Poisson's ratio of simple planar ‘isotropic’ solids in two dimensions

Abstract

The influence of molecular geometry on the Poisson's ratio has been investigated for a few twodimensional (2D) hard body systems (hard discs, hard dimers, hard cyclic trimers, and hard cyclic hexamers) forming elastically isotropic solid phases. The Poisson's ratio of the studied periodic and aperiodic solids was determined by Monte Carlo simulations using the analysis of the box fluctuations in the constant pressure ensemble (NpT ) with variable box shape. The results obtained for all the studied systems showed that the Poisson's ratio grows when the density is decreased. It has been also found that the Poisson's ratio decreases with increasing number of discs in the molecule and its value for hard trimers is negative near close packing.

Negative Poisson’s ratio of two-dimensional hard cyclic tetramers

“…During last decade, there has been an increasing interest in the discovery and investigation of different physical systems [2][3][4][5][6][7][8][9][10][11][12] and/or models [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] which exhibit auxetic behavior (negative Poisson's ratio). This interest is motivated by at least two reasons.…”

“…Here, we devote our attention to the effects of molecule geometry and crystallographic structure. It has been shown that the geometry and specifically the anisotropy of a molecule can be of critical importance to the elasticity of the system [37,26,36]. Various kinds of disorder such as point and structural defects [38,39], voids [40], size polidyspersity of particles [41][42][43][44], and orientational disorder [37] also change the elastic properties of the system.…”

“…In general, the elastic properties of a system/material depend on several variables, including the crystallographic structure of the system [1], the intermolecular interaction potential [34,35], and the geometry of the molecules [26,36]. Here, we devote our attention to the effects of molecule geometry and crystallographic structure.…”

On the mechanical properties and auxetic potential of various organic networked polymers

“…This led to the discovery of numerous auxetic materials [1,2,, ranging from synthetic polymeric foams [10][11][12][13][14][15][16] to naturally occurring silicates and zeolites [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Additionally, a number of auxetic models and structures have also been identified [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

Finite Element Modelling of Different 2D Re Entrant Structures of Auxetic Materials

“…The other classes are namely chiral structures [7][8][9], rotating rigid/semi-rigid units [10][11][12][13][14], angle-ply laminates [15,16], hard molecules [17][18][19][20], micro porous polymers [21][22][23], and liquid crystalline polymer [24 -26]. In particular, the important 2D re-entrant structures are structurally hexagonal honeycomb, double arrow head structures, structures formed from lozenge grids, structure formed from sinusoidal ligaments, and structure formed from square grids [27].…”