Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties

Abstract

A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poisson's ratio (auxetic), zero Poisson's ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.

Smart hexagonal truss systems exhibiting negative compressibility through constrained angle stretching

“…On the other hand, for non re-entrant honeycombs, a negative Poisson's ratio is observed if they deform through stretching of the ribs [5,6]. More recently, it was shown that honeycombs and other cellular solids deforming through changes in angles between the cell walls (hinging mechanism) may exhibit the rare property of negative linear compressibility (NLC) [16,18]. In the latter case, negative linear compressibility is observed when certain conditions are satisfied through a mechanism that is not dissimilar to other main mechanisms known so far to be responsible for NLC, such as that employed by Baughman et al to explain the predicted NLC in some carbon allotropes [10], by Fortes et al to explain the experimentally measured NLC in methanol monohydrate [15] and by Cairns et al to explain the giant NLC response measured in the α-polymorph of zinc dicyanoaurate [19].…”

“…the property of becoming wider rather than thinner when uniaxially stretched [1][2][3][4][5][6][7][8][9]) and the property of negative linear compressibility (i.e. the ability to expand in at least one dimension rather than shrinking upon the application of an externally applied hydrostatic pressure [9][10][11][12][13][14][15][16][17][18][19][20][21]). Uses 5 www.um.edu.mt/science/metamaterials.…”

Poisson's ratio over two centuries: challenging hypotheses

“…29,75 Poisson's ratio therefore applies to architectural frameworks just as it does to colloids, for example, or to the atomic architecture of the mechanically active components that all materials are constructed from. This awareness has become of great practical significance, offering scope for reverse engineering from the macro to the micro scale, 76,77 bridging the gap between continuum and atomistic topologies.…”

“…Since then, numerous mechanical models have been devised that mimic reentrant geometry and, in engineering terms, could operate on any length scale. 76,77 Furthermore, 'Work on these strange materials is not meant just for our entertainment; negative Poisson's ratio materials may be useful for a variety of reasons.' 75 By 1991 the unusual mechanical behaviour of expansion under tension was attracting wider attention and was coined 'auxetic' 76 by Ken Evans, basing this on the Greek noun for 'growth' (aú´j1si6, or auxesis).…”

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

“…One should equally not preclude that real materials based on the models proposed here could also benefit from other superior properties. 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.…”