Buckling of a thin elastic rod inside a horizontal cylindrical constraint

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 experimental model system is developed to systematically study the sequence of instabilities 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 cylindrical 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 clearance. Due to this imperfection sensitivity, the critical buckling loads can be reduced significantly 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.