Derivation of the fourth-order tangent operator based on a generalized eigenvalue problem

Continuous and algorithmic forms of the fourth-order tangent operator corre sponding to isotropic multiplicative elasto-plasticity are derived by gener alizing an approach originally developed for finite elasticity. The Lagrang ian description of large-strain elasto-plasticity leads to a generalized ei genvalue problem which facilitates certain tensor representations with resp ect to a reciprocal set of left and right eigenvectors, The tangent operato rs take an extremely simple form due to the resolution in the basis spanned by the right eigenvectors. Remarkably, these new developments reveal that the algorithmic version of the tangent operator preserves the structure of the continuous counterpart. (C) 1999 Elsevier Science Ltd. All rights reser ved.