Цитирование: | 1. Jiang, T., Huang, R., Zhu, Y., Interfacial sliding and buckling of monolayer graphene on a stretchable substrate. Adv Funct Mater 24 (2014), 396–402.
2. Allinger, N.L., Yuh, Y.H., Lii, J.-H., Molecular mechanics: the MM3 force field for hydrocarbons. 1. J Am Chem Soc 111 (1989), 8551–8566.
3. Blondel, A., Karplus, M., New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: elimination of singularities. J Comput Chem 17 (1996), 1132–1141.
4. Brenner, D.W., Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of dimond films. Phys Rev B 42 (1990), 9458–9471.
5. Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B., Sinnott, S.B., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J Phys: Condens Matter 14:4 (2002), 783–802.
6. Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., et al. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc 117 (1995), 5179–5197.
7. Los, J.H., Ghiringhelli, L.M., Meijer, E.J., Fasolino, A., Improved long-range reactive bond-order potential for carbon. I. construction. Phys Rev B, 72, 2005, 214102.
8. Mayo, S.L., Olafson, B.D., Goddard, W.A., DREIDING: a generic force field for molecular simulations. J Phys Chem 94 (1990), 8897–8909.
9. Stuart, S.J., Tutein, A.B., Harrison, J.A., A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys 112:14 (2000), 6472–6486.
10. Tersoff, J., Modeling solid-state chemistry: interatomic potentials for multicomponent systems. Phys Rev B 39 (1989), 5566–5568.
11. Ansari, R., Shahabodini, A., Alipour, A., Rouhi, H., Stability of a single-layer graphene sheet with various edge conditions: a non-local plate model. Proc Inst Mech Eng, Part N: J Nanomater Nanoeng Nanosyst 226 (2012), 51–60.
12. Ansari, R., Sahmani, S., Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations. Appl Math Modell 37 (2013), 7338–7351.
13. Ansari, R., Shahabodini, A., Rouhi, H., Prediction of the biaxial buckling and vibration behavior of graphene via a nonlocal atomistic-based plate theory. Compos Struct 95 (2013), 88–94.
14. Arroyo, M., Belytschko, T., An atomistic-based finite deformation membrane for single layer crystalline films. J Mech Phys Solids 50 (2002), 1941–1977.
15. Arroyo, M., Belytschko, T., Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes. Int J Numer Methods Eng 59 (2004), 419–456.
16. Arroyo, M., Belytschko, T., Finite crystal elasticity of carbon nanotubes based on the exponential cauchy-born rule. Phys Rev B, 69, 2004, 115415.
17. Farajpour, A., Ghayesh, M.H., Farokhi, H., A review on the mechanics of nanostructures. Int J Eng Sci 133 (2018), 231–263.
18. Ghaffari, R., Duong, T.X., Sauer, R.A., A new shell formulation for graphene structures based on existing ab-initio data. Int J Solids Struct 135 (2018), 37–60.
19. Ghannadpour, S.A.M., Moradi, F., Tornabene, F., Exact analytical solutions to the problem of relative post-buckling stiffness of thin nonlocal graphene sheets. Thin-Walled Struct, 151, 2020, 106712.
20. Hollerer, S., Celigoj, C.C., Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model. Comput Mech 51:5 (2013), 765–789.
21. Hollerer, S., Numerical validation of a concurrent atomistic-continuum multiscale method and its application to the buckling analysis of carbon nanotubes. Comput Methods Appl Mech Eng 270 (2014), 220–246.
22. Kumar, S., Parks, D.M., On the hyperelastic softening and elastic instabilities in graphene. Proc R Soc A, 471, 2015, 20140567.
23. Lu, Q., Huang, R., Nonlinear mechanics of single-atomic-layer graphene sheets. Int J Appl Mech 1 (2009), 443–467.
24. Pradhan, S.C., Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys Lett A 373 (2009), 4182–4188.
25. Pradhan, S.C., Murmu, T., Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics. Comput Mater Sci 47 (2009), 268–274.
26. Qian, D., Zhou, Z., Zheng, Q., Coarse-grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach. Int J Numer Methods Eng 102 (2015), 450–467.
27. Sahmani, S., Fattahi, A.M., Development of efficient size-dependent plate models for axial buckling of single-layered graphene nanosheets using molecular dynamics simulation. Microsyst Technol 24:2 (2018), 1265–1277.
