General formulation for local integration in standard elastoplasticity with an arbitrary hardening model

This paper describes a general method for deriving the plastic corrections and the consistent tangent modulus for a wide range of arbitrary non-linear hardening models within the framework of standard small strains elastoplasticity. The features of the proposed formulation are: (i) the local solution is obtained through an iterative procedure. The plastic corrections are given in closed forms exhibiting one scalar function denoted by Galg and three fourth-order tensors Dalg, Galg, Lalg, which are shown to be the algorithmic discrete counterparts of usual theoretical continuum quantities, (ii) the consistent tangent modulus has a symmetrical expression involving the same quantities. Finite element computations are performed using a particular non-linear kinematic hardening model and allow to exhibit the ratcheting phenomenon usually observed on mechanical components subjected to cyclic loadings.