Abstract
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.
Highlights
Auxetics are systems or materials which possess the unusual property of a negative Poisson’s ratio.[1,2] This means that these systems expand in the transverse direction when subjected to a uniaxial tensile load
The simulations conducted in this work may be divided into two main parts: first, a range of rotating square and anti-tetrachiral honeycombs were studied in order to evaluate the effect of ligament length on mechanical properties, and, secondly, an optimized ‘hybrid’ geometry was modelled and its mechanical response compared with those of two corresponding rotating squares and anti-tetrachiral honeycombs
In order to ensure that all of the parameters are unitless and the results of this study may be applied to these metamaterial geometries regardless of the base material used, the Young’s moduli and shear modulus are presented as an effective percentage of the obtained modulus of the specific geometry divided by the material modulus (Emat 1⁄4 200000 MPa and Gmat 1⁄4 76923 MPa) and denoted by Ex*, Ey* and G*
Summary
Auxetics are systems or materials which possess the unusual property of a negative Poisson’s ratio.[1,2] This means that these systems expand in the transverse direction when subjected to a uniaxial tensile load. This property arises primarily from the geometry and deformation mechanisms of the systems and, as a result of this, auxeticity is considered to be scaleindependent. There are various geometries which give rise to auxeticity, with the most well-known being reentrant structures, including hexagonal honeycombs and star-shaped geometries,[14,15,16,17] rotating unit systems,[18,19,20] chiral honeycombs,[21,22,23,24,25,26,27] buckling-based architectures[28,29] and folding/origami metamaterials.[30]
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