Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction

doi:10.1007/s10483-022-2909-6

Abstract

Abstract: The structural instability of multi-walled carbon nanotubes (MWCNTs) has captured extensive attention due to the unique characteristic of extremely thin hollow cylinder structure. The previous studies usually focus on the buckling behavior without considering the effects of the wall number and initial pressure. In this paper, the axial buckling behavior of MWCNTs with the length-to-outermost radius ratio less than 20 is investigated within the framework of the Donnell shell theory. The governing equations for the infinitesimal buckling of MWCNTs are established, accounting for the van der Waals (vdW) interaction between layers. The effects of the wall number, initial pressure prior to buckling, and aspect ratio on the critical buckling mode, buckling load, and buckling strain are discussed, respectively. Specially, the four-walled and twenty-walled CNTs are studied in detail, indicating the fact that the buckling instability may occur in other layers besides the outermost layer. The obtained results extend the buckling analysis of the continuum-based model, and provide theoretical support for the application of CNTs.

Key words: multi-walled carbon nanotubes (MWCNTs), buckling load, cylindrical shell model, instability region, buckling mode

2010 MSC Number:

37K05
37M15

Xinlei LI, Jianfei WANG. Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1857-1872.

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References

[1] KUMAR, S., RANI, R., DILBAGHI, N., TANKESHWAR, K., and KIM, K. H. Carbon nanotubes: a novel material for multifaceted applications in human healthcare. Chemical Society Reviews, 46, 158–196(2017)
[2] YUAN, Y., ZHAO, K., SAHMANI, S., and SAFAEI, B. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes. Applied Mathematics and Mechanics (English Edition), 41(4), 587–604(2020) https://doi.org/10.1007/s10483-020-2600-6
[3] SUN, T., GUO, J., and PAN, E. Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium. Applied Mathematics and Mechanics (English Edition), 42(8), 1077–1094(2021) https://doi.org/10.1007/s10483-021-2743-6
[4] IIJIMA, S. Helical microtubes of graphitic carbon. nature, 354, 56–58(1991)
[5] BAI, Y., ZHANG, R., YE, X., ZHU, Z., XIE, H., SHEN, B., CAI, D., LIU, B., ZHANG, C., JIA, Z., ZHANG, S., LI, X., and WEI, F. Carbon nanotube bundles with tensile strength over 80 GPa. Nature Nanotechnology, 13, 589–595(2018)
[6] BHATTACHARYYA, A., SETH, G. S., KUMAR, R., and CHAMKHA, A. J. Simulation of Cattaneo-Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial rotating disks. Journal of Thermal Analysis and Calorimetry, 139, 1655– 1670(2019)
[7] ABBASI, S. A., KIM, T. H., SOMU, S., WANG, H., CHAI, Z., UPMANYU, M., and BUSNAINA, A. Fabrication of a nanoelectromechanical bistable switch using directed assembly of SWCNTs. Journal of Physics D: Applied Physics, 53, 23LT02(2020)
[8] SAMY, M. M., MOHAMED, M. G., EL-MAHDY, A. F. M., MANSOURE, T. H., WU, K. C., and KUO, S. W. High-performance supercapacitor electrodes prepared from dispersions of tetrabenzonaphthalene-based conjugated microporous polymers and carbon nanotubes. ACS Applied Materials and Interfaces, 13, 51906–51916(2021)
[9] LEE, W. S. and CHOI, J. Hybrid integration of carbon nanotubes and transition metal dichalcogenides on cellulose paper for highly sensitive and extremely deformable chemical sensors. ACS Applied Materials and Interfaces, 11, 19363–19371(2019)
[10] ZHANG, J. and WANG, C. Buckling of carbon honeycombs: a new mechanism for molecular mass transportation. The Journal of Physical Chemistry C, 121, 8196–8203(2017)
[11] GENOESE, A., GENOESE, A., and SALERNO, G. Buckling and post-buckling analysis of single wall carbon nanotubes using molecular mechanics. Applied Mathematical Modelling, 83, 777–800(2020)
[12] WANG, C. M., ZHANG, Y. Y., XIANG, Y., and REDDY, J. N. Recent studies on buckling of carbon nanotubes. Applied Mechanics Reviews, 63, 030804(2010)
[13] SILVESTRE, N., FARIA, B., and CANONGIA LOPES, J. N. A molecular dynamics study on the thickness and post-critical strength of carbon nanotubes. Composite Structures, 94, 1352–1358(2012)
[14] XU, X. J. and DENG, Z. C. Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory. Applied Mathematics and Mechanics (English Edition), 35(9), 1115–1128(2014) https://doi.org/10.1007/s10483-014-1855-6
[15] WANG, J. F., SHI, S. Q., YANG, J. P., and ZHANG, W. Multiscale analysis on free vibration of functionally graded graphene reinforced PMMA composite plates. Applied Mathematical Modelling, 98, 38–58(2021)
[16] YAKOBSON, B. I., BRABEC, C. J., and BERNHOLC, J. Nanomechanics of carbon tubes: instabilities beyond linear response. Physical Review Letters, 76, 2511–2514(1996)
[17] RU, C. Q. Effective bending stiffness of carbon nanotubes. Physical Review B, 62, 9973–9976(2000)
[18] BIAN, L. C. and WANG, Y. W. Temperature-related study on buckling properties of double-walled carbon nanotubes. European Journal of Mechanics-A/Solids, 80, 103875(2020)
[19] MOHAMED, N., MOHAMED, S. A., and ELTAHER, M. A. Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model. Engineering with Computers, 37, 2823–2836(2020)
