Journal of Elasticity

, Volume 126, Issue 2, pp 155–171 | Cite as

Effect of Material Nonlinearity on Spatial Buckling of Nanorods and Nanotubes

  • Prakhar Gupta
  • Ajeet KumarEmail author


We show the importance of incorporating material nonlinearity for accurate determination of spatial buckling of nanorods and nanotubes. Both the nanorods and nanotubes are modeled as a special Cosserat rod whose nonlinear material laws are obtained using the recently proposed helical Cauchy-Born rule. We first present Euler buckling of solid diamond nanorods whose normalized buckling load, obtained from fully atomistic calculations, exhibits an interesting trend. The buckling load starts from unity at large aspect ratio of the nanorod, then as the aspect ratio is decreased, the buckling load increases slowly and finally decreases rapidly. We attribute this trend to material nonlinearity of the nanorod’s core at large compressive strain. We also discuss how surface stress affects buckling in nanorods. We then present the effect of compression and twist on buckling of single-walled carbon nanotubes. Interestingly, for highly twisted nanotubes, fully atomistic calculations show the first buckled mode to be different from a typical Euler buckling mode. Both the observations about nanorods and nanotubes are accurately replicated in the finite element special Cosserat rod simulation when the material nonlinearity is also incorporated. However, the simulation results exhibit completely different trend when only linear material laws are incorporated.


Cauchy-Born rule Special Cosserat rod Elastic constitutive modeling Surface stress Euler buckling 

Mathematics Subject Classification

74B20 74A25 74Q15 



P. Gupta acknowledges the financial support received from DST-INSPIRE fellowship and A. Kumar acknowledges the support from SERB, India through the grant YSS/2014/000023.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Applied MechanicsIIT DelhiNew DelhiIndia

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