Plastic limit pressure of spherical vessels with combined hardening involving large deformation

• Sequential limit analysis is extended to consider combined hardening.
• Exact solutions of plastic limit pressure are developed.
• The onset of instability of a spherical vessel is derived and solved numerically.

The paper aims to investigate plastic limit pressure of spherical vessels of nonlinear combined isotropic/kinematic hardening materials. The Armstrong-Frederick kinematic hardening model is adopted and the Voce hardening law is incorporated for isotropic hardening behavior. Analytically, we extend sequential limit analysis to deal with combined isotropic/kinematic hardening materials. Further, exact solutions of plastic limit pressure were developed analytically by conducting both static and kinematic limit analysis. The onset of instability was also derived and solved iteratively by Newton's method. Numerically, elastic–plastic analysis is also performed by the commercial finite-element code ABAQUS incorporated with the user subroutine UMAT implemented with user materials of combined hardening. Finally, the problem formulation and the solution derivations presented here are validated by a very good agreement between the numerical results of exact solutions and the results of elastic–plastic finite-element analysis by ABAQUS.