28. Silvestre, N., Length dependence of critical measures in single-walled carbon nanotubes. Int J Solids Struct 45 (2008), 4902–4920.
29. Silvestre, N., On the accuracy of shell models for torsional buckling of carbon nanotubes. Eur J Mech A Solids 32 (2012), 103–108.
30. Singh, S., Patel, B.P., Large deformation static and dynamic response of carbon nanotubes by mixed atomistic and continuum models. Int J Mech Sci 135 (2018), 565–581.
31. Wang, C.M., Tay, Z.Y., Chowdhuary, A.N.R., Duan, W.H., Zhang, Y.Y., Silvestre, N., Examination of cylindrical shell theories for buckling of carbon nanotubes. Int J Struct Stab Dyn 11 (2011), 1035–1058.
32. Wilber, J.P., Buckling of graphene layers supported by rigid substrates. J Comput Theor Nanosci 7:11 (2010), 2338–2348.
33. Zhang, K., Arroyo, M., Adhesion and friction control localized folding in supported graphene. J Appl Phys, 113(19), 2013, 193501.
34. Bets, K.V., Yakobson, B.I., Spontaneous twist and intrinsic instabilities of pristine graphene nanoribbons. Nano Res 2:2 (2009), 161–166.
35. Cao, G., Atomistic studies of mechanical properties of graphene. Polymers (Basel) 6 (2014), 2404–2432.
36. Chang, I.-L., Chiang, B.-C., Mechanical buckling of single-walled carbon nanotubes: atomistic simulations. J Appl Phys, 106(11), 2009, 114313.
37. Chang, T., Torsional behavior of chiral single-walled carbon nanotubes is loading direction dependent. Appl Phys Lett, 90(20), 2007, 201910.
38. Damasceno, D.A., Mesquita, E., Rajapakse, R.K.N.D., Pavanello, R., Atomic-scale finite element modelling of mechanical behaviour of graphene nanoribbons. Int J Mech Mater Des 15:1 (2019), 145–157.
39. Fereidoon, A., Aleaghaee, S., Taraghi, I., Mechanical properties of hybrid graphene/tio2 (rutile) nanocomposite: a molecular dynamics simulation. Comput Mater Sci 102 (2015), 220–227.
40. Glukhova, O.E., Mechanical properties of graphene sheets. Aliofkhazraei, M., Ali, N., Milne, W.I., Ozkan, C.S., Mitura, S., Gervasoni, J.L., (eds.) Graphene science handbook: mechanical and chemical properties, 2016, CRC Press, Taylor and Francis Group, London, 61–78.
41. Huang, J., Han, Q., A molecular dynamics study on wrinkles in graphene with simply supported boundary under in-plane shear. J Nanomater, 2017, 2017, 1326790.
42. Liew, K.M., Wong, C.H., He, X.Q., Tan, M.J., Meguid, S.A., Nanomechanics of single and multiwalled carbon nanotubes. Phys Rev B, 69, 2004, 115429.
43. Neek-Amal, M., Peeters, F.M., Graphene nanoribbons subjected to axial stress. Phys Rev B, 82, 2010, 085432.
44. Sgouros, A.P., Kalosakas, G., Papagelis, K., Galiotis, C., Compressive response and buckling of graphene nanoribbons. Sci Rep, 8, 2018, 9593.
45. Silvestre, N., Faria, B., Canongia Lopes, J.N., A molecular dynamics study on the thickness and post-critical strength of carbon nanotubes. Compos Struct 94 (2012), 1352–1358.
46. Wilber, J.P., Clemons, C.B., Young, G.W., Buldum, A., Quinn, D.D., Continuum and atomistic modeling of interacting graphene layers. Phys Rev B, 75, 2007, 045418.
47. Xiang, Y., Shen, H.-S., Tension buckling of graphene: a new phenotype. Solid State Commun 192 (2014), 20–23.
48. Xiang, Y., Shen, H.-S., Compressive buckling of rippled graphene via molecular dynamics simulations. Int J Struct Stab Dyn, 16(10), 2016, 1550071.
49. Yakobson, B.I., Brabec, C.J., Bernholc, J., Nanomechanics of carbon tubes: instabilities beyond linear response. Phys Rev Lett 76 (1996), 2511–2514.
50. Zhang, H.-Y., Jiang, J.-W., Chang, T., Guo, X., Park, H.S., The effects of free edge interaction-induced knotting on the buckling of monolayer graphene. Int J Solids Struct 100–101 (2016), 446–455.
51. Zhang, Y., Liu, F., Maximum asymmetry in strain induced mechanical instability of graphene: compression versus tension. Appl Phys Lett, 99(24), 2011, 241908.
52. Zhao, J., Guo, X., Lu, L., Small size effect on the wrinkling hierarchy in constrained monolayer graphene. Int J Eng Sci 131 (2018), 19–25.
53. Korobeynikov, S.N., Alyokhin, V.V., Annin, B.D., Babichev, A.V., Quasi-static buckling simulation of single-layer graphene sheets by the molecular mechanics method. Math Mech Solids 20:7 (2015), 836–870.
54. Annin, B.D., Baimova, Yu.A., Mulyukov, R.R., Mechanical properties, stability, and buckling of graphene sheets and carbon nanotubes (review). J Appl Mech Tech Phys 61:5 (2020), 834–846.
55. Chandra, Y., Adhikaria, S., Saavedra Flores, E.I., Figiel, Ł., Advances in finite element modelling of graphene and associated nanostructures. Mater Sci Eng, R, 140, 2020, 100544.
56. Alyokhin, V.V., Annin, B.D., Babichev, A.V., Korobeynikov, S.N., Free vibrations and buckling of graphene sheets. Dokl Phys 58:11 (2013), 487–490.
57. Aminpour, H., Rizzi, N.L., On the necking of graphene nanostructures. Int J Multiscale Comput Eng 18:1 (2020), 103–128.
58. Chang, T., Li, G., Guo, X., Elastic axial buckling of carbon nanotubes via a molecular mechanics model. Carbon N Y 43 (2005), 287–294.
59. Chang, T., Guo, W., Guo, X., Buckling of multiwalled carbon nanotubes under axial compression and bending via a molecular mechanics model. Phys Rev B, 72, 2005, 064101.
60. Cong, Y., Yvonnet, J., Zahrouni, H., Simulation of instabilities in thin nanostructures by a perturbation approach. Comput Mech 53:4 (2014), 739–750.
61. Duan, W.H., Gong, K., Wang, Q., Controlling the formation of wrinkles in a single layer graphene sheet subjected to in-plane shear. Carbon N Y 49 (2011), 3107–3112.
62. Favata, A., Micheletti, A., Podio-Guidugli, P., Pugno, N.M., Geometry and self-stress of single-wall carbon nanotubes and graphene via a discrete model based on a 2nd-generation REBO potential. J Elast 125 (2016), 1–37.
63. Favata, A., Micheletti, A., Podio-Guidugli, P., Pugno, N.M., How graphene flexes and stretches under concomitant bending couples and tractions. Meccanica 52:7 (2017), 1601–1624.
64. Feng, C., Liew, K.M., He, P., Wu, A., Predicting mechanical properties of carbon nanosprings based on molecular mechanics simulation. Compos Struct 114 (2014), 41–50.
65. Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G., On the derivation of the elastic properties of lattice nanostructures: the case of graphene sheets. Composites, Part B 115 (2017), 316–329.
66. Genoese, A., Genoese, A., Salerno, G., On the nanoscale behaviour of single-wall c, BN and sic nanotubes. Acta Mech 230:3 (2019), 1105–1128.
67. Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G., Buckling analysis of single-layer graphene sheets using molecular mechanics. Front Mater, 6, 2019, 26.
68. Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G., On the in-plane failure and post-failure behaviour of pristine and perforated single-layer graphene sheets. Math Mech Solids 24 (2019), 3418–3443.
69. Genoese, A., Genoese, A., Salerno, G., Hexagonal boron nitride nanostructures: a nanoscale mechanical modeling. J Mech Mater Struct 15 (2020), 249–275.
70. Genoese, A., Genoese, A., Salerno, G., Buckling and post-buckling analysis of single wall carbon nanotubes using molecular mechanics. Appl Math Modell 83 (2020), 777–800.
71. Genoese, A., Genoese, A., Salerno, G., In-plane and out-of-plane tensile behaviour of single-layer graphene sheets: a new interatomic potential. Acta Mech 231:7 (2020), 2915–2930.
