Negative linear compressibility from rotating rigid units

Abstract

The possibility of achieving the anomalous property of negative linear compressibility through a mechanism involving the rotations of rigid units is presented and discussed through analytical modelling. It is shown that some rotating rigid units with particular geometric features and connectivities will expand rather than contract in certain directions when a hydrostatic pressure is applied. The conditions required for this anomalous property to be achieved via rotations are elucidated in terms of specific geometric and structural requirements as well as their Poisson's ratio and stiffness properties.

Negative Compressibility of 3D Cellular Models Constructed by Hinging Hexagonal Truss Mechanism

“…And the expressions of Poisson's ratios of these two models are same due to the same framework structure so the euqation, β L (OX i ) (Model I) = 2 β L (OX i ) (Model III) , can be easily to understand. More than that, through the comparison of these two models, it can be indicated that in addition to the geometry features which have already been widely discussed , the arrangement of the framework structure can also have a great effect on the compressibility properties and arranging the framework in a dense way just like the Model III is not conductive to the enhancement of negative compressibility effect.…”

“…And the expressions of Poisson's ratios of these two models are same due to the same framework structure so the euqation, β L (OX i ) (Model I) ¼ 2β L (OXi ) (Model III) , can be easily to understand. More than that, through the comparison of these two models, it can be indicated that in addition to the geometry features which have already been widely discussed [10][11][12][13][14][15][16] , the arrangement of the framework structure can also have a great effect on the compressibility properties and arranging the framework in a dense way just like the Model III is not conductive to the enhancement of negative compressibility effect. Before comparing the compressibility properties of the Models I and II, we need to analyze the compressibility properties of the hinging hexagonal truss mechanism, which is helpful to understand the differences of the linear compressibility properties between these two models.…”

“…By using a combination of finite element simulations and analytical derivations, it was shown that NLC can be exhibited in body‐ or face‐centered tetragonal structures . It has also been shown that some systems made from rotating rigid units which are usually associated with auxeticity can also exhibit negative linear compressibility for certain conditions . Moreover Miller et al identified several relatively common materials which displayed NLC and presented several potential applications.…”

“…It has also been shown that some systems made from rotating rigid units which are usually associated with auxeticity can also exhibit negative linear compressibility for certain conditions. [15][16][17] Moreover Miller et al [18] identified several relatively common materials which displayed NLC and presented several potential applications. Cairns and Goodwin [19] reviewed the phenomenology of negative compressibility in multifarious materials and presented a mechanistic understanding of negative compressibility.…”

“…Although many different structures have been proposed and analyzed, a limitation in the development of negative compressibility materials still remains, that is, most of negative compressibility structures are only studied in two-dimensional space such as wine-rack-type and hexagonal honeycombs structures, [3,10] truss-type systems, [11] bi-material strips [12][13] and rotating rigid units. [15][16][17] Although 2D models are simpler to analyze and sometimes they can predict the behaviors of particular projections of a complex 3D model where the linear compressibility is measured, their limitations lie in the fact that negative area compressibility (i.e., NAC) is not possible to be achieved in a 2D system just like the negative volume compressibility (i.e., NVC) behavior is forbidden in classical thermodynamics. [3,20] Also sometimes the simplification from 3D models to planar structures can lead to the differences between conclusions and actual results, for example, Choi and Lakes [21,22] proposed a 14-sided polyhedron model and gave the expressions of Young's moduli and Poisson's ratios by simplifying this complex 3D model to a 2D structure.…”