On the plastic buckling of curved carbon nanotubes - Publication - MOST Wiedzy


On the plastic buckling of curved carbon nanotubes


This research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stress-strain is concerned with Ramberg–Osgood law on the basis of deformation and flow theories of plasticity. To seize the nano-mechanical behavior of the CCNT, the nonlocal strain gradient elasticity theory is taken into account. The obtained differential equations are solved using the Rayleigh–Ritz method based on a new admissible shape function which is able to analyze stability problems. To authorize the solution, some comparisons are illustrated which show a very good agreement with the published works. Conclusively, the best findings confirm that a plastic analysis is crucial in predicting the mechanical strength of CCNTs.


  • 3


  • 0

    Web of Science

  • 2



artykuły w czasopismach
Published in:
Theoretical and Applied Mechanics Letters no. 10, pages 46 - 56,
ISSN: 2095-0349
Publication year:
Bibliographic description:
Malikan M.: On the plastic buckling of curved carbon nanotubes// Theoretical and Applied Mechanics Letters -Vol. 10,iss. 1 (2020), s.46-56
Digital Object Identifier (open in new tab) 10.1016/j.taml.2020.01.004
Bibliography: test
  1. J. Chakrabarty, Applied Plasticity, 2nd Edition, Springer, New York, 2000. open in new tab
  2. K. Song, Y. Zhang, J. Meng, et al., Structural polymer-based car- bon nanotube composite fibers: Understanding the processing- structure-performance relationship, Materials 6 (2013) 2543-2577. open in new tab
  3. I. Mehdipour, A. Barari, A. Kimiaeifar, et al., Vibrational analys- is of curved single-walled carbon nanotube on a Pasternak elastic foundation, Advances in Engineering Software 48 (2012) 1-5. open in new tab
  4. E. Cigeroglu, H. Samandari, Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method, Physica E 64 (2014) 95-105. open in new tab
  5. F.N. Mayoof, M.A. Hawwa, Chaotic behavior of a curved car- bon nanotube under harmonic excitation, Chaos, Solitons and Fractals 42 (2009) 1860-1867. open in new tab
  6. P. Soltani, A. Kassaei, M.M. Taherian, Nonlinear and quasi-lin- ear behavior of a curved carbon nanotube vibrating in an elec- tric force field; analytical approach, Acta Mechanica Solida Sin- ica 27 (2014) 97-110. open in new tab
  7. M. Arefi, A. Zenkour, Influence of magneto-electric environ- ments on size-dependent bending results of three-layer piezo- magnetic curved nanobeam based on sinusoidal shear deform- ation theory, Journal of Sandwich Structures Materials 21 (2017) 2751-2778. open in new tab
  8. N. Mohamed, M.A. Eltaher, S.A. Mohamed, et al., Numerical open in new tab
  9. analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations, Inter- national Journal of Non-Linear Mechanics 101 (2018) 157-173. open in new tab
  10. M. Nejati, R. Dimitri, F. Tornabene, et al., Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by func- tionally graded wavy carbon nano-tubes with temperature-de- pendent properties, Applied Sciences 7 (2017) 1-24. open in new tab
  11. G.-L. She, F.-G. Yuan, B. Karami, et al., On nonlinear bending behavior of FG porous curved nanotubes, International Journal of Engineering Science 135 (2019) 58-74. open in new tab
  12. H.Y. Sarvestani, H. Ghayoor, Free vibration analysis of curved nanotube structures, International Journal of Non-Linear Mechanics 86 (2016) 167-173. open in new tab
  13. B. Wang, Z. Deng, H. Ouyang, et al., Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory, Physica E 66 (2015) 283-292. open in new tab
  14. M. Malikan, V.B. Nguyen, R. Dimitri, et al., Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory, Material Re- search Express 6 (2019) 075041. open in new tab
  15. P. Bijlaard, On the plastic buckling of plates, Journal of Aero- nautical Sciences 17 (1950) 485-493. open in new tab
  16. D. Durban, Z. Zuckerman, Elastoplastic buckling of rectangular plates in biaxial compression/tension, International Journal of Mechanical Sciences 41 (1999) 751-765. open in new tab
  17. J.W. Hutchinson, Plastic buckling, Advances in Applied Mech- anics 14 (1970) 67-144. open in new tab
  18. X.M. Wang, J.C. Huang, Elastic/plastic buckling analyses of rectangular plates under biaxial loadings by the differential quadrature method, Thin-Walled Structures 47 (2009) 879-889. open in new tab
  19. W. Zhang, X.W. Wang, Elastic/plastic buckling analysis of thick rectangular plates by using the differential quadrature method, Computers & Mathematics with Applications 61 (2011) 44-61. open in new tab
