On the effective elastic constants of anti-tetra chiral tubular structure

Abstract

Anti-tetra chiral honeycomb is a typical auxetic metamaterial that exhibits excellent auxetic behavior. Based on anti-tetra chiral honeycomb, previous studies proposed a 3D tubular structure and performed detailed investigations on its tensile and compressive force–displacement responses. The basic elastic mechanical properties, i.e., the effective elastic constants (elastic modulus and Poisson’s ratio) of such a structure, were not investigated in those works. To understand the underlying microstructural mechanisms, a theoretical model under the infinitesimal deformation assumption is developed in the present work by adopting a simple energy-based approach. The analytical solutions, as validated by systematic finite element (FE) analyses, elucidate different roles of the microstructural geometry on the effective elastic constants of the anti-tetra chiral tubular structure. The results show that the anti-tetra chiral tubular structure exhibits tunable effective elastic Poisson’s ratios (from −4 to −0.3) and elastic modulus (over two orders of magnitude) in broad ranges. To provide valuable guidelines for the design of metamaterials, sensitivity analysis of the geometrical parameters on the effective elastic constants is finally conducted.