Axisymmetric wrinkling of cylinders with finite strain

A simple analytical solution for the bifurcation buckling of a cylinder und er axial loading is provided including finite-strain effects. Thus, the sma ll strain theory result of Batterman is generalized. In addition to the thi n shell theory solution (excluding shear deformations), a solution includin g shear deformation effects is also given. All solutions can be evaluated f or either the flow or deformation theory of plasticity. The finite-strain c onstitutive theory used is one in which small strain type relationships app ly between the Jauman rate of the Kirchhoff stress tensor and the deformati on rate tensor. The analytical results are compared to finite-element analy ses to test the validity of the assumptions made. The solutions are explici t. Starting with a point on the stress-strain curve, one calculates explici tly 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 indica te that finite strains have an important stabilizing effect, leading to hig her bifurcation strains.