Rotating squares auxetic metamaterials have the peculiar feature of a negative Poisson’s ratio. This work proposes and examines how an innovative variable arcs fillet solution, at the interconnection regions between the rotating units, improves the structural response of a titanium alloy-based rotating squares metamaterial. Through a 2D finite element (FE) model of the auxetic structure, we investigated and optimized two fillet configurations: first, a double circular arcs profile; second, a combined elliptical and circular arc fillet. According to the FE results, the optimal configuration of the combined elliptical and circular arc fillet allows an overall 3% elastic strain of the metamaterial, with a Poisson’s ratio (PR) equal to ca. −1. In order to assess the deformation behavior of the proposed metamaterial, we performed a tensile test on a prototype of the optimal solution, 3D printed in Onyx material. The experimental displacement field of the specimen, measured through digital image correlation, exhibited excellent agreement with the FE predictions, with a PR equal to ca. −1 up to a 3% overall strain.

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The work presents a novel polyhedral mechanical metamaterial based on rotating triangular prisms connected by their corners, which possesses the ability to attain large values of negative Poisson’s ratio (NPR). Through a kinematic model of the proposed rotating structure, we evaluate the auxeticity of the system by varying the geometrical parameters of the polyhedrons composing the elementary cell of the structure. The kinematic results highlight the peculiar NPR of the system, whose values are nearly constant over significant strain ranges. Focusing on the most promising auxetic mechanisms we designed chiral architectures that replace the ideal hinges at the corners with curved-shape ligaments, and validated these configurations through 3D printed specimens. The specimens were tested under uniaxial compression and simulated through finite element analyses. Experimental results exhibited an excellent agreement with computational predictions in terms of elastic modulus and auxeticity, showing a value of Poisson’s ratio up to -1.3 for one of the designs. Our findings demonstrate the highly auxetic property of rotating polyhedral systems, which allow the design of novel architected materials useful, for example, in biomechanical applications.

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.