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

Abstract

Continuous and algorithmic forms of the fourth-order tangent operator corresponding to isotropic multiplicative elasto-plasticity are derived by generalizing an approach originally developed for finite elasticity. The Lagrangian description of large-strain elasto-plasticity leads to a generalized eigenvalue problem which facilitates certain tensor representations with respect to a reciprocal set of left and right eigenvectors. The tangent operators 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.