An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates

The paper is devoted to numerical realization of elastoplastic problems. The main goal is to improve implementation of the related constitutive problems. This can be done if plastic flow rules are defined by subdifferentials of plastic potentials. Then just one plastic multiplier is used even if the plastic potentials are nondifferentiable for unknown stress tensors. Further, the implicit Euler time discretization scheme is considered and the standard elastic predictor plastic corrector method is used to find the discretized constitutive solution. Due to the presence of the one multiplier, it is possible to construct a unique system of nonlinear equations within the plastic correction regardless the unknown stress tensor lies on the smooth portion of the yield surface or not. Plastic criteria given by the Haigh-Westergaard coordinates are investigated in this paper (PART I). The suggested method is in detail studied on the problem containing the DruckerPrager criterion, a nonassociative plastic flow rule and a nonlinear isotropic hardening. It is shown that for this problem, one can a priori decide whether the unknown stress tensor will lie on the smooth portion or at the apex of the yield surface. The corresponding tangential (consistent) stiffness matrix is constructed and the elastoplastic problem is solved by the semismooth Newton method. The new method is implemented within the in house software SIFEL and several numerical experiments are introduced.