A framework for formulating and implementing non-associative plasticity models for shell buckling computations

In modelling the behavior of thick-walled metal shells under compressive loads, the use of J2 flow theory can lead to unrealistic buckling estimates, while alternative ‘corner’ models, despite offering good predictions, have not been widely adopted for structural computations due to their complexity. The present work develops a new and efficient plasticity model for predicting the structural response of compressed metal shells. It combines the simplicity of the Von Mises yield surface, with a non-associative flow rule, mimicking the effect of a yield surface corner. This allows for tracing the equilibrium path of the loaded shell and identifying consistently structural instability, employing a single constitutive model. A robust backward-Euler integration scheme, suitable for both three-dimensional (solid) and shell elements is developed, along with the corresponding consistent algorithmic moduli for nonlinear isotropic hardening materials, accounting rigorously for the nonlinear dependence of plastic straining on the direction of strain increments. The model is implemented in ABAQUS as a user material subroutine. Simulations of thick-walled metal cylinders under compression predict structural instability in good agreement with experimental data.