Unimode metamaterials exhibiting negative linear compressibility and negative thermal expansion

Abstract

Unimode metamaterials made from rotating rigid triangles are analysed mathematically for their mechanical and thermal expansion properties. It is shown that these unimode systems exhibit positive Poisson's ratios irrespective of size, shape and angle of aperture, with the Poisson's ratio exhibiting giant values for certain conformations. When the Poisson's ratio in one loading direction is larger than +1, the systems were found to exhibit the anomalous property of negative linear compressibility along this direction, that is, the systems expand in this direction when hydrostatically compressed. Also discussed are the thermal expansion properties of these systems under the assumption that the units exhibit increased rotational agitation once subjected to an increase in temperature. The effect of the geometric parameters on the aforementioned thermo-mechanical properties of the system, are discussed, with the aim of identifying negative behaviour.

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.…”

“…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.…”

A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility

“…Here it should be mentioned that, apart from the planar rotational structures (for example, rotating rigid squares, parallelograms, triangles, etc. [26][27][28][29][30][31][32]), 3D rotational structures constructed of cubes linked at certain edges or vertices, either directly or through ligaments [71][72][73], can also be employed. When such systems are stretched or compressed, the cubic units rotate and angles between the adjacent sides change, leading to spatial expansion or shrinkage that may be conducive of auxetic behavior.…”

“…Note that the factor of 2 is necessary, since it is being assumed that triangular units are located both above and below the plane of the 'rotating squares', where they could either have the same base-in which case the aforementioned triangular unit would be half of a rhombic structure, having diagonals of length r and 2h (see Figure 1)-or at different locations. The use of rhombic units, having triangular units both above and below the 'rotating squares base' and forming a wine-rack/Milton's unimode-like system [31,43,44], has the advantage that the system is easily tessellatable and will not shear. Note also that, assuming that the squares are perfectly rigid (as is normally assumed in the idealized 'rotating squares' model), the length r is a function of the single variable θ, the angles between the squares, and is given by:…”

“…In tandem, there has also been a significant amount of research aimed at exploring new mechanisms leading to anomalous behaviors. Examples of such mechanisms include the rotating rigid unit mechanisms [26][27][28][29][30][31][32], the umbrella-style mechanism [33][34][35], the re-entrant honeycomb deforming through hinging or flexure [35][36][37], etc. leading to NPR, as well as the wine-rack mechanism leading to NLC [23][24][25]38], together with the formulation of mathematical models to fully elucidate their behaviors [8,22,[26][27][28][29][30][31]38].…”