensions using quadrilateral trusses with free angles at each joint. Using discrete element method simulations, we identify all possible grain configurations for N=6 and 7 monodisperse, frictionless and frictional particles over the full range of truss shapes. We then join the trusses together into a large ring and determine G/B for the ring structure in terms of the elastic moduli for the individual particle-filled trusses.  We show that we are able to design ring structures with extremely small G/B using specific grain arrangements in each truss. We validate the simulation results by comparing them to experiments on ring structures formed from 3D-printed truss elements and particles.