Auxetic behaviour from rotating rhombi

Abstract

Auxeticity (i.e. negative Poisson's ratios) is associated with particular geometrical features and deformation mechanisms of a system. Among the potential systems that may exhibit such behaviour are rotating rigid units. Here we discuss how rigid rhombi of the same shape and size can be connected in two different ways to give rise to two distinct systems: the Type α and Type β rotating rhombi. We derive the mechanical properties, for the Type β system and compare it to those of the Type α to highlight the differences between the two systems namely that Type α systems are highly anisotropic and can exhibit both negative and positive Poisson's ratios which depend on the shape of the rhombi and the angle between them whereas Type β systems are isotropic with a constant in-plane Poisson's ratio of –1. Furthermore we show that by constructing the rhombi from five truss-type elements, where the one forming the diagonal has a different thermal expansion than the other four identical trusses, the Poisson's ratios for the Type α systems can also be made temperature dependent, in contrast with Type β systems which remain unaffected by temperature changes.