Loading and Unloading of Prandtl-Reuss Plastic Material with Isotropic Work-Hardening

Abstract

Here the loading and unloading behaviors are investigated theoretically for the Prandtl-Reuss plastic material with the isotropic work-hardening, which was derived in the preceding paper. The constitutive equations consist of the mechanical equation of rate type and the evolutional equation of a scalar internal state variable α. The steady extension is analyzed and the stress-logarithmic strain relations are formulated, where α plays as a parameter. The steady extension in the uniaxial stress is also analyzed for the incompressible material. The material function of the type M(α)=M₀(1+aα)ⁿ is adopted, where M₀, a and n are the material constants. The function specifies the yield phenomenon and the work-hardening. The constants a and n represent, respectively, the magnitude of the work-hardening and the variation of it. The results of the numerical calculations are depicted.