Auxetic behaviour from rotating rigid units

Abstract

PACS 62.20.-x, 81.90.+c 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.

Three decades of auxetic polymers: a review

“…Upon applying a load on an auxetic material or structure in one direction, it expands in the perpendicular direction and exhibits a negative Poisson's ratio. Therefore, a correct cooperation between the internal structure of the material and the way it deforms when loaded gives rise to auxeticity (43)(44)(45)(46)(47)(48)(49). The classification of auxetic behavior into complete auxetic, auxetic, partially auxetic and nonauxetic has been reported in Refs.…”

On the mechanical properties and auxetic potential of various organic networked polymers

“…This led to the discovery of numerous auxetic materials [1,2,, ranging from synthetic polymeric foams [10][11][12][13][14][15][16] to naturally occurring silicates and zeolites [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Additionally, a number of auxetic models and structures have also been identified [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

“…For example, the Poisson's ratios in the naturally occurring silicate α-cristobalite and in various zeolites have been explained using models based on connected rigid units which, when loaded in tension, rotate relative to each other to form a more open structure [27,28,42,50], whilst the auxeticity in the liquid-crystalline polymers synthesised by Griffin et al have been attributed to a model involving the rotation of laterally attached rods [33][34][35].…”

Low Porosity Metallic Periodic Structures with Negative Poisson's Ratio

“…In all of these cases, careful design of the microstructure has lead to effective Poisson's ratios ν < 0, despite the fact that the bulk materials are characterized by ν > 0. In particular, it has been shown that auxetic behavior can be achieved in a variety of highly porous materials [10], including foams with re-entrant [11][12][13][14][15] and chiral [16,17] microstructure, microporous polymeric materials [18], networks of rigid units [19] and skeletal structures [20]. Moreover, negative Poisson's ratio has also been shown in non-porous systems, such as laminates [21,22], sheets assemblies of carbon nanotubes [23], composites [24] and polycrystalline thin films [25].…”