Simple model potential for the description of elastic properties of single-layer graphene (original) (raw)
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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.
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.
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.
Bending Rigidity and Gaussian Bending Stiffness of Single-Layered Graphene
Nano Letters, 2013
Bending rigidity and Gaussian bending stiffness are the two key parameters that govern the rippling of suspended graphenean unavoidable phenomenon of twodimensional materials when subject to a thermal or mechanical field. A reliable determination about these two parameters is of significance for both the design and the manipulation of graphene morphology for engineering applications. By combining the density functional theory calculations of energies of fullerenes and single wall carbon nanotubes with the configurational energy of membranes determined by Helfrich Hamiltonian, we have designed a theoretical approach to accurately determine the bending rigidity and Gaussian bending stiffness of single-layered graphene. The bending rigidity and Gaussian bending stiffness of single-layered graphene are 1.44 eV (2.31 × 10 −19 N m) and −1.52 eV (2.43 × 10 −19 N m), respectively. The bending rigidity is close to the experimental result. Interestingly, the bending stiffness of graphene is close to that of lipid bilayers of cells about 1−2 eV, which might mechanically justify biological applications of graphene.
Solid State Communications Elastic properties of single-layered graphene sheet
An atomistic simulation method is adopted to investigate the elastic characteristics of defect-free single-layered graphene sheet (SLGS). To this end, the equivalent structural beam is employed to model interatomic forces of the covalently bonded carbon atoms. The beam properties are computed by considering the covalent bond stiffnesses. To calculate the Young's modulus, shear modulus and Poisson's ratio of the SLGS, the equivalent continuum sheet model is proposed and the effect of chirality on the SLGS elastic properties is examined. It is perceived that there exists a good agreement between the atomistic modeling results and the data available in the literature.
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.
Edge elastic properties of defect-free single-layer graphene sheets
Applied Physics Letters, 2009
An energetic model is proposed to describe the edge elastic properties of defect-free single-layer graphene sheets. Simulations with the adaptive intermolecular reactive empirical bond order potential are used to extract the edge stress and edge moduli for different edges structures, namely, zigzag and armchair edges, zigzag and armchair edges terminated with hydrogen, and reconstructed zigzag and armchair edges. It is found that the properties of graphene are sensitively dependent on the edge structures; armchair and zigzag edges with and without hydrogen termination are in compression, while reconstructed edges are in tension.
Nonlinear Elasticity of Monolayer Graphene
By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.
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.