A DISPLACEMENT-LIKE FINITE-ELEMENT MODEL FOR J(2) ELASTOPLASTICITY - VARIATIONAL FORMULATION AND FINITE-STEP SOLUTION

The displacement-like finite element formulation for finite-step J(2) elastoplasticity is revisited in this paper. The classical com putatio nal strategy, according to which, plastic loading is tested at the Gau ss points of each element and an independent return mapping algorithm is performed for given incremental displacements, is consistently deri ved from a suitably discretized version of a min-max variational princ iple. The sequence of solution phases to be performed within each load step adopting a full Newton's 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 Newton's method, the consistent e lastoplastic tangent operator must be exploited even at the first iter ation of each load step subsequent to the first yielding of the struct ural model. This is in contrast with the traditional implementation ac cording to which the elastic operator is used at the first iteration o f each load step. The effectiveness of the present approach is shown b y a set of numerical examples referred to plane strain problems. (C) 1 998 Elsevier Science S.A.