Constitutive derivatives in finite elastic-plastic deformation and calculations for kinematic hardening

In this paper, three new corotational rates and corresponding stress constitutive derivatives are suggested. The stresses of simple shear in finite elastic deformation are analysed and calculated. Using Mises type yield criterion, the constitutive model and fundamental equation of combined isotropic-kinematic hardening are developed. The calculated result for simple shear of kinematic hardening is given. From the results, this proved that utilizing the spins and associated stress rates advanced in this paper, the oscillating phenomena of stress for monotonically increasing strain can fully be eliminated. It is clearly shown by comparison with other results that our analysed and calculated conclusions are correct and satisfactory.