72. Guo, X., Leung, A.Y.T., Jiang, H., He, X.Q., Huang, Y., Critical strain of carbon nanotubes: an atomic-scale finite element study. ASME J Appl Mech 74:2 (2007), 347–351.
73. Gupta, S.S., Batra, R.C., Elastic properties and frequencies of free vibrations of single-layer graphene sheets. J Comput Theor Nanosci 7:10 (2010), 2151–2164.
74. Gupta, S.S., Agrawal, P., Batra, R.C., Buckling of single-walled carbon nanotubes using two criteria. J Appl Phys, 119(24), 2016, 245106.
75. Hollerer, S., Buckling analysis of carbon nanotubes — a molecular statics investigation into the influence of non-bonded interactions. Int J Numer Methods Eng 91 (2012), 397–425.
76. Korayem, A.H., Duan, W.H., Zhao, X.L., Wang, C.M., Buckling behavior of short multi-walled carbon nanotubes under axial compression loads. Int J Struct Stab Dyn, 12(6), 2012, 1250045.
77. Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V., Application of the molecular mechanics method to simulation of buckling of single-walled carbon nanotubes. Eng Fract Mech 130 (2014), 83–95.
78. Korobeynikov, S.N., Alyokhin, V.V., Annin, B.D., Babichev, A.V., Buckling simulation of single layer graphene sheets by the molecular mechanics method. Pietraszkiewicz, W., Gorski, J., (eds.) Shell structures: theory and applications, Vol. 3. Proceedings of the 10th SSTA International Conference, Gdansk, Poland, 16–18 October 2013, 2014, CRC Press/Balkema, London, 207–210.
79. Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V., Simulation of mechanical parameters of graphene using the DREIDING force field. Acta Mech 229:6 (2018), 2343–2378.
80. Lin, F., Xiang, Y., Shen, H.-S., Buckling of graphene embedded in polymer matrix under compression. Int J Struct Stab Dyn, 15(7), 2015, 1540016.
81. Liu, B., Zhang, Z., Chen, Y., Atomistic statics approaches - molecular mechanics, finite element method and continuum analysis. J Comput Theor Nanosci 5:9 (2008), 1891–1913.
82. Lu, Q., Huang, R., Excess energy and deformation along free edges of graphene nanoribbons. Phys Rev B, 81, 2010, 155410.
83. Majzoobi, G.H., Payandehpeyman, J., Nojini, Z.B., An investigation into the torsional buckling of carbon nanotubes using molecular and structural mechanics. Int J Nanosci 10 (2011), 989–993.
84. Merli, R., Lázaro, C., Monleón, S., Domingo, A., Geometrical nonlinear formulation of a molecular mechanics model applied to the structural analysis of single-walled carbon nanotubes. Int J Solids Struct 58 (2015), 157–177.
85. Nasdala, L., Ernst, G., Development of a 4-node finite element for the computation of nano-structured materials. Comput Mater Sci 33 (2005), 443–458.
86. Nasdala, L., Kempe, A., Rolfes, R., The molecular dynamic finite element method (MDFEM). CMC-Comput Mater Continua 19:1 (2010), 57–104.
87. Nasdala, L., Kempe, A., Rolfes, R., Are finite elements appropriate for use in molecular dynamic simulations?. Compos Sci Technol 72 (2012), 989–1000.
88. Nazarloo, A.S., Ahmadian, M.T., Firoozbakhsh, K., On the mechanical characteristics of graphene nanosheets: a fully nonlinear modified morse model. Nanotechnology, 31(11), 2020, 115708.
89. Rochefort, A., Avouris, P., Lesage, F., Salahub, D.R., Electrical and mechanical properties of distorted carbon nanotubes. Phys Rev B 60 (1999), 13824–13830.
90. Sears, A., Batra, R.C., Macroscopic properties of carbon nanotubes from molecular-mechanics simulations. Phys Rev B, 69, 2004, 235406.
91. Singh, S., Patel, B.P., Nonlinear elastic properties of graphene sheet using MM3 potential under finite deformation. Composites, Part B 136 (2018), 81–91.
92. Wackerfuß, J., Molecular mechanics in the context of the finite element method. Int J Numer Methods Eng 77 (2009), 969–997.
