Axisymmetric Wrinkling of Cylinders with Finite Strain

A simple analytical solution for the bifurcation buckling of a cylinder under axial loading is provided including finite-strain effects. Thus, the small strain theory result of Batterman is generalized. In addition to the thin shell theory solution (excluding shear deformations), a solution including shear deformation effects is also given. All solutions can be evaluated for either the flow or deformation theory of plasticity. The finite-strain constitutive theory used is one in which small strain type relationships apply between the Jauman rate of the Kirchhoff stress tensor and the deformation rate tensor. The analytical results are compared to finite-element analyses to test the validity of the assumptions made. The solutions are explicit. Starting with a point on the stress-strain curve, one calculates explicitly the diameter-to-thickness ratio D/t for a cylinder that will buckle at that level of stress and strain (repeating this as necessary to generate a plot of wrinkling strains as a function of D/t). Unless the tangent modulus at bifurcation is large compared to the stress, the results clearly indicate that finite strains have an important stabilizing effect, leading to higher bifurcation strains.