A unit-cell-based three-dimensional molecular mechanics analysis for buckling load, effective elasticity and Poisson's ratio determination of the nanosheets

References

• Oberlin A, Endo M, Koyama T. Filamentous growth of carbon through benzene decomposition. J Cryst Growth. 1976;32:335–349.
   Web of Science ®Google Scholar
• Iljima S. Helical microtubules of graphitic carbon. Lett Nature. 1991;354:56–58.
   Web of Science ®Google Scholar
• Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric field effect in atomically thin carbon films. Science. 2004;306:666–669.
   PubMed Web of Science ®Google Scholar
• Chopra NG, Luyken RJ, Cherry L, Crespi VH, Cohen ML, Louie SG, et al. Boron Nitride nanotubes. Science. 1995;269:966–967.
   PubMed Web of Science ®Google Scholar
• Corso M, Auwarter W, Muntwiler M, Tamai A, Greber T, Osterwalder J. Boron nitride nanomesh. Science. 2004;303:217–220.
   PubMed Web of Science ®Google Scholar
• Han WQ, Wu L, Zhu Y, Watanabe K, Taniguchi T. Structure of chemically derived mono- and few-atomic-layer boron nitride sheets. Appl Phys Lett. 2008;93:223103.
   Web of Science ®Google Scholar
• Zeng H, Zhi Ch, Zhang Z, Wei X, Wang X, Guo W, et al. White graphenes: boron nitride nanoribbons via Boron Nitride unwrapping. Nano Lett. 2010;10:5049–5055.
   PubMed Web of Science ®Google Scholar
• Song L, Ci L, Lu H, Sorokin PB, Jin Ch, Ni J, et al. Large scale growth and characterization of atomic hexagonal boron nitride layers. Nano Lett. 2010;10:3209–3215.
   PubMed Web of Science ®Google Scholar
• Lee KH, Shin HJ, Lee J, Lee I, Kim G, Choi JY, et al. Large-scale synthesis of high-quality hexagonal boron nitride nanosheets for large-area graphene electronics. Nano Lett. 2012;12:714–718.
   PubMed Web of Science ®Google Scholar
• Pakdel A, Bando Y, Golberg D. Nano boron nitride flatland. Chem Soc Rev. 2014;43:934–959.
   PubMed Web of Science ®Google Scholar
• Sofo JO, Chaudhari AS, Barber GD. Graphane: a two-dimensional hydrocarbon. Phys. Rev. B. 2007;75:153401.
   Web of Science ®Google Scholar
• Pei QX, Zhang YW, Shenoy VB. A molecular dynamics study of the mechanical properties of hydrogen functionalized graphene. Carbon. 2010;48:898–904.
   Web of Science ®Google Scholar
• Lamari FD, Levesque D. Hydrogen absorption on functionalized graphene. Carbon. 2011;49:5196–5200.
   Web of Science ®Google Scholar
• Huang J, Wong CH. Thickness, chirality and pattern dependence of elastic properties of hydrogen functionalized graphene. Comput. Mater. Sci. 2014;92:192–198.
   Web of Science ®Google Scholar
• Hao X, Qiang H, Xiaohu Y. Buckling of defective single-walled and double-walled carbon nanotubes under axial compression by molecular dynamics simulation. Compos. Sci. Tech. 2008;68:1809–1814.
   Web of Science ®Google Scholar
• Neek-Amal M, Peeters FM. Linear reduction of stiffness and vibration frequencies in defected circular monolayer grapheme. Phys. Rev. B. 2010;81:235437.
   Web of Science ®Google Scholar
• Ajori S, Ansari R, Mirnezhad M. Mechanical properties of defective γ-graphyne using molecular dynamics simulations. Mater Sci. Eng. A. 2013;561:34–39.
   Web of Science ®Google Scholar
• Mortazavi B, Remond Y. Investigation of tensile response and thermal conductivity of boron-nitride nanosheets using molecular dynamics simulation. Phys. E. 2012;44:1846–1852.
