Elastically isotropic auxetic and zero-Poisson’s ratio TPMS-based metamaterials

Abstract

Triply periodic minimal surfaces (TPMS) can create high performance, multifunctional, metamaterials that are lightweight and have highly tailorable properties. However, such TPMS structures are typically highly anisotropic in terms of stiffness, which is often undesirable for applications where loading direction is variable or unknown a priori. In this paper, a new TPMS-based design strategy is presented based on shape function mapping to achieve elastic isotropy. The optimised TPMS-based isotropic designs reveal a wide design space in terms of Young's modulus and Poisson's ratio. At 20% relative density, the Poisson's ratio is shown to be tuneable between the extremes of v = 0.29, conventional behaviour, and (Formula presented.) = −0.38, auxetic behaviour. A unique design point is identified with both a zero Poisson's ratio and elastic isotropy. Design optimisation is performed using finite element analysis, which is subsequently experimentally validated with additively manufactured demonstrators and uniaxial compression testing.