Hypoelasticity-based analytical stress solutions in the simple shearing process

摘要

In the present work a set of hypoelasticity-based analytical stress solutions of simple shearing is formulated. The rate constitutive equations based on the Jaumann, Green-Naghdi, Oldroyd, Truesdell, Cotter-Rivlin, logarithmic and Omega(E)- and Omega(L)-based stress rates are exploited. From a representation principle of the material spins, a concise formula of the spin tensors for simple shearing is derived. Based on the derived spin equation a novel analytical stress solution related to the Omega(L)-based stress rates is formulated. For completeness the issued stress solutions in conjunction with the other stress rates are also reformulated. All analytical stress solutions are illustrated and compared. [References: 14]