Anisotropic Hardening of Initially Orthotropic Materials

Source abstract

Abstract A hardening model for an orthotropic material is proposed. The corresponding anisotropic parameters are the components of a fourth order tensor function of the plastic strain, entering a quadratic equation for the yield surface. Assuming polynomial dependence on the plastic strain, the most general form of a polynomial fourth order orthotropic tensor function of a second order symmetric tensor is constructed. This is obtained by imposing on the anisotropic parameters form‐invariance conditions under the orthogonal group of coordinate transformations associated with orthotropic symmetries. This yields the appropriate form of polynomial dependence of these parameters on the corresponding integrity basis. An interesting conclusion is that in addition to the initial orthotropic parameters, new anisotropic parameters appear with plastic strain. Kinematic hardening is also considered. The form‐invariance of the rate constitutive equations is discussed.