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.

An Auxetic Metamaterial Based on Rotating and Nonrotating Rigid Units Inspired by an Aztec Geometric Pattern

“…A partially auxetic metamaterial is one which manifests both auxetic and nonauxetic behavior, depending on the direction of applied stress. [29,42,[50][51][52][53][54] Although nonauxetic, the mechanical properties of this metamaterial under off-axis loading are recommended for future work to complement the current investigation. It is also proposed that the metamaterial may well be used for attaining anisotropic auxetic behavior with specific or even extreme on-axes properties at small and large deformations.…”

“…A partially auxetic metamaterial is one which manifests both auxetic and nonauxetic behavior, depending on the direction of applied stress. [ 29,42,50–54 ]…”

“…[22][23][24] Of late, a number of reports on new auxetic geometries have been made by inspiration from historical, cultural, and religious sources, such as Islamic geometric patterns [25][26][27] and the Maltese cross. [28,29] As an extension to auxetic systems related to rotating units, [14][15][16][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] this article introduces an auxetic metamaterial based on a combination of rotating and nonrotating rigid units. Specifically, this metamaterial consists of rotating triangles and nonrotating rhombi, by inspiration from an Aztec design.…”

“…For this reason, the metamaterial can be classified as being partially auxetic. A partially auxetic metamaterial is one which manifests both auxetic and nonauxetic behavior, depending on the direction of applied stress [29,42,[50][51][52][53][54]. Although nonauxetic, the mechanical properties of this metamaterial under off-axis loading are recommended for future work to complement the current investigation.…”

Metamaterials with Poisson's ratio discontinuity by means of fragmentation–reconstitution rotating units

“…The problem of indentation is crucial for the impact behaviour of structures. For a comprehensive overview of auxetic materials and metamaterials, the reader is referred to some recent reviews [23,[35][36][37][38][39][40][41][42][43][44][45][46][47] and monographs [48][49][50][51][52], which not only elucidate the various micro-lattice geometries that give rise to auxetic behaviour but also contain exhaustive literature reviews. Among the various microstructural geometries, one of the earliest types of auxetic systems is that of rotating rigid units.…”