On rotating rigid parallelograms and their potential for exhibiting auxetic behaviour

Abstract

Auxetic systems have the anomalous property of becoming wider when uniaxially stretched, i.e. exhibit a negative Poisson's ratio. One of the mechanisms which can give rise to this property is based on rotating rigid units, in particular 2D rigid polygons which are connected together at their corners through hinges and rotate relative to each other when uniaxially stretched. This work extends earlier preliminary work on connected rigid parallelograms and presents expressions for the mechanical properties for all the types of planar systems that can be constructed from rigid parallelograms of equal size connected at their vertices through flexible hinges. In particular, we derive and discuss the mechanical properties for the Type Iα, Iβ and IIβ rotating parallelograms which were not previously analysed and compare them with the properties of the Type IIα systems. We show that despite being rather similar to each other, the different types of ‘rotating parallelograms’ have very different mechanical properties and different abilities to exhibit auxetic behaviour.

Maximizing negative thermal expansion via rigid unit modes: a geometry-based approach

“…In this respect, it should be highlighted that the systems studied here had previously been analysed vis-à-vis their negative Poisson's ratio (auxetic) potential [51,53,[67][68][69] where it was shown that the non-fully open forms of these constructs are able to exhibit the anomalous property of getting wider rather than thinner when uniaxially stretched. Based on the current and earlier work [50,51,53,67,68,70], it is envisaged that one may be able to engineer materials which would be both auxetic and also exhibit NTE characteristics, as has been done via a different paradigm [28,30,[71][72][73] and thus provide a route for the design of new multifunctional materials exhibiting superior thermo-mechanical characteristics. For example, multifunctional (heat and pressure sensitive) materials have the potential to be used in applications involving body armour and protective packaging, whereby the material would react accordingly to changes in the external parameters.…”

Untitled

“…Also, the number of the stripes in a unit cell can affect the auxetic effect of the fabric and must be taken into account during design of this kind of fabric. Auxetic knitted fabrics developed based on rotating rectangles: Several studies have revealed that an auxetic effect can successfully be induced by using rotating units such as squares [53], rectangles [54], triangles [55], rhombi [56] and parallelograms [57]. One such example based on rigid rectangles connected together at their vertices by hinges is demonstrated in Figure 14.…”

Hierarchical Fibers with a Negative Poisson’s Ratio for Tougher Composites

“…Due to their special deformation characteristics, the NPR materials have also drawn considerable attentions in the past years. Many kinds of interesting prototypes have been exploited, such as re-entrant honeycombs [23,24], chiral honeycombs [25,26], re-entrant foams [27,28], microporous polymers, particulate composites, fiber reinforced and laminated composites, auxetic yarns and nanocomposites [29], hybrid materials [30,31,32] and networks of 2D and 3D rigid blocks [33,34,35,36,37,38,39,40,41], etc. Compared with conventional materials, the NPR materials could have enhanced compressive strength, shear stiffness, indentation resistance and toughness, self-adaptive vibration damping and shock absorption, reduction in thermal stresses, etc.…”