Study on the generalized Prandtl-Reuss constitutive equation and the corotational rates of stress tensor (Q1289423)

Two shortcommings of the Prandtl-Reuss constitutive equations of nonlinear elastic-plastic materials are pointed out: 1) the lack of a rational justification for using the additive decomposition of the total deformation rate into the elastic and plastic parts in deriving this law, and 2) the difficulty to explain the phenomenon of the simple shear stress oscillation, difficulty which seems to be due to an inadequate choosing of objective rates of the stress tensor. The authors use the material corotational rate of the stress tensor to derive a generalized Prandtl-Reuss constitutive equation governing the behaviour of a nonlinear elastic material which seems to clarify the simple shear oscillation phenomenon. In obtaining this constitutive equation, the authors do not use the above mentioned additive decomposition of the deformation rate. The contents of the paper: 1. Introduction; 2. Generalized Prandtl-Reuss equations based on material corotational rates; 3. Analysis of the cause of the simple shear stress oscillation; 4. Generalized Prandtl-Reuss equations based on a modified relative corotational rates; 4.1. Prandtl-Reuss equations of kinematic hardening materials, 4.2. Prandtl-Reuss equations of von Mises-type isotropic hardening materials; 5. Numerical calculation of a simple shear deformation; 6. Conclusions.