93. Wang, S., Ma, Y., Pan, F., Shao, L., Chen, Y., A mode-independent energy method in morphology prediction of graphene on substrates with nanoscale asperities. Int J Mech Sci 146–147 (2018), 355–365.
94. Yang, K., Chen, Y., Pan, F., Wang, S., Ma, Y., Liu, Q., Buckling behavior of substrate supported graphene sheets. Materials (Basel), 9(1), 2016, 32.
95. Annin, B.D., Korobeynikov, S.N., Babichev, A.V., Computer simulation of a twisted nanotube buckling. J Appl Ind Math 3:3 (2009), 318–333.
96. Annin, B.D., Alekhin, V.V., Babichev, A.V., Korobeynikov, S.N., Computer simulation of nanotube contact. Mech Solids 45:3 (2010), 352–369.
97. Annin, B.D., Alekhin, V.V., Babichev, A.V., Korobeynikov, S.N., Molecular mechanics method applied to problems of stability and natural vibrations of single-layer carbon nanotubes. Mech Solids 47:5 (2012), 544–559.
98. Eberhardt, O., Wallmersperger, T., Energy consistent modified molecular structural mechanics model for the determination of the elastic properties of single wall carbon nanotubes. Carbon N Y 95 (2015), 166–180.
99. Eberhardt, O., Wallmersperger, T., Advanced molecular structural mechanics model for carbon nanotubes incorporating the 2nd generation REBO potential. Int J Eng Sci, 144, 2019, 103137.
100. Favata, A., Micheletti, A., Podio-Guidugli, P., A nonlinear theory of prestressed elastic stick-and-spring structures. Int J Eng Sci 80 (2014), 4–20.
101. Firouz-Abadi, R.D., Moshrefzadeh-Sany, H., Mohammadkhani, H., Sarmadi, M., A modified molecular structural mechanics model for the buckling analysis of single layer graphene sheet. Solid State Commun 225 (2016), 12–16.
102. Galhofo, D., Silvestre, N., Atomistic FE modelling of the monotonic and hysteretic out-of-plane behaviour of graphene. Physica E, 122, 2020, 114182.
103. Georgantzinos, S.K., Markolefas, S., Giannopoulos, G.I., Katsareas, D.E., Anifantis, N.K., Designing pinhole vacancies in graphene towards functionalization: effects on critical buckling load. Superlattices Microstruct 103 (2017), 343–357.
104. Georgantzinos, S.K., Giannopoulos, G.I., Thermomechanical buckling of single walled carbon nanotubes by a structural mechanics method. Diamond Relat Mater 80 (2017), 27–37.
105. Giannopoulos, G.I., Elastic buckling and flexural rigidity of graphene nanoribbons by using a unique translational spring element per interatomic interaction. Comput Mater Sci 53 (2012), 388–395.
106. Giannopoulos, G.I., Tsiros, A.P., Georgantzinos, S.K., Prediction of elastic mechanical behavior and stability of single-walled carbon nanotubes using bar elements. Mech Adv Mater Struct 20 (2013), 730–741.
107. Hu, N., Nunoya, K., Pan, D., Okabe, T., Fukunaga, H., Prediction of buckling characteristics of carbon nanotubes. Int J Solids Struct 44 (2007), 6535–6550.
108. Korobeynikov, S.N., Alyokhin, V.V., Annin, B.D., Babichev, A.V., Using stability analysis of discrete elastic systems to study the buckling of nanostructures. Arch Mech 64:4 (2012), 367–404.
109. Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V., On mechanical moduli of single layer graphene sheets. Pietraszkiewicz, W., Witkowski, W., (eds.) Shell structures: theory and applications, Vol. 4. Proceedings of the 11th SSTA international conference, Gdansk, Poland, 11–13 October 2017, 2018, CRC Press/Balkema, London, 109–112.
110. Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V., On the molecular mechanics of single layer graphene sheets. Int J Eng Sci 133 (2018), 109–131.
111. Li, C., Chou, T.-W., A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Struct 40 (2003), 2487–2499.
112. Li, C., Chou, T.-W., Elastic moduli of multi-walled carbon nanotubes and the effect of van der waals forces. Compos Sci Technol 63 (2003), 1517–1524.
