On combined isotropic and kinematic hardening effects in plastic flow processes

Abstract Attention is focused on the description of the combined isotropic and kinematic hardening effects in plastic solids. It has been found that making use of the simple geometrical relation permits us to determine the coefficient in the evolution equation describing the kinematic hardening of the Ziegler type in such a way that the evolution law is consistent with the loading criterion and satisfies the time independence requirement. On the other hand this method leaves room for the identification procedure for the material constants based on available experimental results. General constitutive and evolution equations for plastic solids are formulated. The plastic potential is assumed different than the yield criterion. Simplifications for the associated flow rule are also investigated. A new evolution law for the anisotropic hardening is discussed. This law represents the linear combination of the Prager and Ziegler kinematic hardening rules. Application of the theory developed to the description of the plastic behavior of damaged solids is given. A particular example is considered. The discussion and the interpretation of the isotropic and anisotropic hardening moduli are presented.