Auxetic structures in architecture : synclastic behaviour of auxetic chiral structures

Abstract

Auxetics are materials, structures or geometric configurations that exhibit counterintuitive behaviour when undergoing in-plane deformations, as they possess a negative Poisson’s ratio. In essence, they expand laterally when stretched and contract laterally when compressed. This class of metamaterials occurs in nature, yet several sub-classes have been synthetically manufactured. Auxetics are predominantly employed in high-tech fields on the micro-scale, such as in biomedical applications and textiles. Since their behaviour is reliant on their geometry, they are scale-independent and their behaviour is reliant on geometric parameters which they possess. It is their scale-independence that brings forward the possibility of operating on the architectural scale. Auxetic structures exhibit a combination of behavioural properties which is unique to this class of materials, such as a high shear stiffness, indentation resistance and the ability to generate synclastic curvatures when undergoing an out-of-plane bending moment. The tailoring of auxetic structures’ Gaussian curvature from planar elements to generate complex topologies has already been presented in past literature, and its potential application in gridshells and bending-active structures has already been discussed. In this study, the potential of the anti-tetrachiral geometry in this field was investigated. The antitetrachiral geometry falls within the category of chiral structures. In chiral geometries, every repeated cell is composed of a circular or polygonal node, with a number of ligaments connected tangentially to each node. The anti-tetrachiral geometry was selected as it expresses an in-plane Poisson’s ratio of -1. This investigation was carried out using Finite Element Analysis, in order to establish relationships between the structure’s geometric parameters and the Gaussian curvature that was developed, ultimately aiming to generate synclastic curvature, which is essential in the application of auxetics to bending-active structures. The results were also compared with previous studies on the antitetrachiral geometry. The in-plane Poisson’s ratio for the anti-tetrachiral geometry resulted, as expected, as being close to -1, with the geometries displaying minor variations due to changes in the geometrical parameters. However, in this study, synclastic curvature was unattainable, with only anticlastic or cylindrical curvature being achieved. Thus, the anti-tetrachiral pattern displayed counterintuitive behaviour, acting auxetically in-plane and non-auxetically out-of-plane.