113. Li, C., Chou, T.-W., Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach. Mech Mater 36 (2004), 1047–1055.
114. Li, C., Chou, T.-W., Elastic properties of single-walled carbon nanotubes in transverse directions. Phys Rev B, 69, 2004, 073401.
115. Namnabat, M.S., Barzegar, A., Barchiesi, E., Javanbakht, M., Nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics. Carbon Lett, 2020, 10.1007/s42823-020-00194-2.
116. Parvaneh, V., Ramezani, A., Yazdi, H.A., Mohammadi, A.H., Heydari, M., The prediction of critical buckling load of graphene sheet with different boundary conditions by a structural mechanics model. Microsyst Technol 27:3 (2021), 629–638.
117. Rouhi, S., Ansari, R., Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets. Physica E 44 (2012), 764–772.
118. Saavedra Flores, E.I., Adhikari, S., Friswell, M.I., Scarpa, F., Hyperelastic modelling of post-buckling response in single wall carbon nanotubes under axial compression. Procedia Eng 10 (2011), 2256–2261.
119. Sakhaee-Pour, A., Elastic buckling of single-layered graphene sheet. Comput Mater Sci 45 (2009), 266–270.
120. Yengejeh, S.I., Kazemi, S.A., Öchsner, A., On the influence of atomic modifications on the structural stability of carbon nanotube hybrids: numerical investigation. Int J Appl Mech, 6(6), 2014, 1450077.
121. Ziaee, S., Buckling of defective carbon nanotubes under axial and transverse loads. Int J Appl Mech, 6(1), 2014, 1450004.
122. Chu, Y., Ragab, T., Basaran, C., The size effect in mechanical properties of finite-sized graphene nanoribbon. Comput Mater Sci 81 (2014), 269–274.
123. Ragab, T., Basaran, C., Shear strength of square graphene nanoribbons beyond wrinkling. J Electron Mater 47:7 (2018), 3891–3896.
124. Zhang, J., Ragab, T., Basaran, C., Comparison of fracture behavior of defective armchair and zigzag graphene nanoribbons. Int J Damage Mech 28:3 (2019), 325–345.
125. Zhang, J., Zhang, W., Ragab, T., Basaran, C., Mechanical and electronic properties of graphene nanomesh heterojunctions. Comput Mater Sci 153 (2018), 64–72.
126. Korobeinikov, S.N., Agapov, V.P., Bondarenko, M.I., Soldatkin, A.N., The general purpose nonlinear finite element structural analysis program PIONER. Sendov, B., Lazarov, R., Dimov, I., (eds.) Proceedings of international conference on numerical methods and applications, 1989, Publishing House of the Bulgarian Academy of Science, Sofia, 228–233.
127. Shima, H., Buckling of carbon nanotubes: a state of the art review. Materials (Basel) 5:1 (2012), 47–84.
128. Wang, C.Y., Zhang, Y.Y., Wang, C.M., Tan, V.B.C., Buckling of carbon nanotubes: a literature survey. J Nanosci Nanotechnol 7:12 (2007), 4221–4247.
129. Wang, C.M., Zhang, Y.Y., Xiang, Y., Reddy, J.N., Recent studies on buckling of carbon nanotubes. Appl Mech Rev, 63(3), 2010, 030804.
130. Korobeynikov, S., The numerical solution of nonlinear problems on deformation and buckling of atomic lattices. Int J Fract 128 (2004), 315–323.
131. Cheng, H.-C., Liu, Y.-L., Hsu, Y.-C., Chen, W.-H., Atomistic-continuum modeling for mechanical properties of single-walled carbon nanotubes. Int J Solids Struct 46 (2009), 1695–1704.
132. Friedrich, M., Stefanelli, U., Graphene ground states. Z Angew Math Phys, 69(3), 2018, 70.
133. Gamboa, A., Vignoles, G.L., Leyssale, J.-M., On the prediction of graphene's elastic properties with reactive empirical bond order potentials. Carbon N Y 89 (2015), 176–187.
134. Korobeynikov, S.N., Discussion on “nonlinear buckling analysis of double-layered graphene nanoribbons based on molecular mechanics” by Namnabat et al. Carbon Lett 2021. doi 10.1007/s42823-020-00194-2. Carbon Lett, 2021, 10.1007/s42823-021-00233-6.
135. Berinskii, I.E., Borodich, F.M., Elastic in-plane properties of 2D linearized models of graphene. Mech Mater 62 (2013), 60–68.
