On the in-plane effective elastic constants of a novel anti-tetrachiral meta-structure with L-type ligaments

A novel anti-tetrachiral with L-type ligaments (LATC) meta-structure was proposed in this work by a combination of the classical anti-tetrachiral (ATC) and anti-tetra-missing rib (ATMR) meta-structures. Finite element (FE) analyses and experimental tests were then carried out to investigate the mechanical performance and the underlying deformation mechanisms of the proposed meta-structure by adopting Polyamide 6/carbon-fiber (PA6/ CF) as the base material. The results indicated that the proposed meta-structure exhibited a tunable constant negative Poisson's ratio (NPR) over a relatively large strain range. To enhance the understanding of the underlying microstructural mechanisms, theoretical formulas for the in-plane effective elastic constants (i.e., effective Poisson's ratio, elastic modulus and shear modulus) of the meta-structure were further derived by employing the energy method. The accuracy of the theoretical formulas was subsequently validated through FE analysis and experimental tests.