A Partially Auxetic Metamaterial Inspired by the Maltese Cross

Abstract

A partially-auxetic metamaterial is introduced, inspired by the Maltese cross. Each unit of this metamaterial consists of a pair of counter-rotating equal-armed crosses, which is interconnected to neighboring units via hinge rods and connecting rods. Based on linkage theory, the on-axes Poisson's ratio was established considering a two-fold symmetrical mechanism, while the (anti)tetrachiral mechanisms were identified for on-axes uniaxial compression. A shearing mechanism is suggested for pure shearing and diagonal loading of the metamaterial with square array. Results suggest that the approximated infinitesimal models are valid for the Poisson's ratio of the two-fold symmetrical and the (anti)tetrachiral mechanisms under on-axis tension and compression, respectively; however, the finite model is recommended for quantifying the Poisson's ratio under pure shear and off-axis loading. This metamaterial manifests microstructural trinity, in which three different loading modes result in three different groups of deformation mechanisms. Finally, suggestions are put forth for some unsolved predictive problems.