Computational anisotropic hardening multiplicative elastoplasticity based on the corrector elastic logarithmic strain rate

In this paper we present a new computational framework for anisotropic elastoplasticity with mixed hardening which presents the following characteristics: (1) it is motivated by a one-dimensional rheological model where the main differences are due to geometric nonlinearities and three-dimensional effects; (2) it uses the Lee multiplicative decomposition; (3) it is valid for anisotropic yield functions; (4) it is valid for any anisotropic stored energy, either linear or nonlinear in logarithmic strains; (5) it is valid for (non-moderate) large elastic strains; (6) it results in a six-dimensional additive corrector update, parallel to that of the infinitesimal theory; (7) it does not explicitly employ plastic strain tensors or plastic metrics, circumventing definitely the “rate issue”; (8) the incremental plastic flow is isochoric using a simple backward-Euler scheme, without explicitly using exponential mappings; (9) no hypothesis is needed for the plastic spin in order to integrate the symmetric flow derived from the dissipation equation; (10) the Mandel stress tensor plays no role in the formulation; (11) it yields a fully symmetric algorithmic linearization consistent with its associative nature and the principle of maximum dissipation; and (12) it recovers the formulation of Simó for isotropy as a particular case.