On the Mathematical Foundation of a Decoupled Directional Distortional Hardening Model for Metal Plasticity in the Framework of Rational Thermodynamics

This study proposes a modification to the yield condition that addresses the mathematical constraints inherent in the Directional Distortional Hardening models developed by Feigenbaum and Dafalias. The modified model resolves both the mathematical inconsistency found in the complete model and the limitations of the r-model. In the complete model, inconsistency arises between the distortional term in the yield surface and the plastic part of the free energy in the absence of kinematic hardening. Additionally, the r-model fails to capture the flattening of the yield surface in the reverse loading direction due to the absence of a fourth-order anisotropic tensor structure in the distortional term. To address these issues, the proposed model introduces a decoupled distortional hardening term in the yield function. This modification enables the simultaneous representation of both flattening and sharpening of the yield surface, and permits isotropic hardening with distortion even without kinematic hardening. A consistent mathematical formulation based on rational mechanics and a corresponding numerical algorithm are also developed, establishing a foundation for future experimental investigations and model validation.

💡 Research Summary

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The paper addresses two fundamental shortcomings in existing directional distortional hardening (DDH) models for metal plasticity: the mathematical inconsistency of the “complete model” proposed by Feigenbaum and Dafalias, and the inability of the subsequent “r‑model” to capture yield‑surface flattening in the reverse loading direction. In the complete model, the distortional term in the yield function is coupled to the back‑stress tensor α through a fourth‑order anisotropic tensor A (H = H₀ + (nᵣ:α) A). Consequently, when α = 0 the distortional contribution vanishes, reducing the yield surface to a classical von Mises form, even though the anisotropic part of the plastic free energy ψ_dis remains non‑zero. This creates a contradiction between the stored energy and the observable yield surface. The r‑model decouples kinematic and distortional hardening by introducing a second‑order orientation tensor r and a scalar scaling factor