Comparison of some stress rates

Abstract This paper introduces a new derivation rule by means of which two new stress rates are defined. Furthermore, the paper compares five stress rates: Jaumann's, Truesdell's, Green-Naghdi's, Sowerby-Chu's and Durban-Baruch's, for simple shear. Elastic, elastic-perfectly plastic and elastic-plastic hardening (isotropic, kinematic, and combined) material models are considered. Different solutions have already been published for these cases, except for Sowerby-Chu and Durban-Baruch time derivatives. Using the new derivation rule the new rate form of the hyperelastic Doyle-Ericksen formula is obtained. Taking advantage of the Sowerby-Chu stress rate a new constitutive equation for hypoelastic material is given.

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