Auxetic behaviour from rotating rigid units

Abstract

Auxetic materials exhibit the unexpected feature of becoming fatter when stretched and narrower when compressed, in other words, they exhibit a negative Poisson’s ratio. This counter-intuitive behaviour imparts many beneficial effects on the material’s macroscopic properties that make auxetics superior to conventional materials in many commercial applications. Recent research suggests that auxetic behaviour generally results from a cooperative effect between the material’s internal structure (geometry setup) and the deformation mechanism it undergoes when submitted to a stress. Auxetic behaviour is also known to be scale-independent, and thus, the same geometry/deformation mechanism may operate at the macro-, micro- and nano- (molecular) level. A considerable amount of research has been focused on the ‘re-entrant honeycomb structure’ which exhibits auxetic behaviour if deformed through hinging at the joints or flexure of the ribs, and it was proposed that this ‘re-entrant’ geometry plays an important role in generating auxetic behaviour in various forms of materials ranging from nanostructured polymers to foams. This paper discusses an alternative mode of deformation involving ‘rotating rigid units’ which also results in negative Poisson’s ratios. In its most ideal form, this mechanism may be constructed in two dimensions using ‘rigid polygons’ connected together through hinges at their vertices. On application of uniaxial loads, these ‘rigid polygons’ rotate with respect to each other to form a more open structure hence giving rise to a negative Poisson’s ratio. This paper also discusses the role that ‘rotating rigid units’ are thought to have in various classes of materials to give rise to negative Poisson’s ratios.