  20. M. Kadkhodayan, M. Maarefdoust, Elastic/plastic buckling of isotropic thin plates subjected to uniform and linearly varying in-plane loading using incremental and deformation theories, Aerospace Science and Technology 32 (2014) 66-83. open in new tab
  21. E. Ruocco, Elastoplastic buckling analysis of thin-walled struc- tures, Aerospace Science and Technology 43 (2015) 176-190. open in new tab
  22. T.M. Aung, C.M. Wang, J. Chakrabarty, Plastic buckling of mod- erately thick annular plates, International Journal of Structural Stability and Dynamics 5 (2005) 337-357. open in new tab
  23. E. Ore, D. Durban, Elastoplastic buckling of annular plates in pure shear, Journal of Applied Mechanics 56 (1989) 644-651. open in new tab
  24. F. Kosel, B. Bremec, Elastoplastic buckling of circular annular plates under uniform in-plane loading, Thin-Walled Structures 42 (2004) 101-117. open in new tab
  25. C.M. Wang, Y. Xiang, J. Chakrabarty, Elastic/plastic buckling of thick plates, International Journal of Solids and Structures 38 (2001) 8617-8640. open in new tab
  26. P.L. Grognec, A. Le van, On the plastic bifurcation and post-bi- furcation of axially compressed beams, International Journal of Non-Linear Mechanics 46 (2011) 693-702. open in new tab
  27. J. Legendre, P.L. Grognec, C. Doudard, et al., Analytical, numer- ical and experimental study of the plastic buckling behavior of thick cylindrical tubes under axial compression, International Journal of Mechanical Sciences 156 (2019) 494-505. open in new tab
  28. U. Lepik, On dynamic buckling of elastic-plastic beams, Inter- national Journal of Non-Linear Mechanics 35 (2000) 721-734. open in new tab
  29. M. Sato, Elastic and plastic deformation of carbon nanotubes, open in new tab
  30. Procedia Engineering 14 (2011) 2366-2372. open in new tab
  31. M.M.S. Fakhrabadi, V. Norouzifard, M. Dadashzadeh, On the atomistic simulation of elastic, plastic, buckling and post-buck- ling behaviors of carbon nanotubes, International Review of Mechanical Engineering 5 (2011) 1053-1056. open in new tab
  32. H. Shima, M. Sato, Elastic and Plastic Deformation of Carbon Nanotubes, CRC Press, Technology & Engineering, (2013). ht- tps://doi.org/10.1201/b15420 open in new tab
  33. W. Ramberg, W. R. Osgood, Description of Stress-strain Curves by Three Parameters, NACA Technical Note No. 902, Washing- ton DC, USA (1943). open in new tab
  34. X. Song, S.-R. Li, Thermal buckling and post-buckling of pinned-fixed Euler-Bernoulli beams on an elastic foundation, Mechanics Research Communications 34 (2007) 164-171. open in new tab
  35. L. Li, H. Tang, Y. Hu, Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature, Composite Structures 184 (2018) 1177-1188. open in new tab
  36. C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasti- city and strain gradient theory and Its Applications in wave propagation, Journal of the Mechanics and Physics of Solids 78 (2015) 298-313. open in new tab
  37. W.-H. Duan, C.-M. Wang, Y.-Y. Zhang, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of Applied Physics 101 (2007) 24305. open in new tab
  38. R. Ansari, S. Sahmani, B. Arash, Nonlocal plate model for free vibrations of single-layered graphene sheets, Physics Letters A 375 (2010) 53-62. open in new tab
  39. M. Malikan, V.B. Nguyen, F. Tornabene, Damped forced vibra- tion analysis of single-walled carbon nanotubes resting on vis- coelastic foundation in thermal environment using nonlocal strain gradient theory, Engineering Science and Technology 21 (2018) 778-786. open in new tab
  40. M. Malikan, V.B. Nguyen, Buckling analysis of piezo-magneto- electric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures 102 (2018) 8-28. open in new tab
  41. M. Malikan, R. Dimitri, F. Tornabene, Effect of sinusoidal cor- rugated geometries on the vibrational response of viscoelastic nanoplates, Applied Sciences 8 (2018) 1432. open in new tab
  42. M. Malikan, V.B. Nguyen, F. Tornabene, Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory, Materials Research Express 5 (2018) 075031. open in new tab
  43. M. Malikan, R. Dimitri, F. Tornabene, Transient response of os- cillated carbon nanotubes with an internal and external damp- ing, Composites: Part B 158 (2019) 198-205. open in new tab
  44. S.K. Jena, S. Chakraverty, M. Malikan, Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium, Engineering with Com- puters (2019). https://doi.org/10.1007/s00366-019-00883-1 open in new tab
  45. S.K. Jena, S. Chakraverty, M. Malikan, et al., Stability analysis of single-walled carbon nanotubes embedded in winkler founda- tion placed in a thermal environment considering the surface effect using a new refined beam theory, Mechanics Based Design of Structures and Machines (2019). open in new tab
