An Analytical Molecular Mechanics Model for Elastic Properties of Graphyne-n

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Juan Hou ◽  
Zhengnan Yin ◽  
Yingyan Zhang ◽  
Tienchong Chang
Keyword(s):  
Mechanical Properties ◽  
Molecular Mechanics ◽  
Elastic Properties ◽  
Poisson’S Ratio ◽  
Building Materials ◽  
Scaling Law ◽  
Poisson's Ratio ◽  
Atomic Structures ◽  
Mechanics Model ◽  
Molecular Mechanics Model

Graphynes, a new family of carbon allotropes, exhibit superior mechanical properties depending on their atomic structures and have been proposed as a promising building materials for nanodevices. Accurate modeling and clearer understanding of their mechanical properties are essential to the future applications of graphynes. In this paper, an analytical molecular mechanics model is proposed for relating the elastic properties of graphynes to their atomic structures directly. The closed-form expressions for the in-plane stiffness and Poisson's ratio of graphyne-n are obtained for small strains. It is shown that the in-plane stiffness is a decreasing function whereas Poisson's ratio is an increasing function of the number of acetylenic linkages between two adjacent hexagons in graphyne-n. The present analytical results enable direct linkages between mechanical properties and lattice structures of graphynes; thereby, providing useful guidelines in designing graphyne configurations to suit their potential applications. Based on an effective bond density analysis, a scaling law is also established for the in-plane stiffness of graphyne-n which may have implications for their other mechanical properties.

Modelling of Negative Poisson's Ratio Nanomaterials: Deformation Mechanisms, Structure-Property Relationships and Applications

2005 ◽  
Vol 23 ◽  
pp. 55-58 ◽  
Author(s):  
A. Alderson ◽  
K.L. Alderson ◽  
K.E. Evans ◽  
J.N. Grima ◽  
M.S. Williams
Keyword(s):  
Molecular Mechanics ◽  
Poisson’S Ratio ◽  
Deformation Mechanisms ◽  
Poisson's Ratio ◽  
Analytical Models ◽  
Second Phase ◽  
Structure Property ◽  
Mechanics Model ◽  
Structure Property Relationships ◽  
Molecular Mechanics Model

Analytical and Molecular Mechanics methods have been used to study the deformation mechanisms acting at the molecular level in the auxetic polymorph of crystalline silica (a-cristobalite). The analytical models indicate that a-cristobalite deforms by concurrent tetrahedral dilation and cooperative rotation when stretched along the x3 axis, and that a second phase is predicted to exist for this loading scenario, having a geometry similar to that of ‘idealised’ b-cristobalite. This is supported by preliminary Molecular Mechanics simulations, which also indicate that the cooperative rotation predicted for loading along x3 is not sufficient to describe the deformation mechanism for loading along x1. A negative hydrostatic pressure offset is observed to lead to a change in the sign of the predicted Poisson’s ratio from positive to negative, leading to improved agreement of the Molecular Mechanics model with experiment.

Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model

2006 ◽  
Vol 462 (2072) ◽  
pp. 2523-2540 ◽  
Author(s):  
Tienchong Chang ◽  
Jingyan Geng ◽  
Xingming Guo
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Molecular Mechanics ◽  
Elastic Properties ◽  
Continuum Mechanics ◽  
Governing Equations ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Mechanics Model ◽  
Molecular Mechanics Model

Molecular mechanics has been widely used to analytically study mechanical behaviour of carbon nanotubes. However, explicit expressions for elastic properties of carbon nanotubes are so far confined to some special cases due to the lack of fully constructed governing equations for the molecular mechanics model. In this paper, governing equations for an analytical molecular mechanics model are fully established. The explicit expressions for five in-plane elastic properties of a chiral single-walled carbon nanotube are derived, which make properties at different length-scales directly connected. The effects of tube chirality and tube diameter are investigated. In particular, the present results show that the classic relationship from the isotropic elastic theory of continuum mechanics between Young's modulus and shear modulus of a single-walled carbon nanotube is not retained. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and also useful to the topic of linking molecular mechanics with continuum mechanics.

A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Jianxing Liu ◽  
Yihui Zhang
Keyword(s):  
Mechanical Properties ◽  
Elastic Modulus ◽  
Theoretical Model ◽  
Poisson’S Ratio ◽  
Strain Range ◽  
Analytic Solutions ◽  
Poisson's Ratio ◽  
Mechanics Model ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Soft network materials that incorporate wavy filamentary microstructures have appealing applications in bio-integrated devices and tissue engineering, in part due to their bio-mimetic mechanical properties, such as “J-shaped” stress–strain curves and negative Poisson's ratios. The diversity of the microstructure geometry as well as the network topology provides access to a broad range of tunable mechanical properties, suggesting a high degree of design flexibility. The understanding of the underlying microstructure-property relationship requires the development of a general mechanics theory. Here, we introduce a theoretical model of infinitesimal deformations for the soft network materials constructed with periodic lattices of arbitrarily shaped microstructures. Taking three representative lattice topologies (triangular, honeycomb, and square) as examples, we obtain analytic solutions of Poisson's ratio and elastic modulus based on the mechanics model. These analytic solutions, as validated by systematic finite element analyses (FEA), elucidated different roles of lattice topology and microstructure geometry on Poisson's ratio of network materials with engineered zigzag microstructures. With the aid of the theoretical model, a crescent-shaped microstructure was devised to expand the accessible strain range of network materials with relative constant Poisson's ratio under large levels of stretching. This study provides theoretical guidelines for the soft network material designs to achieve desired Poisson's ratio and elastic modulus.

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