Simple model potential for the description of elastic properties of single-layer graphene (original) (raw)
Elastic in-plane properties of 2D linearized models of graphene
Mechanics of Materials, 2013
Graphene is a monolayer of carbon atoms packed into a two-dimensional honeycomb lattice. This allotrope can be considered as mother of all graphitic forms of carbon. The elastic in-plane properties of graphene are studied and various existing linearized models of its elastic deformations are critically re-examined. Problems related to modelling of graphene by nonlinear multi-body potentials of inter action are also discussed. It is shown that experimental results for small deformations can be well described by both the two-parametric molecular mechanics model developed by Gillis in 1984, while some popular models have serious flaws and often the results obtained using these models do not have physical meaning. It is argued that in order to study elastic constants of linearized models of graphene layers, it is very convenient to use the four parameter molecular mechanics model. The advantages of this approach is demonstrated by its application to the Tersoff and Brenn er nonlinear interaction potentials, and by its comparison with the Gillis two-parametric model.
Meccanica, 2019
In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner-Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is implemented.
The Journal of Physical Chemistry C, 2012
In this study, the Young's and flexural moduli of single-and double-layer graphene have been theoretically investigated using periodic boundary condition (PBC) density functional theory (DFT) with the PBE, HSE06 H , and M06L functionals in conjunction with the 6-31G* and the 3-21G basis sets. The unit-cell size and shape dependence as well as the directional dependencies of the mechanical properties have also been investigated. Additionally, the calculated stretching and flexural strain-stress curves are reported. Finally, finiteelement simulations have been performed so as to find a homogeneous equivalent isotropic transverse material for single-layer graphene, in order to reproduce mechanical behavior in both tensile and bending sollicitations.
Solid State Communications, 2014
The elastic deformation of a single-layer nanostructured graphene sheet is investigated using an atomistic-based continuum approach. This is achieved by equating the stored energy in a representative unit cell for a graphene sheet at atomistic scale to the strain energy of an equivalent continuum medium under prescribed boundary conditions. Proper displacement-controlled (essential) boundary conditions which generate a uniform strain field in the unit cell model are applied to calculate directly one elastic modulus at a time. Three atomistic finite element models are adopted with an assumption that the force interaction among carbon atoms can be modeled by either spring-like or beam elements. Thus, elastic moduli for graphene structure are determined based on the proposed modeling approach. Then, effective Young's modulus and Poisson's ratio are extracted from the set of calculated elastic moduli.
Numerical investigation of elastic mechanical properties of graphene structures
Materials and Design, 2010
The computation of the elastic mechanical properties of graphene sheets, nanoribbons and graphite flakes using spring based finite element models is the aim of this paper. Interatomic bonded interactions as well as van der Waals forces between carbon atoms are simulated via the use of appropriate spring elements expressing corresponding potential energies provided by molecular theory. Each layer is idealized as a spring-like structure with carbon atoms represented by nodes while interatomic forces are simulated by translational and torsional springs with linear behavior. The non-bonded van der Waals interactions among atoms which are responsible for keeping the graphene layers together are simulated with the Lennard-Jones potential using appropriate spring elements. Numerical results concerning the Young's modulus, shear modulus and Poisson's ratio for graphene structures are derived in terms of their chilarity, width, length and number of layers. The numerical results from finite element simulations show good agreement with existing numerical values in the open literature.
Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description
Physical Review B, 2009
The nonlinear in-plane elastic properties of graphene are calculated using density-functional theory. A thermodynamically rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. Upon accounting for the symmetries of graphene, a total of fourteen nonzero independent elastic constants are determined by least-squares fit to the ab initio calculations. The nonlinear continuum description is valid for infinitesimal and finite strains under arbitrary in-plane tensile loading in circumstance for which the bending stiffness can be neglected. The continuum formulation is suitable for incorporation into the finite element method.
A method for developing the equivalent continuum model of a single layer graphene sheet
Thin Solid Films, 2008
A method is presented to develop the equivalent continuum model for a single-layered graphene sheet. This method integrates molecular dynamics method as an exact numerical solution with theory of shell as an analytical method. The force-depth results achieved from molecular dynamics simulation of nanoindentation of a single graphene sheet are compared with the formulation for large deflection of circular plates loaded at the centre. As a result, the effective Young's modulus and mechanical thickness of the sheet wall are independently obtained. The validity of this approach is verified by comparing finite element modeling of nano-indentation of a single graphene sheet with molecular dynamics results available in the literature. Presented results demonstrate that the proposed method could provide a valuable tool for studying the mechanical behaviour of single-layered graphene sheets, as well as efficiency of continuum theory in nano-structured material.
Homogenized Elastic Properties of Graphene for Small Deformations
Materials, 2013
In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force) and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.
Homogenized elastic properties of graphene for moderate deformations
Coupled systems mechanics, 2015
This paper presents a simple procedure of obtaining a substitute, homogenized mechanical response of single layer graphene sheet. The procedure is based on the judicious combination of molecular mechanics simulation results and homogenization method. Moreover, a series of virtual experiments are performed on the representative graphene lattice. Following these results, the constitutive model development is based on the well established continuum mechanics framework, that is, the non-linear membrane theory which includes the hyperelastic model in terms of principal stretches. A proof-of-concept and performance is shown on a simple model problem where the hyperelastic strain energy density function is chosen in polynomial form.
Journal of the Mechanics and Physics of Solids
We consider a discrete model of a graphene sheet with atomic interactions governed by a harmonic approximation of the 2nd-generation Brenner potential that depends on bond lengths, bond angles, and two types of dihedral angles. A continuum limit is then deduced that fully describes the bending behavior. In particular, we deduce for the first time an analytical expression of the Gaussian stiffness, a scarcely investigated parameter ruling the rippling of graphene, for which contradictory values have been proposed in the literature. We disclose the atomic-scale sources of both bending and Gaussian stiffnesses and provide for them quantitative evaluations.