  46. https://doi.org/10.1080/15397734.2019.1698437 open in new tab
  47. G.L. She, F.G. Yuan, Y.R. Ren, et al., Nonlinear bending and vi- bration analysis of functionally graded porous tubes via a non- open in new tab
  48. local strain gradient theory, Composite Structures 203 (2018) 614-623. open in new tab
  49. G.L. She, K.M. Yan, Y.L. Zhang, et al, Wave propagation of func- tionally graded porous nanobeams based on non-local strain gradient theory, European Physical Journal Plus 133 (2018) 368. open in new tab
  50. R. Ansari, S. Sahmani, H. Rouhi, Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh-Ritz technique, Computational Materials Science 50 (2011) 3050-3055. open in new tab
  51. K.K. Pradhan, S. Chakraverty, Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz meth- od, Composites: Part B 51 (2013) 175-184. open in new tab
  52. M. Teifouet, A. Robinson, S. Adali, Buckling of nonuniform car- bon nanotubes under concentrated and distributed axial loads, Mechanical Sciences 8 (2017) 299-305. open in new tab
  53. M. Teifouet A. Robinson, S. Adali, Buckling of nonuniform and axially functionally graded nonlocal Timoshenko nanobeams on Winkler-Pasternak foundation, Composite Structures 206 (2018) 95-103.
  54. M. Malikan, M.N. Sadraee Far, Differential quadrature method for dynamic buckling of graphene sheet coupled by a vis- coelastic medium using neperian frequency based on nonlocal elasticity theory, Journal of Applied and Computational Mech- anics 4 (2018) 147-160. open in new tab
  55. M. Malikan, M. Jabbarzadeh, S. Dastjerdi, Non-linear static sta- bility of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasti- city using nonlocal continuum, Microsystem Technologies 23 (2017) 2973-2991. open in new tab
  56. M.E. Golmakani, M. Malikan, M.N. Sadraee Far, et al., Bending and buckling formulation of graphene sheets based on nonloc- al simple first order shear deformation theory, Materials Re- search Express 5 (2018) 065010. open in new tab
  57. M.E. Golmakani, M. Ahmadpour, M. Malikan, Thermal buck- ling analysis of circular bilayer graphene sheets resting on an elastic matrix based on nonlocal continuum mechanics, Journ- al of Applied and Computational Mechanics (2019). DOI:10.22055/JACM.2019.31299.1859 open in new tab
  58. C.M. Wang, Y.Y. Zhang, S.S. Ramesh, et al., Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory, Journal of Physics D: Applied Physics 39 (2006) 3904-3909. open in new tab
  59. S.C. Pradhan, G.K. Reddy, Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasti- city theory and DTM, Computational Materials Science 50 (2011) 1052-1056. open in new tab
  60. J.B. Gunda, Thermal post-buckling & large amplitude free vi- bration analysis of Timoshenko beams: Simple closed-form solutions, Applied Mathematical Modelling 38 (2014) 4548-4558. open in new tab
  61. R. Ansari, S. Sahmani, H. Rouhi, Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions, Physics Letters A 375 (2011) 1255-1263. open in new tab
  62. W.H. Duan, C.M. Wang, Exact solutions for axisymmetric bend- ing of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18 (2007) 385704. open in new tab
  63. A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54 (1983) 4703-4710. open in new tab
  64. B.I. Yakobson, C.J. Brabec, J. Bernholc, Nanomechanics of car- open in new tab
  65. bon tubes: instabilities beyond linear response, Physical Re- view Letters 76 (1996) 2511-2514. open in new tab
  66. R.E. Miller, V.B. Shenoy, Size-dependent elastic properties of nanosized structural elements, Nanotechnology 11 (2000) 139. open in new tab
  67. X. Chen, C.Q. Fang, X. Wang, The influence of surface effect on vibration behaviors of carbon nanotubes under initial stress, Physica E 85 (2017) 47-55. open in new tab
  68. L. Li, Y. Hu, Post-buckling analysis of functionally graded nano- beams incorporating nonlocal stress and microstructure-de- pendent strain gradient effects, International Journal of Mech- open in new tab
  69. anical Sciences 120 (2017) 159-170. open in new tab
  70. Q. Ma, D.R. Clarke, Size Dependent Hardness in Silver Single Crystals, Journal of Materials Research 10 (1995) 853-863. open in new tab
  71. W.J. Pooleh, M.F. Ashby, N.A. Fleck, Micro-Hardness of An- nealed and Work-Hardened Copper Polycrystals, Scripta Ma- terialia 34 (1996) 559-564. open in new tab
  72. Y.Y. Lim, M.M. Chaudhri, Effect of the Indenter Load on the Nano hardness of Ductile Metals: An Experimental Study of Polycrystalline Work-Hardened and Annealed Oxygen-Free Copper, Philosophical Magazine A 79 (1999) 2979-3000.
Verified by:
Gdańsk University of Technology

seen 3 times

Recommended for you

Meta Tags