Maximum Poisson's Ratios in Planar Isotropic Crystals of Binary Hard Discs at High Pressures

Abstract

Several isotropic two‐dimensional crystalline structures are described that exhibit maximum values of the Poisson's ratio at very high pressures. The considered crystals are formed by hard discs of two different diameters which are very close to each other. The investigations of the models are based on Monte Carlo simulations in the isobaric–isothermal ensemble with variable shape of the periodic box.

Auxetics and Other Systems of Anomalous Characteristics

“…Finally, in the paper Maximum Poisson's ratios in planar isotropic crystals of binary hard discs at high pressures by Tretiakov, Bilski, and Wojciechowski , several isotropic two‐dimensional crystalline model structures, formed by hard discs of two slightly different diameters, are studied by Monte Carlo simulations in the isobaric–isothermal ensemble with variable shape of the periodic box. Some of the structures are shown to exhibit maximum values of Poisson's ratio in the limit of very high pressures, i.e.…”

On the Compressibility Properties of the Wine‐Rack‐Like Carbon Allotropes and Related Poly(phenylacetylene) Systems

“…This, together with the behaviour under shear loading, merits further investigation. It should also be appreciated that the work by Tretiakov et al has also studied what can be considered as very similar structures to what was studied but using a rather different intermolecular potential. This work by Tretiakov et al had suggested completely different properties, thus highlighting the critical role of the intermolecular potential on the macroscopic properties of the systems studied.…”

Edge Effects of a Hexagonal Honeycomb on the Poisson's Ratio and Young's Modulus

“…To investigate further, the worst-case scenario when n ¼ 1, Figure 6 compares the Poisson's ratio and Young's modulus obtained numerically with the analytical models represented by the simple model derived in this work (Equations (29) and (30)), the advanced model (Equations (59) and (60)), and the standard results (Equations (31) and (32)). Here, the typical configuration consisting of l ¼ 2 h and t E ¼ t I , corresponding to α ¼ 2 and χ ¼ 1, were used.…”

“…The equations so derived contain correction factors that account for the effective bending lengths as well as axial and shear deformations. If these corrections are ignored, the resultant equations become once again Equation (29) and (30). Before proceeding, it is important to note that the advanced model does not consider the deformation induced in the intersecting parts of the ligaments.…”

“…Although the possibility of material exhibiting a negative Poisson's ratio was known by the first half of the 20th Century, [2] interest in the subject took off only in the late 1980s [3] after the groundbreaking work of people of the like of Lakes, [4] Wojciechowski, [5,6] and Evans et al [7][8][9] Compared with their conventional counterparts, auxetic materials have been shown to exhibit improved performance such as larger shear stiffness [4,10] and fracture toughness [4,11] as well as higher indentation resistance. [4,12,13] For this reason, their properties have been investigated using a variety of methods including analytical, [14][15][16][17][18] numerical, [19][20][21][22][23][24][25][26][27][28][29][30] and experimental [19,21,31,32] techniques. They have also been proposed for a diversity of applications ranging from shoes [33] and personal protective equipment [34] to stents [35,36] and dilator for medical application.…”