Buckling, barrelling, and surface instabilities of a finite, transversely isotropic circular cylinder

This paper investigates all possible geometric instabilities, such as buckling, barrelling, surface wrinkling, and orange-peel mode instabilities, for a finite length transversely isotropic circular cylinder under axisymmetric tension or compression. The constitutive responses of the cylinder can, in general, be transversely isotropic, compressible, and elastic-plastic; and no existence of rate potential is assumed. A general procedure is given to calculate the smallest critical ratio of radius to length, ${\left ( a/L) \right )_{cr}}$, of a circular cylinder that separates the buckling (antisymmetric) and the barrelling (axisymmetric) instabilities. Numerical results show that ${\left ( a/L \right )_{cr}}$ is very sensitive to the constitutive model used. The stress at the maximum load point is obtained as the first term of the axisymmetric long wavelength limit; the Euler buckling formula is obtained as the first term of the antisymmetric long wavelength limit. Three different types of surface instabilities are considered. The eigenstress for the longitudinal short wavelength limit corresponds to that for the wrinkling instability of a halfspace under plane deformations; the circumferential short wavelength limit is always possible; and the longitudinal and circumferential short wavelength limit, which corresponds to the surface instability with an “orange-peel” appearance, is available along the tensile elliptic-parabolic boundary. Numerical results show that eigenmodes of $n \ge 2$ (where $n$ is the circumferential wave number) can be the first bifurcation encountered under tension depending on the geometric ratio, $a/L$. However, such eigenmodes will not be the first possible bifurcation under compression unless the ratio of the incremental transverse shear modulus to the incremental longitudinal shear modulus drops below, approximately, 0.25.