A return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first-order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure-independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.
1. Introduction
Effective time integration algorithms for general isotropic yield criteria in elastoplasticity are still under investigation. In order to advance the solution in time, the elastic predictor and plastic corrector scheme, based on the elastoplastic operator split, is a widely accepted method for time integration of the constitutive equations in flow theory. The computational attractiveness of these one-step schemes is cost efficiency with regard to the necessary number of floating point operations. This is achieved by means of simple function evaluations for the solution of the elastic problem in the 'predicting step' and an efficient strategy for solving the implicit algebraic equations of the plastic 'correcting' step. Despite major computational success with the so-called 'radial return mapping algorithm' for J,-plasticity see Reference 9, a similar solution strategy has not been proposed for general isotropic yield surfaces, where comparable advantage of the isotropic properties can be made as in the case of the Prandtl-Reuss flow theory for the solution of the governing algebraic equations.
GOVERNING EQUATIONS AND DISCRETIZATION
2. I . Constitutive equations
The constitutive equations of classical plasticity are derived from the elastic, W, and plastic potential functions. For isotropic material models, the potentials depend on the invariants of the stress, u, or strain tensor, E. It is advantageous to separate the spherical part, p, from the stress deviator, S, S = up l with p = f tru, 1 = CSiJ (1) *Visiting Scholar