Texture evolution in polycrystals due to rotation of the atomic lattice in single grains results in a complex macroscopic mechanical behavior which cannot be reasonably captured only by classical isotropic or kinematic hardening in general. More precisely and focusing on standard rate-independent plasticity theory, the complex interplay at the microscale of a polycrystal leads to an evolving macroscopic anisotropy of the yield surface, also known as distortional or differential hardening. This effect is of utmost importance, if non-radial loading paths such as those associated with forming processes are to be numerically analyzed. In the present paper, different existing distortional hardening models are critically reviewed. For a better comparison, they are reformulated into the modern framework of hyperelastoplasticity, and the same objective time derivative is applied to all evolution equations. Furthermore, since the original models are based on a Hill-type yield function not accounting for the stress differential effect as observed in hcp metals such as magnesium, respective generalizations are also discussed. It is shown that only one of the resulting models can fulfill the second law of thermodynamics. That model predicts a high curvature of the yield function in loading direction, while the opposite region of the yield function is rather flat. Indeed, such a response can be observed for some materials such as aluminum alloys. In the case of magnesium, however, that does not seem to be true. Therefore, a novel constitutive model is presented. Its underlying structure is comparably simple and the model is thermodynamically consistent. Conceptually, distortional hardening is described by an Armstrong-Frederick-type evolution equation. The predictive capabilities of the final model are demonstrated by comparisons

a b s t r a c tMany important physical effects of materials undergoing plasticity at the macroscale cannot be captured realistically by isotropic and kinematic hardening only. For instance, the evolution of the texture in polycrystals results macroscopically in a distorted yield surface. This paper deals with adequate hardening models for such a distortion. To be more precise, a novel general frame for finite strain plasticity models is elaborated. To the best knowledge of the authors, it is the first one combining the following features: (1) proof of thermodynamical consistency; (2) decomposition of distortional hardening into dynamic hardening (due to currently active dislocations) and latent hardening (due to currently inactive dislocations); (3) difference of the yield surface's curvature in loading direction and in the opposite direction. The cornerstone of this model is a new plastic potential for the evolution equations governing distortional hardening. Although this type of hardening is characterized through a fourth-order tensor as internal variable, the structure of the aforementioned potential is surprisingly simple. Even though the final model is rather complex, it requires only few model parameters. For these parameters, in turn, physically sound bounds based on the convexity condition of the yield surface can be derived. Three different examples demonstrate the predictive capabilities of the novel framework.

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A Fe-34.5 wt % Mn-0.04 wt % C ultra-high Mn steel with a fully recrystallised fine-grained structure was produced by cold rolling and subsequent annealing. The steel exhibited excellent cryogenic temperature properties with enhanced work hardening rate, high tensile strength, and high uniform elongation. In order to capture the unique mechanical behaviour, a constitutive model within finite strain plasticity framework based on Hill-type yield function was established with standard Armstrong-Frederick type isotropic hardening. In particular, the evolution of isotropic hardening was determined by the content of martensite; thus, a relationship between model parameters and martensite content is built explicitly.