Abstract
The constitutive equations of a plastic material with kinematic work-hardening are proposed. A symmetric tensor internal state variable, called the translation tensor, is introduced. The plastic potential is assumed to be a scalar function of the translated stress, which is the difference between the stress and the translation. A rate type mechanical constitutive equation is defined which relates linearly the stress rate to the stretching and has a coefficient depending on the translated stress, and a rate type evolutional equation is also defined which is the linear relation between the translation rate and the plastic stretching. The loading, the neutral and the unloading states are defined, respectively, by the positive, zero and negative values of the deviatoric translated stress power. The constitutive equation and the evolutional equation are newly defined in the above three states. From the mechanical constitutive relation in the loading state the yield criterion and the plastic flow rule are derived. The criterion obtained shows the kinematic work-hardening.
