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Buckling and Post-Buckling of Thin Elastoplastic Cylindrical Shells With Finite Rotations


 An elastoplastic thin shell model is presented in this work in order to compute the buckling and post-buckling behavior of cylindrical shell-type structures. Standard assumptions in the shell kinematics allow us to develop a large deformation and finite rotation model for thin shells from the three-dimensional continuum.
 An elastoplastic constitutive model for thin shells is derived from the three-dimensional framework, assuming the plane stress condition. The von Mises yield criterion is adopted including non-linear isotropic and linear kinematic hardening.
 The resulting non-linear system is solved by a Newton-Raphson solution procedure, including the consistent linearization of the shell kinematics and the elastoplastic material model.
 The high non-linearities due to the buckling-type instabilities, especially those occuring in the neighbourhood of critical points, necessitate the use of an appropriate step-length control. An arc-length method has been successfully implemented for passing through limit points (load or displacement peaks) where pure load or displacement controls fail. The proposed method is effective in handling both sharp snap-throughs and snap-backs.
 Two numerical examples are presented in view of the assessment of the proposed approach and a particular attention is devoted to the post-buckling of hollow cylinders under axial compression. We identify several types of buckling mode for these structures, among which the axisymmetric mode, the “diamond” mode and the “elephant foot” mode, depending on geometry and boundary conditions.