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

TL;DR

This paper introduces a mathematically consistent modification to the directional distortional hardening model in metal plasticity, enabling better representation of yield surface changes and isotropic hardening without kinematic hardening.

Contribution

It proposes a decoupled distortional hardening term that resolves previous inconsistencies and limitations in existing models, grounded in rational thermodynamics.

Findings

Resolves mathematical inconsistency in the complete model.

Enables simultaneous flattening and sharpening of the yield surface.

Supports isotropic hardening with distortion without kinematic hardening.

Abstract

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.