   Web of Science ®Google Scholar
• Wagner P, Ivanovskaya VV, Rayson MJ, Briddon P, Ewels CP. Mechanical properties of nanosheets and nanotubes using a new geometry independent volume definition. J. Phys. Cond. Matter. 2013;25:155302.
   PubMed Web of Science ®Google Scholar
• Andrew RC, Mapasha RE, Ukpong AM, Chetty N. Mechanical properties of graphene and boronitrene. Phys. Rev. B. 2012;85:125428.
   Web of Science ®Google Scholar
• Kudin KN, Scuseria GE, Yakobson BI. C2F BN and C nanoshell elasticity from ab initio computations. Phys. Rev. B. 2001;64:235406.
   Web of Science ®Google Scholar
• Peng Q, Ji W, De S. Mechanical properties of the hexagonal boron nitride monolayer: Ab initio study. Comput. Mater Sci. 2012;56:11–17.
   Web of Science ®Google Scholar
• Peng Q, Zamiri AR, Ji W, De S. Elastic properties of hybrid graphene/boron nitride monolayer. Acta Mech. 2012;223:2591–2596.
   Web of Science ®Google Scholar
• Li C, Chou TW. A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 2003;40:2487–2499.
   Web of Science ®Google Scholar
• Moon WH, Hwang HJ. Molecular mechanics of structural properties of boron nitride nanotubes. Phys. E. 2004;23:26–30.
   Web of Science ®Google Scholar
• Tserpes KI, Papanikos P. Finite element modeling of single-walled carbon nanotubes. Compos. Part B. 2005;36:468–477.
   Web of Science ®Google Scholar
• Scarpa F, Adhikari S, Phani AS. Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology. 2009;20:065709.
   PubMed Web of Science ®Google Scholar
• Scarpa F, Adhikari S, Gil AJ, Remillat C. The bending of single layer graphene sheets: the lattice versus continuum approach. Nanotechnology. 2010;21:125702.
   PubMed Web of Science ®Google Scholar
• Song J, Huang Y, Jiang H, Hwang KC, Yu MF. Deformation and bifurcation analysis of boron-nitride nanotubes. Int. J. Mech. Sci. 2006;48:1197–1207.
   Web of Science ®Google Scholar
• Song J, Wu J, Huang Y, Hwang KC. Continuum modeling of boron nitride nanotubes. Nanotechnology. 2008;19:445705.
   PubMed Web of Science ®Google Scholar
• Jiang L, Guo W. A molecular mechanics study on size-dependent elastic properties of single-walled boron nitride nanotubes. J Mech Phys Solids. 2011;59:1204–1213.
   Web of Science ®Google Scholar
• Le MQ. Prediction of Young's Modulus of hexagonal monolayer sheets based on molecular mechanics. Int J Mech Mater Design. 2015;11:15–24.
   Web of Science ®Google Scholar
• Garg A, Tai K. Genetic programming for modeling vibratory finishing process: Role of experimental designs and fitness functions. Lect. Notes Comput Sci. 2013;8298:23–23.
   Google Scholar
• Garg A, Garg A, Tai K, Barontini S, Stokes A. A Computational intelligence-based genetic programming approach for the simulation of soil water retention curves. Trans Porous Med. 2014;103:497–513.
   Web of Science ®Google Scholar
• Garg A, Tai K. Stepwise approach for the evolution of generalized genetic programming model in prediction of surface finish of the turning process. Adv Eng Software. 2014;78:16–27.
   Web of Science ®Google Scholar
• Garg A, Tai K. An ensemble approach of machine learning in evaluation of mechanical property of the rapid prototyping fabricated prototype. Appl Mech Mater. 2014;575:493–496.
   Google Scholar
• Vijayaraghavan1 V, Garg A, Wong CH, Tai K, Regalla SP, Tsai MC. Density characteristics of laser-sintered three-dimensional printing parts investigated by using an integrated finite element analysis-based evolutionary algorithm approach. Proc Inst Mech Eng Part B: J Eng Manufact. 2014 :0954405414558131.
