H. Abichou, H. Zahrouni, and M. Potier-ferry, Asymptotic numerical method for problems coupling several nonlinearities, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.51-52, pp.5795-5810, 2002.
DOI : 10.1016/S0045-7825(02)00497-8

W. Aggoune, H. Zahrouni, and M. Potier-ferry, High-order prediction???correction algorithms for unilateral contact problems, Journal of Computational and Applied Mathematics, vol.168, issue.1-2, pp.1-9, 2004.
DOI : 10.1016/j.cam.2003.05.015

W. Aggoune, H. Zahrouni, and M. Potier-ferry, Asymptotic numerical methods for unilateral contact, International Journal for Numerical Methods in Engineering, vol.1, issue.6, pp.605-631, 2006.
DOI : 10.1002/nme.1714

M. Arroyo and T. Belytschko, Nonlinear Mechanical Response and Rippling of Thick Multiwalled Carbon Nanotubes, Physical Review Letters, vol.91, issue.21, p.505, 2003.
DOI : 10.1103/PhysRevLett.91.215505

T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff, Atomistic simulations of nanotube fracture, Physical Review B, vol.65, issue.23, p.65, 2002.
DOI : 10.1103/PhysRevB.65.235430

E. H. Boutyour, H. Zahrouni, M. Potier-ferry, and M. Boudi, for buckling analysis of shell structures with large rotations, Journal of Computational and Applied Mathematics, issue.168, pp.77-85, 2004.

E. H. Boutyour, H. Zahrouni, M. Potier-ferry, and M. Boudi, Bifurcation points and bifurcated branches by an asymptotic numerical method and Pad?? approximants, International Journal for Numerical Methods in Engineering, vol.60, issue.12, pp.1987-2012, 2004.
DOI : 10.1002/nme.1033

D. W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B, vol.42, issue.15, pp.9458-9471, 1990.
DOI : 10.1103/PhysRevB.42.9458

Y. Chandra, R. Chowdhury, S. Adhikari, and F. Scarpa, Elastic instability of bilayer graphene using atomistic finite element, Physica E: Low-dimensional Systems and Nanostructures, vol.44, issue.1, pp.12-16, 2011.
DOI : 10.1016/j.physe.2011.06.020

I. Charpentier and M. Potier-ferry, Diff??rentiation automatique de la m??thode asymptotique num??rique typ??e : l'approche Diamant, Comptes Rendus M??canique, vol.336, issue.3, pp.336-340, 2008.
DOI : 10.1016/j.crme.2007.11.022

B. Cochelin, A path-following technique via an asymptotic-numerical method, Computers & Structures, vol.53, issue.5, pp.1181-1192, 1994.
DOI : 10.1016/0045-7949(94)90165-1

B. Davidovitcha, R. D. Schrolla, D. Vellab, M. Adda-bediab, and E. A. Cerdad, Prototypical model for tensional wrinkling in thin sheets, Proceedings of the National Acadamy of Sciences of the United States of America, pp.227-18232, 2011.
DOI : 10.1073/pnas.1108553108

R. Fletcher and M. J. Powell, A Rapidly Convergent Descent Method for Minimization, The Computer Journal, vol.6, issue.2, pp.163-168, 1963.
DOI : 10.1093/comjnl/6.2.163

R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, The Computer Journal, vol.7, issue.2, pp.149-154, 1964.
DOI : 10.1093/comjnl/7.2.149

G. I. Giannopoulos, Elastic buckling and flexural rigidity of graphene nanoribbons by using a unique translational spring element per interatomic interaction, Computational Materials Science, vol.53, issue.1, pp.388-395, 2012.
DOI : 10.1016/j.commatsci.2011.08.027

S. Govindjee and J. L. Sackman, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Communications, vol.110, issue.4, pp.227-230, 1999.
DOI : 10.1016/S0038-1098(98)00626-7

C. Jiang, S. Singamaneni, E. Merrick, and V. V. Tsukruk, Complex Buckling Instability Patterns of Nanomembranes with Encapsulated Gold Nanoparticle Arrays, Nano Letters, vol.6, issue.10, pp.2254-2259, 2006.
DOI : 10.1021/nl061630n

Y. Koutsawa, I. Charpentier, E. M. Daya, and M. Cherkaoui, A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.3-4, pp.572-577, 2008.
DOI : 10.1016/j.cma.2008.09.003

URL : https://hal.archives-ouvertes.fr/hal-00374092

H. Lahmam, J. M. Cadou, H. Zahrouni, N. Damil, and M. Potier-ferry, High order predictorcorrector algorithms, International Journal for Numerical Methods in Engineering, issue.55, pp.685-704, 2002.

