A Green–Naghdi approach to finite anisotropic rate-independent and rate-dependent thermo-plasticity in logarithmic Lagrangean strain–entropy space

The paper presents a phenomenological model of rate-independent and rate-dependent thermo-plasticity in the logarithmic Lagrangean strain–entropy space at finite strains. The formulation and computational implementation are based on an additive decomposition of the strain measure into an elastic and plastic part as proposed by Green and Naghdi. A rate-independent and rate-dependent constitutive model in the logarithmic Lagrangean strain–entropy space is developed for the modelling of isotropic elastic and anisotropic plastic material behaviour. Furthermore, the notion of a plastic metric as proposed by Miehe, an isotropic hardening variable and the notion of a plastic entropy as proposed by Simo and Miehe dominate the internal variable description. The model keeps the classical general return-mapping scheme in the implicit integration algorithm of the internal variables of associative thermo-plasticity. The resulting coupled thermo-mechanical problem is solved staggeredly via an isentropic phase for the deformation and an iso-geometrical phase for the thermal field. Representative numerical simulations demonstrate the performance of the proposed model.