A comparison between rotating squares and anti-tetrachiral systems: Influence of ligaments on the multi-axial mechanical response

Rotating unit systems are one of the most important and well-known classes of auxetic mechanical metamaterials. As their name implies, when loaded, these systems deform primarily via rotation of blocks of material, which may be connected together either directly through joints (or 'joint-like' connections made by overlapping vertices of the rotating units) as in the case of rotating rigid polygonal-unit systems or by ligaments/ribs as in the case of chiral honeycombs. In this work, we used Finite Element Analysis to investigate the effect which the presence/absence of ligaments has on the on-axis and off-axis mechanical properties of these systems by analysing two of the most well-known structures which characterise these two cases: the rotating square system and the anti-tetrachiral honeycomb. It was found that while the presence of ligaments has a negligible effect on the on-axis Poisson's ratio of these systems, it has a profound influence on nearly all other mechanical properties as well as on the off-axis loading behaviour. Systems with ligaments were found to exhibit a high level of anisotropy and also a severely reduced level of stiffness in comparison to their non-ligamented counterparts. On the other hand, the rotating square system suffers from high localized stress-intensities and has a very low strain-tolerance threshold. In addition, an optimized 'hybrid' geometry which is specifically designed to capture the best features of both the anti-tetrachiral and rotating square system, was also analysed. This work shows the main differences between ligament-based and non-ligament-based auxetic structures and also highlights the importance of considering the off-axis mechanical response in addition to the on-axis properties when investigating such systems.