[20] HE, X. Q., KITIPORNCHAI, S., and LIEW, K. M. Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. Journal of the Mechanics and Physics of Solids, 53, 303–326(2005)
[21] SILVESTRE, N., WANG, C. M., ZHANG, Y. Y., and XIANG, Y. Sanders shell model for buckling of single-walled carbon nanotubes with small aspect ratio. Composite Structures, 93, 1683–1691(2011)
[22] LEISSA, A. W. Vibration of Shells, NASA, Washington, D. C. (1973)
[23] LOUHGHALAM, A., IGUSA, T., and TOOTKABONI, M. Dynamic characteristics of laminated thin cylindrical shells: asymptotic analysis accounting for edge effect. Composite Structures, 112, 22–37(2014)
[24] JAUNKY, N. and KNIGHT, N. F. An assessment of shell theories for buckling of circular cylindrical laminated composite panels loaded in axial compression. International Journal of Solids and Structures, 36, 3799–3820(1999)
[25] GULYAEV, V. I., LUGOVOI, P. Z., and LYSYUK, N. A. Propagation of harmonic waves in a cylindrical shell (Timoshenko model). International Applied Mechanics, 39, 472–478(2003)
[26] XIANG, Y., WANG, C. M., LIM, C. W., and KITIPORNCHAI, S. Buckling of intermediate ring supported cylindrical shells under axial compression. Thin-Walled Structures, 43, 427–443(2005)
[27] STROZZI, M., ELISHAKOFF, I. E., MANEVITCH, L. I., and GENDELMAN, O. V. Applicability and limitations of Donnell shell theory for vibration modelling of double-walled carbon nanotubes. Thin-Walled Structures, 178, 109532(2022)
[28] TIMESLI, A., BRAIKAT, B., JAMAL, M., and DAMIL, N. Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression. Comptes Rendus Mécanique, 345, 158–168(2017)
[29] GUPTA, S., PRAMANIK, S., SMITA, DAS, S. K., and SAHA, S. Dynamic analysis of wave propagation and buckling phenomena in carbon nanotubes (CNTs). Wave Motion, 104, 102730(2021)
[30] HE, X. Q., QU, C., QIN, Q. H., and WANG, C. M. Buckling and postbuckling analysis of multiwalled carbon nanotubes based on the continuum shell model. International Journal of Structural Stability and Dynamics, 7, 629–645(2007)
[31] YAO, X. and HAN, Q. Postbuckling prediction of double-walled carbon nanotubes under axial compression. European Journal of Mechanics-A/Solids, 26, 20–32(2007)
[32] SUN, Y., YAO, X., and HAN, Q. Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition. Science China-Physics Mechanics & Astronomy, 54, 1659–1665(2011)
[33] SUN, C., LIU, K., and HONG, Y. Dynamic shell buckling behavior of multi-walled carbon nanotubes embedded in an elastic medium. Science China-Physics Mechanics & Astronomy, 56, 483– 490(2013)
[34] GARG, A., CHALAK, H. D., BELARBI, M. O., ZENKOUR, A. M., and SAHOO, R. Estimation of carbon nanotubes and their applications as reinforcing composite materials: an engineering review. Composite Structures, 272, 114234(2021)
[35] RU, C. Q. Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. Journal of the Mechanics and Physics of Solids, 49, 1265–1279(2001)
[36] WANG, C. Y., RU, C. Q., and MIODUCHOWSKI, A. Axially compressed buckling of pressured multiwall carbon nanotubes. International Journal of Solids and Structures, 40, 3893–3911(2003)
[37] WANG, J. F. and ZHANG, W. An equivalent continuum meshless approach for material nonlinear analysis of CNT-reinforced composites. Composite Structures, 188, 116–125(2018)
[38] GHORBANPOUR ARANI, A., RAHMANI, R., AREFMANESH, A., and GOLABI, S. Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale. Journal of Mechanical Science and Technology, 22, 429–439(2008)
[39] HE, X. Q., KITIPORNCHAI, S., WANG, C. M., XIANG, Y., and ZHOU, Q. A nonlinear van der Waals force model for multiwalled carbon nanotubes modeled by a nested system of cylindrical shells. Journal of Applied Mechanics, 77, 061006(2010)
[40] SAITO, R., DRESSELHAUS, G., and DRESSELHAUS, M. S. Physical Properties of Carbon Nanotubes, Imperial College Press, London (1998)
[41] HARIK, V. M. Mechanics of carbon nanotubes: applicability of the continuum-beam models. Computational Materials Science, 24, 328–342(2002)
[42] SUN, C. Q., LIU, K. X., and HONG, Y. S. Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions. Acta Mechanica Sinica, 28, 83–90(2012)
[43] RU, C. Q. Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube. Journal of Applied Physics, 87, 7227–7231(2000)
[44] SAITO, R., MATSUO, R., KIMURA, T., DRESSELHAUS, G., and DRESSELHAUS, M. S. Anomalous potential barrier of double-wall carbon nanotube. Chemical Physics Letters, 348, 187– 193(2001)
[45] HE, X. Q., KITIPORNCHAI, S., WANG, C. M., and LIEW, K. M. Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells. International Journal of Solids and Structures, 42, 6032–6047(2005)
[46] AMABILI, M. A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach. Journal of Sound and Vibration, 264, 1091–1125(2003)
[47] LIEW, K. M., WONG, C. H., HE, X. Q., TAN, M. J., and MEGUID, S. A. Nanomechanics of single and multiwalled carbon nanotubes. Physical Review B, 69, 115429(2004)
[48] SHI, J. X., NATSUKI, T., and NI, Q. Q. Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure. Applied Physics A-Materials Science & Processing, 117, 1103–1108(2014)