   Google Scholar
• Garg A, Vijayaraghavan V, Wonga CH, Tai K, Sumithra K, Gao L, Singru PM. Combined CI-MD approach in formulation of engineering moduli of single layer graphene sheet. Simul Model Pract Theory. 2014;48:93–111.
   Web of Science ®Google Scholar
• Vijayaraghavan V, Garg A, Wong CH, Tai K, Sumithra K, Singru PM, Gao L, Mahapatra SS. On the study of machining characteristics of 2-D nanoscale material. Nanosci Nanotechnol Lett. 2014;6(12):1079–1086.
   Web of Science ®Google Scholar
• Garg A, Vijayaraghavan V, Wonga CH, Tai K, Singru PM, Mahapatra SS, Sangwan KS. Investigation of mechanical strength of 2D nanoscale structures using a molecular dynamics based computational intelligence approach. Int J Mod Phys B. 2015;29(1):1450242(18).
   Web of Science ®Google Scholar
• Wang CM, Zhang YY, Ramesh SS, Kitipornchai S. Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory. J Phys D. 2006;39:3904–3909.
   Google Scholar
• Wang Q, Duan WH, Liew KM, He XQ. Inelastic buckling of carbon nanotubes. Appl Phys Lett. 2007;90:033110.
   Web of Science ®Google Scholar
• Pradhan SC. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys Lett A. 2009;373:4182–4188.
   Web of Science ®Google Scholar
• Samaei AT, Abbasion S, Mirsayar MM. Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory. Mech Res Commun. 2011;38:481–485.
   Web of Science ®Google Scholar
• Wang Q, Wang CM. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes. Nanotechnology. 2007;18:075702.
   PubMed Web of Science ®Google Scholar
• Arash B, Wang Q. A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput Mater Sci. 2012;51:303–313.
   Web of Science ®Google Scholar
• Narendar S. Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects. Compos Struct. 2011;93:3093–3103.
   Web of Science ®Google Scholar
• Farajpour A, Mohammadi M, Shahidi AR, Mahzoon M. Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Phys E. 2011;43:1820–1825.
   Web of Science ®Google Scholar
• Farajpour A, Shahidi AR, Mohammadi M, Mahzoon M. Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics. Compos Struct. 2012;94:1605–1615.
   Web of Science ®Google Scholar
• Narendar S, Gopalakrishnan S. Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory. Acta Mech. 2012;223:395–413.
   Web of Science ®Google Scholar
• Ansari R, Rouhi S, Aryayi M, Mirnezhad M. On the buckling behavior of single-walled silicon carbide nanotubes. Sci Iran. 2012;19:1984–1990.
   Web of Science ®Google Scholar
• Tourki Samaei A. Hosseini Hashemi Sh. Buckling analysis of graphene nanosheets based on nonlocal elasticity theory. Int J Nano Dim. 2012;2:227–232.
   Google Scholar
• Ansari R, Rouhi S, Mirnezhad M, Aryayi M. Stability characteristics of single-layered silicon carbide nanosheets under uniaxial compression. Phys E. 2013;53:22–28.
   Web of Science ®Google Scholar
• Bedroud M, Hosseini-Hashemi S, Nazemnezhad R. Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity. Acta Mech. 2013;224:2663–2676.
   Web of Science ®Google Scholar
• Hosseini-Hashemi S, Kermajani M, Nazemnezhad R. An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory. Europ J Mech A/Solids. 2015: 5129–5143.
   Google Scholar
• Rappe AK, Casewit CJ, Colwell KS, Goddard WA, Skiff WM. UFF a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc. 1992;114:10024–10035.
   Web of Science ®Google Scholar
• Kaneko T. On Timoshenko's correction for shear in vibrating beams. J Phys D Appl Phys. 1975;8:1927–1936.
