Isotropic Metamaterial Stiffness Beyond Hashin-Shtrikman Upper Bound

TL;DR

This paper demonstrates that the Hashin-Shtrikman upper bound for isotropic stiffness can be surpassed using anisotropic materials and structures, challenging long-standing theoretical limits through computational and simulation methods.

Contribution

It introduces a novel approach showing that anisotropic structures can exceed the Hashin-Shtrikman upper bound for isotropic stiffness, supported by first-principles calculations and finite element simulations.

Findings

Hashin-Shtrikman bound can be exceeded with anisotropic structures

Anisotropic material and structural anisotropies reinforce each other

Plate SC design yields properties similar to single crystal nickel

Abstract

Since its introduction more than 60 years ago, the Hashin-Shtrikman upper bound has stood as the theoretical limit for the stiffness of isotropic composites and porous solids, acting as an important reference against which the moduli of heterogeneous structural materials are assessed. Here, we show through first-principles calculations, supported by finite element simulations, that the Hashin-Shtrikman upper bound can be exceeded by the isotropic elastic response of an anisotropic structure constructed from an anisotropic material. The material and structural anisotropies mutually reinforce each other to realize the overall isotropic response, without incurring the mass penalty faced by the hybridization of geometries with complementary anisotropies. 3 designs were investigated (plate BCC, plate FCC and plate SC) but only plate SC yielded a solution for the anisotropic properties of the material, which are remarkably similar to that of single crystal nickel and single crystal ferrite.