Abstract: Jaumann rate, generalized Jaumann rate，Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials. The oscillatory response is dependent on objective rate adopted,independent on elastoplastic models. Normal stress is unequal to zero during simple shear finite deformation.

Key words: finite deformation, endochronic equation, simple shear oscillation, objective rate