136. Berinskii, I., Altenbach, H., In-plane and out-of-plane elastic properties of two-dimensional single crystal. Acta Mech 228:2 (2017), 683–691.
137. Cao, Q., Geng, X., Wang, H., Wang, P., Liu, A., Lan, Y., et al. A review of current development of graphene mechanics. Crystals, 8(9), 2018, 357.
138. Dmitriev, S.V., Baimova, Yu.A., Savin, A.V., Kivshar, Yu.S., Stability range for a flat graphene sheet subjected to in-plane deformation. JETP Lett 93:10 (2011), 571–576.
139. Savin, A.V., Kivshar, Yu.S., Hu, B., Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys Rev B, 82, 2010, 195422.
140. Girifalco, L.A., Hodak, M., Lee, R.S., Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys Rev B 62 (2000), 13104–13110.
141. Korobeynikov, S.N., Nonlinear equations of deformation of atomic lattices. Arch Mech 57:6 (2005), 435–453.
142. Bathe, K.-J., Finite element procedures. 1996, Prentice Hall, Upper Saddle River, New Jersey.
143. Bathe, K.-J., Dvorkin, E.N., On the automatic solution of nonlinear finite element equations. Comput Struct 17 (1983), 871–879.
144. Sokol, T., Witkowski, M., The equilibrium path determination in nonlinear analysis of structures. Papadrakakis, M., Topping, B.H.V., (eds.) Advances in non-linear finite element methods: Proceedings of the 2nd international conference on computational structures technology, 1994, Civil-Comp Press, Edinburgh, 35–45.
145. Wagner, W., Wriggers, P., A simple method for the calculation of postcritical branches. Eng Comput 5:2 (1988), 103–109.
146. Alshalal, I., Feng, Z.C., Detection of symmetry breaking bifurcations using finite element analysis packages. Int J Non Linear Mech 106 (2018), 70–79.
147. Kuznetsov, V.V., Levyakov, S.V., Secondary loss of stability of an euler rod. J Appl Mech Tech Phys 40:6 (1999), 1161–1162.
148. Kuznetsov, V.V., Levyakov, S.V., Complete solution of the stability problem for elastica of euler's column. Int J Non Linear Mech 37 (2002), 1003–1009.
149. Levyakov, S.V., States of equilibrium and secondary loss of stability of a stright rod loaded by an axial force. J Appl Mech Tech Phys 42:2 (2001), 321–327.
150. Wu, B., Secondary buckling of an elastic strut under axial compression. Z Angew Math Mech 75 (1995), 741–751.
151. Goss, V.G.A., The history of the planar elastica: insights into mechanics and scientific method. Sci Educ 18:8 (2009), 1057–1082.
152. Cazzolli, A., Dal Corso, F., Snapping of elastic strips with controlled ends. Int J Solids Struct 162 (2019), 285–303.
153. Cazzolli, A., Misseroni, D., Dal Corso, F., Elastica catastrophe machine: theory, design and experiments. J Mech Phys Solids, 136, 2020, 103735.
154. Harvey, P.S., Virgin, L.N., Tehrani, M.H., Buckling of elastic columns with second-mode imperfections. Meccanica 54:8 (2019), 1245–1255.
155. Plaut, R.H., Dillard, D.A., Virgin, L.N., Postbuckling of elastic columns with second-mode imperfection. J Eng Mech 132:8 (2006), 898–901.
156. Tarantino, M.G., Danas, K., Programmable higher-order euler buckling modes in hierarchical beams. Int J Solids Struct 167 (2019), 170–183.
157. Wang, Q., Zou, H.-L., Deng, Z.-C., Snap-through of a pinned-clamped elastica with arbitrarily movable support at the clamped end. Mech Res Commun, 110, 2020, 103617.
158. Kuznetsov, V.V., Levyakov, S.V., Elastica of an Euler rod with clamped ends. J Appl Mech Tech Phys 41:3 (2000), 544–546.
159. Levyakov, S.V., Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends. Mech Res Commun 36 (2009), 612–617.
160. Levyakov, S.V., Kuznetsov, V.V., Stability analysis of planar equilibrium configurations of elastic rods subjected to end loads. Acta Mech 211 (2010), 73–87.
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