A. Lejeune, F. Béchet, H. Boudaoud, N. Mathieu, and M. Potier-ferry, Object-oriented design to automate a high order non-linear solver based on asymptotic numerical method, Advances in Engineering Software, vol.48, pp.70-88, 2012.
DOI : 10.1016/j.advengsoft.2012.02.012

Q. Lu and B. Bhattacharya, The role of atomistic simulations in probing the small-scale aspects of fracture???a case study on a single-walled carbon nanotube, Engineering Fracture Mechanics, vol.72, issue.13, pp.2037-2071, 2005.
DOI : 10.1016/j.engfracmech.2005.01.009

E. Mallil, H. Lahmam, N. Damil, and M. Potier-ferry, An iterative process based on homotopy and perturbation techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13-14, pp.13-14
DOI : 10.1016/S0045-7825(00)00198-5

M. Medale and B. Cochelin, A parallel computer implementation of the Asymptotic Numerical Method to study thermal convection instabilities, Journal of Computational Physics, vol.228, issue.22
DOI : 10.1016/j.jcp.2009.07.032

URL : https://hal.archives-ouvertes.fr/hal-00487339

P. M. Morse, Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels, Physical Review, vol.34, issue.1, pp.57-64, 1929.
DOI : 10.1103/PhysRev.34.57

A. Najah, B. Cochelin, N. Damil, and M. Potier-ferry, A critical review of asymptotic numerical methods, Archives of Computational Methods in Engineering, vol.16, issue.Supp., pp.3-22, 1998.
DOI : 10.1007/BF02736748

M. Neek-amal and F. Peeters, Buckled circular monolayer graphene: a graphene nano-bowl, Journal of Physics: Condensed Matter, vol.23, issue.4, 2011.
DOI : 10.1088/0953-8984/23/4/045002

S. Nezamabadi, J. Yvonnet, H. Zahrouni, and M. Potier-ferry, A multilevel computational strategy for handling microscopic and macroscopic instabilities, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.27-29, pp.2099-2110, 2009.
DOI : 10.1016/j.cma.2009.02.026

URL : https://hal.archives-ouvertes.fr/hal-00692235

S. Nezamabadi, H. Zahrouni, and J. Yvonnet, Solving hyperelastic material problems by asymptotic numerical method, Computational Mechanics, vol.37, issue.1, pp.77-92, 2011.
DOI : 10.1007/s00466-010-0531-z

URL : https://hal.archives-ouvertes.fr/hal-00692222

S. Nezamabadi, H. Zahrouni, J. Yvonnet, and M. Potier-ferry, A Multiscale Finite Element Approach for Buckling Analysis of Elastoplastic Long Fiber Composites, International Journal for Multiscale Computational Engineering, vol.8, issue.3, pp.287-301, 2010.
DOI : 10.1615/IntJMultCompEng.v8.i3.50

URL : https://hal.archives-ouvertes.fr/hal-01468352

M. Potier-ferry, N. Damil, B. Braikat, J. Descamps, J. M. Cadou et al., Traitement des fortes non-lin??arit??s par la m??thode asymptotique num??rique, Comptes Rendus de l'Académie des Sciences -Series IIB -Mechanics-Physics-Chemistry- Astronomy, pp.171-177, 1997.
DOI : 10.1016/S1251-8069(99)80022-0

D. D. Quinn, J. P. Wilber, C. B. Clemons, G. W. Young, and A. Buldum, Buckling instabilities in coupled nano-layers, International Journal of Non-Linear Mechanics, vol.42, issue.4, pp.681-689, 2007.
DOI : 10.1016/j.ijnonlinmec.2007.03.012

D. C. Rapaport, The art of molecular dynamics simulation, 2004.

E. Riks, The Application of Newton???s Method to the Problem of Elastic Stability, Journal of Applied Mechanics, vol.39, issue.4, pp.1060-1065, 1972.
DOI : 10.1115/1.3422829

E. Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures, vol.15, issue.7, pp.529-551, 1979.
DOI : 10.1016/0020-7683(79)90081-7

C. Q. Ru, Column buckling of multiwalled carbon nanotubes with interlayer radial displacements, Physical Review B, vol.62, issue.24, p.962, 2000.
DOI : 10.1103/PhysRevB.62.16962

C. Q. Ru, Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube, Journal of Applied Physics, vol.87, issue.10, p.7227, 2000.
DOI : 10.1063/1.372973

C. Q. Ru, Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium, Journal of the Mechanics and Physics of Solids, vol.49, issue.6, pp.1265-1279, 2001.
DOI : 10.1016/S0022-5096(00)00079-X

C. Q. Ru, Degraded axial buckling strain of multiwalled carbon nanotubes due to interlayer slips, Journal of Applied Physics, vol.89, issue.6, p.3426, 2001.
DOI : 10.1063/1.1347956

R. D. Schroll, E. Katifori, and B. Davidovitch, Elastic Building Blocks for Confined Sheets, Physical Review Letters, vol.106, issue.7, p.301, 2011.
DOI : 10.1103/PhysRevLett.106.074301

J. Tersoff, New empirical approach for the structure and energy of covalent systems, Physical Review B, vol.37, issue.12, pp.6991-7000, 1988.
DOI : 10.1103/PhysRevB.37.6991

H. Vandeparre, M. Piñeirua, F. Brau, B. Roman, J. Bico et al., Wrinkling Hierarchy in Constrained Thin Sheets from Suspended Graphene to Curtains, Physical Review Letters, vol.106, issue.22, p.301, 2011.
DOI : 10.1103/PhysRevLett.106.224301

URL : https://hal.archives-ouvertes.fr/hal-00549423

C. Y. Wang, C. Q. Ru, and A. Mioduchowski, Elastic Buckling of Multiwall Carbon Nanotubes under High Pressure, Journal of Nanoscience and Nanotechnology, vol.3, issue.1, pp.199-208, 2003.
DOI : 10.1166/jnn.2003.185

Q. Wanga, K. Liewb, and W. Duana, Modeling of the mechanical instability of carbon nanotubes, Carbon, vol.46, issue.2, pp.285-290, 2008.
DOI : 10.1016/j.carbon.2007.11.022

B. I. Yakobson, C. J. Brabec, and J. Bernholc, Nanomechanics of Carbon Tubes: Instabilities beyond Linear Response, Physical Review Letters, vol.76, issue.14, pp.2511-2514, 1996.
DOI : 10.1103/PhysRevLett.76.2511

H. W. Yap, R. S. Lakes, and R. W. Carpick, Mechanical Instabilities of Individual Multiwalled Carbon Nanotubes under Cyclic Axial Compression, Nano Letters, vol.7, issue.5, pp.1149-1154, 2007.
DOI : 10.1021/nl062763b

H. Zahrouni, W. Aggoune, J. Brunelot, and M. Potier-ferry, Asymptotic Numerical Method for strong nonlinearities, Revue Europ??enne des ??l??ments Finis, vol.175, issue.7, pp.97-118, 2004.
DOI : 10.3166/reef.13.97-118

H. Zahrouni, B. Cochelin, and M. Potier-ferry, Computing finite rotations of shells by an asymptotic-numerical method, Computer Methods in Applied Mechanics and Engineering, vol.175, issue.1-2, pp.71-85, 1999.
DOI : 10.1016/S0045-7825(98)00320-X

H. Zahrouni, M. Potier-ferry, H. Elasmar, and N. Damil, Asymptotic Numerical Method for Nonlinear Constitutive Laws, Revue Europ??enne des ??l??ments Finis, vol.10, issue.4, pp.841-869, 1998.
DOI : 10.1080/12506559.1998.10511344

Q. Zheng, Y. Geng, S. Wang, Z. Li, and J. K. , Effects of functional groups on the mechanical and wrinkling properties of graphene sheets, Carbon, vol.48, issue.15, pp.4315-4322, 2010.
DOI : 10.1016/j.carbon.2010.07.044