Non-associative J2 plasticity model for finite element buckling analysis of shells in the inelastic range

The development and numerical implementation of a special-purpose constitutive model is described for investigating the structural stability of cylindrical metal shells under axial compression and bending, which buckle in the inelastic range. The model employs von Mises yield surface (J2 plasticity) and the rate form of J2 deformation theory, leading to a non-associated flow rule. Special emphasis is given on plastic flow continuity. The numerical implementation is conducted through both the classical Euler-backward and Euler-forward substitution numerical schemes, where stress and strain tensors are described in curvilinear coordinates, with the extra constraint of zero normal stress through the shell thickness. The numerical results will be compared with available experimental data. The model is implemented within an in-house finite element technique for the nonlinear analysis of relatively thick cylindrical metal shells that uses a “tube-element” discretization, and it is employed for the solution of some benchmark problems.