A displacement-like finite element model for J2 elastoplasticity: Variational formulation and finite-step solution Original Research Article

The displacement-like finite element formulation for finite-step J2 elastoplasticity is revisited in this paper. The classical computational strategy, according to which, plastic loading is tested at the Gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements, is consistently derived from a suitably discretized version of a min-max variational principle. The sequence of solution phases to be performed within each load step adopting a full Newtonʹs method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized. It is further shown that, in order to increase the rate of convergence and the stability properties of the Newtonʹs method, the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model. This is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step. The effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems.