Preserving elastic anisotropy with tessellations of granular packings

TL;DR

This paper introduces methods to design tessellated granular materials that maintain high elastic anisotropy, surpassing crystalline solids, by limiting grain rearrangements and tuning voxel configurations.

Contribution

The study develops a novel approach to preserve and tune elastic anisotropy in granular materials through tessellations, enabling anisotropic properties far exceeding those of atomic crystals.

Findings

Granular materials can achieve elastic anisotropy up to 100 times that of crystalline compounds.

Maximal anisotropy occurs at specific pressure and grain number conditions, pN^2~1.

Heterogeneous tessellations allow further tuning of elastic anisotropy and deformation response.

Abstract

Multiscale periodic metamaterials have been designed for numerous applications, such as impact absorption, acoustic cloaking, photonic band gaps, and mechanical logic gates. This prior work has focused on optimizing mesoscale structure for desired bulk isotropic properties. In contrast, we seek to develop materials with highly anisotropic elastic properties. To quantify elastic anisotropy, we introduce two rotationally invariant, normalized quantities that characterize the anisotropic response to shear and compression, respectively, $A_G$ and $A_C$. We find that typical crystalline solids possess average elastic anisotropy $\overline{A}_G \approx 0.15$ and $\overline{A}_C \approx 0.09$. Compared to atomic crystals, jammed granular materials can attain elastic anisotropies that are several orders of magnitude larger. Since grain rearrangements reduce anisotropy in granular materials, to preserve strong elastic anisotropy, we design tessellated granular materials that consist of multiple connected grain-filled voxels, which limit rearrangements and enable highly anisotropic elastic properties. Bulk granular packings with $N$ grains prepared at pressure $p$ have maximal anisotropy for $pN^2\sim1$ and become isotropic in the large-$pN^2$ limit. We show that homogeneously tessellated granular systems can inherit the elastic response of the constituent voxel configurations with elastic anisotropy up to $100$ times that of crystalline compounds over a range of $pN^2$. We show further methods to tune the elastic anisotropy of tessellations by designing heterogeneously patterned voxel configurations and tessellations that allow large boundary deformations.