Extreme Mechanics Letters 3 (2015) 36–44 Contents lists available at ScienceDirect Extreme Mechanics Letters journal homepage: www.elsevier.com/locate/eml Buckling of a thin elastic rod inside a horizontal cylindrical constraint J.T. Miller a,1 , T. Su b , J. Pabon b , N. Wicks b , K. Bertoldi c,d , P.M. Reis a,e,* a Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b Schlumberger-Doll Research, One Hampshire Street, Cambridge, MA 02139, USA c School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA d Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA e Department Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA article info Article history: Received 20 January 2015 Accepted 4 March 2015 Available online 15 March 2015 Keywords: Thin elastic rods Buckling Geometric nonlinearities abstract We present results from an experimental and numerical investigation on the compression, and consequent buckling, of a slender rod constrained inside a horizontal cylinder. An ex- perimental model system is developed to systematically study the sequence of instabili- ties from straight-to-sinusoidal and sinusoidal-to-helical configurations. We quantify the associated buckling loads as a function of the radial clearance between the rod and cylindri- cal constraint. These results are compared to existing theoretical predictions. While good agreement is obtained for large values of the radial clearance, significant deviations are found when the geometric imperfections of the setup are comparable to the radial clear- ance. Due to this imperfection sensitivity, the critical buckling loads can be reduced sig- nificantly by up to a factor of three. The findings from this model system can be applied to practical applications across a range of length scales due to the geometric (rather than material) nonlinearities involved in the deformations of rods. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction Buckling of slender rodlike structures under lateral con- finement can lead to complex geometric nonlinearities and is ubiquitous in both natural and engineered settings, across a wide range of length scales. Examples include DNA packings inside viral capsules [1], silicon nanowires at- tached to stretchable substrates [2], jamming of nanorods confined inside a channel [3], coiling of rods onto rigid sur- faces [4,5] plant roots penetrating into substrates that have * Corresponding author at: Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail address: preis@mit.edu (P.M. Reis). 1 Now a Research Associate with Schlumberger-Doll Research. a graded stiffness [6] and kilometer-long pipes inside of a borehole in oil well operations [7,8]. In the context of drilling, the buckling of a rod inside a vertical cylinder was first investigated by Lubinski et al. [9,7], using equilibrium methods and neglecting the effect of friction. For the case of an inclined, or horizontal, cylin- drical constraint, past a first critical load, P s , the rod takes on a sinusoidal configuration, with a well defined wave- length, λ s c . Lateral deflections of the buckled rod are pe- nalized by the combined effect of elastic and gravitational potential energies, which makes higher buckling modes more energetically favorable than the first mode. Follow- ing energy methods, expressions for P s and λ s c were de- rived by Paslay and Bogey [8] and Dawson and Paslay [10], respectively. Further compression past a second critical load, P h , results in the rod transitioning into a helical configuration. Chen et al. [11] obtained an expression for http://dx.doi.org/10.1016/j.eml.2015.03.002 2352-4316/© 2015 Elsevier Ltd. All rights reserved.