   Web of Science ®Google Scholar
• Boldrin L, Scarpa F, Chowdhury R, Adhikari S. Effective mechanical properties of hexagonal boron nitride nanosheets. Nanotechnology. 2011;22:505702.
   PubMed Web of Science ®Google Scholar
• Chowdhurry R, Wang CY, Adhikari S, Scarpa F. Vibration and symmetry-breaking of boron nitride nanotubes. Nanotechnology. 2010;21:365702.
   PubMed Web of Science ®Google Scholar
• Casewit CJ, Colwell KS, Rappe AK. Application of a universal force field to main group compounds. J Am Chem Soc. 1992;114:10046–10053.
   Web of Science ®Google Scholar
• Casewit CJ, Colwell KS, Rappe AK. Application of universal force field to organic molecules. J Am Chem Soc. 1992;114:10035–10046.
   Web of Science ®Google Scholar
• Rappe AK, Colwell KS, Casewit CJ. Application of a universal force field to metal complexes. Inorg Chem. 1993;32:3438–3450.
   Web of Science ®Google Scholar
• Si MS, Li JY, Shi HG, Niu XN, Xue DS. Divacancies in graphitic boron nitride sheets. EPL. 2009;86:46002.
   Web of Science ®Google Scholar
• Akdim B, Kim SN, Naik RR, Maruyama B, Pender MJ, Pachter R. Understanding effects of molecular adsorption at a single-wall boron nitride nanotube interface from density functional theory calculations. Nanotechnology. 2009;20:355705.
   PubMed Web of Science ®Google Scholar
• Mirzaei M, Giahi M. Computational investigation of the electronic and structural properties of ultra-small-diameter boron nitride nanotubes. Phys B. 2010;405:2542–2544.
   Web of Science ®Google Scholar
• Boresi AP, Schmidt RJ. Advanced mechanics of materials. 6th Ed John Wiley and Sons Inc., New York; 2003.
   Google Scholar
• Ugural AC. Stresses in plates and shells. 3rd Ed. CRC Press, Boca Raton; 2009.
   Google Scholar
• Panchal MB, Upadhyay SH. Boron nitride nanotube-based biosensor for acetone detection: molecular mechanics-based simulation. Mol Sim. 2014;40:1035–1042.
   Web of Science ®Google Scholar
• Le MQ. Young's modulus prediction of hexagonal nanosheets and nanotubes based on dimensional analysis and atomistic simulations. Meccanica. 2014;49:1709–1719.
   Web of Science ®Google Scholar
• Verma V, Jindal VK, Dharamvir K. Elastic moduli of a boron nitride nanotube. Nanotechnology. 2007;18:435711.
   Web of Science ®Google Scholar
• Panchal MB, Upadhyay SH. Vibrational characteristics of defective single walled BN nanotube based nanomechanical mass sensors: Extended defect or dislocation line. Sens Actuators A Phys. 2013;203:160–167.
   Web of Science ®Google Scholar
• Mayo SL, Olafson BD, Goddard WA. DREIDING: A generic force field for molecular simulations. J Phys Chem. 1990;94:8897–8909.
   Web of Science ®Google Scholar
• Bosak A, Serrano J, Krisch M, Watanabe K, Taniguchi T, Kanda H. Elasticity of hexagonal boron nitride: Inelastic x-ray scattering measurements. Phys Rev B. 2006;73:041402.
   Web of Science ®Google Scholar
• Oh ES. Elastic properties of various Boron-Nitride structures. Metals Mater Int. 2011;17:21–27.
   Web of Science ®Google Scholar
• Oh ES. Elastic properties of boron-nitride nanotubes through the continuum lattice approach. Mater Lett. 2010;64:859–862.
   Web of Science ®Google Scholar
• Santosh M, Maiti PK, Sood AK. Elastic Properties of Boron Nitride Nanotubes and Their Comparison with Carbon Nanotubes. J Nanosci Nanotech. 2009;9:5425–5430.
   PubMed Web of Science ®Google Scholar