Out-of-plane doming behaviour from constrained auxetics

Abstract

Auxetics expand laterally when uniaxially stretched. In many cases, this behaviour has been attributed to the interplay between the geometry of the system and its deformation mechanism. This work revisits a class of 2D motifs, the so-called chiral honeycombs, which are closely associated with auxetic behaviour. More specifically, we show that systems based on this motif, particularly those having a Poisson's ratio of −1, can be engineered with specific constraints that limit the in-plane expansion, with the result that on inducing deformation of the systems, these veer out-of-plane to form dome-like structures. This effect is demonstrated in simple prototypes and it is shown through a simplified mathematical model that the extent of curvature can be controlled through the various parameters that describe such structures.