Simple model for directional distortional hardening in metal plasticity within thermodynamics

Directional distortion, observed in many experiments on various types of metals, refers to the formation of a region of high curvature (sharpening) on the yield surface approximately in the direction of loading, and a region of low curvature (flattening) approximately in the opposite direction. Constitutive modeling of directional distortion was recently presented by the writers where an evolving fourth-order tensor-valued internal variable was introduced. In the current paper a much simpler mathematical formulation describing directional distortional hardening is presented without the use of a fourth-order tensor, in conjunction with kinematic and isotropic hardening. Two versions of the model in ascending level of complexity follow similar lines of development, which include derivation of all hardening rules on the basis of conditions sufficient to satisfy the thermodynamic dissipation inequality. As a tradeoff for its simplicity the present model does not fit experimental data as well as the model with the evolving fourth-order tensor, but it still captures the salient features of directional distortion in a rather satisfactory way.