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

• Published in: Computer methods in applied mechanics and engineering Vol. 198; no. 41; pp. 3262 - 3277
• Main Author: Ulz, Manfred H.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.09.2009; Elsevier
• Subjects: Anisotropy; Computational techniques; Exact sciences and technology; Finite element method; Finite thermo-plasticity; Fundamental areas of phenomenology (including applications); Green–Naghdi; Inelasticity (thermoplasticity, viscoplasticity...); Isentropic split; Logarithmic strain; Mathematical methods in physics; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Finite element method; Finite thermo-plasticity; Isentropic split; Logarithmic strain; Anisotropy; Green–Naghdi; Constitutive equation; High strain; Entropy; Modeling; Return mapping; Inelasticity; Green-Naghdi; Elastoplasticity; Isotropic hardening; Plasticity; Stress measurement; Strain rate; Numerical integration; Lagrangian; Logarithmic function; Thermomechanical properties; Isentropy; Green function; Phenomenological model; Internal variable material
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2009.06.006

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.