Elasticity of anti-tetrachiral anisotropic lattices

This work describes the theoretical, numerical and experimental in-plane and out-of-plane elastic behavior of a class of anti-tetrachiral lattice structures with in-plane negative Poisson's ratios and anisotropic behavior. Closed form analytical solutions related to the uniaxial stiffness, in-plane Poisson's ratio and bounds for the transverse shear modulus are derived, and compared against homogenization-based finite element methods and experimental tests performed on rapid prototyping-made samples. The benchmarked models are then used to investigate the behaviors of the anisotropic negative Poisson's ratio structures against the geometry parameters defining the unit cell. The results show the existence of large variations in linear elastic constants and degree of anisotropy, which can be achieved by changing the lattice geometry parameters. The analysis presented in this work provides meaningful guidance to assist design anti-tetrachiral anisotropic lattices, which could serve as sandwich panel cores in aerospace applications.