Nonlinear Euler buckling

TL;DR

This paper investigates the buckling behavior of hyperelastic cylindrical tubes under compression, developing analytical and numerical methods to determine nonlinear corrections to Euler buckling and the transition between buckling and barrelling.

Contribution

It introduces a combined analytical and numerical approach for nonlinear buckling analysis of hyperelastic tubes, extending classical Euler theory with first nonlinear corrections.

Findings

Derived the range of validity for Euler buckling formula

Identified parameters where buckling transitions to barrelling

Calculated nonlinear corrections for third-order elasticity

Abstract

The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are developed using the exact solution of Wilkes for the linearized problem within the Stroh formalism. Using these methods, the range of validity of the Euler buckling formula and its first nonlinear corrections are obtained for third-order elasticity. The values of the geometric parameters (tube thickness and slenderness) where a transition between buckling and barrelling is observed are also identified.