Thermodynamically and variationally consistent modeling of distortional hardening: application to magnesium

To capture the complex elastoplastic response of many materials, classical isotropic and kinematic hardening alone are often not sufficient. Typical phenomena which cannot be predicted by the aforementioned hardening models include, among others, cross hardening or more generally, the distortion of the yield function. However, such phenomena do play an important role in several applications in particular, for non-radial loading paths. Thus, they usually cannot be ignored. In the present contribution, a novel macroscopic model capturing all such effects is proposed. In contrast to most of the existing models in the literature, it is strictly derived from thermodynamical arguments. Furthermore, it is the first macroscopic model including distortional hardening which is also variationally consistent. More explicitly, all state variables follow naturally from energy minimization within advocated framework. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)