A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.