Biaxial Buckling of Single Layer Graphene Sheet Based on Nonlocal Plate Model and Molecular Dynamics Simulation
The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1130007Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF
 Ma, Q. and Clarke, D. R. (1995), “Size dependent Hardness of Silver Single Crystals”, Materials Research, Vol. 10, pp. 853-63.
 Ebrahimi, F. Salari, E. (2015), “Thermal buckling and free vibration analysis of size dependent Timoshenko FG”, Composite Structures, vol. 128, pp. 363-380.
 Murmu, T. and Pradhan, S.C. (2009), “Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model”, Physica E, Volume 41, Issue 8, pp. 1628-1633.
 R, Ansari, S., Sahmani, (2013), “Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations”, Applied Mathematical Modelling, Volume 37, Issues 12–13, Pages 7338–7351.
 S. Kitipornchai, X.Q. He, K.M. Liew (2005), “Continuum model for the vibration of multilayered graphene sheets,” Phys. Rev. B 72 075443.
 K.M. Liew, X.Q. He, S. Kitipornchai (2006), “Continuum model for the vibration of multilayered graphene sheets,” Acta Mater. 54 4229.
 R, Ansari, R, Rajabiehfard, B., Arash, B. (2010),“Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets”, Computational Materials Science, Volume 49, Issue 4, pp. 831-838..
 L. Shen, H.S. Shen, C.L. Zhang (2010), “Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments,” Comput. Mater. Sci. 48 680.
 S.C. Pradhan, J.K. Phadikar, (2009), “Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models,” Phys. Lett. A 373 1062.
 T S. Narendar, S. Gopalakrishnan, (2009), “Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes”, Comput. Mater. Sci. 47 - 526...
 B. Arash, R. Ansari, (2010), “Evaluation of nonlocal parameter in the vibrations of single-walled carbon nanotubes with initial strain,” Physica E 42 - 2058.
 M.J. Hao, X.M. Guo, Q. Wang, Eur. J. (2010), “Small-scale effect on torsional buckling of multi-walled carbon nanotubes,” Mech. A/Solids 29 (2010) 49.
 T. Natsuki, X.W. Lei, Q.Q. Ni, M. Endo, (2010), “Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium,” Phys. Lett. A 374 -2670.
 A.C. Eringen, J. Appl. (1983), “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” Phys. 54, 4703.
 S.K. Jang, C.W. Bert, A.G. Striz, (1989), “Application of differential quadrature to static analysis of structural components,” Int J. Num. Methods Eng. 28, 561
 R. Bellman, B.G. Kashef, J. Casti, J. (1972), “Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations”, Comput. Phys. 10, 40
 A.N. Sherbourne, M.D. Pandey, (1991), “Differential quadrature method in the buckling analysis of beams and composite plates,” Comput. Struct. 40, 903
 C. Shu, (2000), “Differential quadrature and its application in engineering,” Springer, Berlin.
 H.-S. Shen, C.-L. Zhang (2006), “Postbuckling prediction of axially loaded double-walledcarbon nanotubes with temperature dependent properties and initial defects”, Phys. Rev. B 74 035410.
 H.-S. Shen, C.-L. Zhang (2007), “Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axialand radial mechanical loads,” Int. J. Solids Struct. 44 1461–1487.
 S. Plimpton (1995), “Fast parallel algorithms for short-range molecular dynamics,” J.Comput. Phys. 117 1–19.
 W. Humphrey, A. Dalke, K. Schulten, (1996) “VMD: visual molecular dynamics” J. Mole. Graph. 14 33–38.
 S.J. Stuart, A.B. Tutein, J.A. Harrison, (2000) “A reactive potential for hydrocarbons with intermolecular interactions”, J. Chem. Phys. 112 6472.
 P.M. Agrawal, B.S. Sudalayandi, L.M. Raff, R. Komanduri, (2006) “A comparison of different methods of Young's modulus determination for single-wall carbon nanotubes (SWCNT) using molecular dynamics (MD) simulations” Comput. Mater. Sci. 38, 271.
 K. Mylvaganam, L. Zhang (2004), “Important issues in a molecular dynamics simulation for characterising the mechanical properties of carbon nanotubes”, Carbon 42, 2025.