Non-associative plasticity for structural instability of cylindrical shells in the inelastic range
Thick-walled cylindrical metal shells, commonly used in tubular structures and pipelines, during their lifetime may be subjected to considerable compressive loads, which can lead to local buckling. In modelling their structural behaviour, the use of standard J2 flow plasticity is known to produce unrealistically high buckling load estimates. Alternative constitutive models, which consider the formation of yield surface ‘corners’, can provide more accurate predictions, but they have been used scarcely, due to the limitations and complexities they introduce. The present work develops an efficient and versatile plasticity model to simulate the structural response of metal shells under compressive loads. It combines the simplicity of a Von Mises yield surface, with a non-associative flow rule, mimicking the effect of a yield surface corner. The model allows for tracing the equilibrium path of the shells and identifying structural instability in a consistent manner. A robust backward-Euler integration scheme is developed, suitable for three-dimensional (solid) and shell finite elements. The corresponding algorithmic moduli are obtained for nonlinear isotropic hardening materials. The nonlinear dependence of plastic strain increments on the direction of total strain increments is accounted for rigorously. The constitutive model is implemented in Abaqus as a user material subroutine (UMAT). Simulations of thick-walled metal cylinders under uniform compression show good agreement with experimental data in predicting the buckling and post-buckling performance of shells. The influence of geometric imperfection is considered, and comparisons are made with models employing the J2 flow plasticity. The reliability of the developed approach is further demonstrated by investigating more demanding problems of bending and pressure in inelastic cylinders, taking into account ovalization, bifurcation instabilities, imperfection. These problems involve non-trivial prebuckling equilibrium paths, non-uniform loading and significant non-proportionality, before instability onsets, which activate the model’s particular features, and illustrate their role in the evolution of buckling. Analyses showcase the model’s capabilities, producing accurate instability estimates, ultimate load and deformation predictions in line with experiments and clarify aspects of the buckling of inelastic shells. Extending a traditional practice, a simple method is presented for estimating the instability of inelastic cylinders under bending and pressure loads, drawing on similarities in their buckling with that of cylinders under compression.