Auxetic Properties of Chiral Hexagonal Cosserat Lattices Composed of Finite‐Sized Particles

Abstract

This article is devoted to the study of auxetic properties of Cosserat hexagonal lattices composed of finite‐sized particles with complex connections. The description of complex connections is given; their mathematical model is elaborated and the properties are studied. The introduction of complex connections enables one varying their structure and component parameters. Due to that there arise possibilities for both simulation of nonchiral lattices with symmetrical bonds and with a chiral microstructure and construction of lattices with desired properties. The discrete and micropolar equations of the lattice are obtained. As a result, the macroparameters are expressed in terms of the lattice microparameters. The dependence of the Poisson's ratio on the lattice microparameters is obtained. It allows finding and analyzing parameters, for which the lattice possesses auxetic properties. The importance of rotational degrees of freedom of particles and chirality for the appearance of auxetic properties is shown. For verification, the results of the calculation of the Poisson's ratio obtained on the basis of theoretically obtained relations are compared with the results of numerical simulation of the stretching of the lattice.

Mechanical Properties of Cubene Crystals

“…Metamaterials with particles having rotational degrees of freedom (polygons or polyhedrons) can be created artificially [ 38 , 39 , 40 , 41 , 42 ]. The rotational degrees of freedom can produce negative thermal expansion [ 21 , 22 , 23 , 24 , 25 ] or auxetic behaviour (negative Poisson’s ratio) [ 38 , 39 , 40 , 41 , 42 ]. The crystal has been potentially used in several applications, such as bearing material for total hip implants [ 43 ].…”

“…Metamaterials with particles having rotational degrees of freedom (polygons or polyhedrons) can be created artificially [38][39][40][41][42]. The rotational degrees of freedom can produce negative thermal expansion [21][22][23][24][25] or auxetic behaviour (negative Poisson's ratio) [38][39][40][41][42].…”

Bending‐Free Lattices as Underlying Optimal Isotropic Microstructures of the Least‐Compliant 2D Elastic Bodies

“…In the study by Wojciechowski, [26] it was also additionally demonstrated that analogous units (soft cyclic hexamers) depending on characteristics of their interactions can exhibit the properties of an auxetic material, the Poisson's ratio of which reaches values between À1 and þ0.8, which covers almost the whole range allowed for 2D isotropic systems. Recently, systems of hexagonal units have been analyzed in the article [27] devoted to the study of auxetic properties of Cosserat hexagonal lattices composed of finite-sized particles with complex connections. It turns out that not only hexagonal, but also triangular units can be used to model the isotropic systems.…”

“…Hundreds (if not thousands) of papers have been devoted to matching the values of geometric and/or material parameters of microstructures in such a way as to enable the control of the effective Poisson's ratio values ν H in the full range of its permissible values, that is, −1 ≤ ν H ≤ 1 and −1 ≤ ν H ≤ 0.5 for 2D and 3D elastic, isotropic bodies, respectively—see for example, the selected and the most current studies. [ 24–60 ] It is worth emphasizing that a clear and simple proving of the earlier permissible ranges of Poisson's ratio for isotropic material was disclosed by Wojciechowski [ 24 ] published almost 20 years ago. More than 30 years ago, the same author showed that simple hexagonal units (hard cyclic hexamers) spontaneously form an auxetic isotropic crystal in two dimensions (see the study by Wojciechowski [ 25 ] ).…”

Reduced Linear Constrained Elastic and Viscoelastic Homogeneous Cosserat Media as Acoustic Metamaterials

“…In particular, reduced elastic Cosserat media are single negative acoustic metamaterials, for which harmonic shear waves are evanescent in a certain frequency domain. Lots of works consider acoustic metamaterials with internal (often rotational) degrees of freedom, on the discrete and continuum level [21][22][23][24][25][26][27].…”