Elastic Stress Ratchetting and Corotational Stress Rates

It is well accepted that stresses should return to their original state after a closed elastic strain cycle. Here, we consider originally unstressed elements undergoing such cycles. We presume isotropic materials and use Truesdell’s hypoelastic law. Depending on the applied corotational stress rate, undesirable stress ratchetting is observed in case of two commonly used objective rates, namely the Zaremba-Jaumann and the Green/Naghdi rates. The strain cycle reaches its original stress-free state when the logarithmic rate is applied