The ordinary differential constitutive equations of endochronic theory are extended to simulate elasto-plastic deformation in the range of finite strain using the concept of corotational rate. Different corotational stress rates (Jaumann, Cotter-Rivlin, Truesdell, Dienes and Mandel) are incorporated into the theory. In addition, a new formulation of the plastic spin, which can be used in the Mandel stress rate, is derived. Theoretical simulations of the axial effects for various materials subjected to simple and pure torsional loading cases are discussed in this study. It is shown that the endochronic theory incorporated with the Mandel stress rate yields the most satisfactory result, as indicated from comparison with the experimental data found in literature. Finally, theoretical investigation of the deformation subjected to finite proportional and non-proportional biaxial compression is presented. The true relationship between stress and strain can be converted to a nominal stress-strain relationship for biaxial loading through the explicit transformation equations derived in this paper. Experimental data tested by Khan and Wang  ("An Experimental study of Large finite Plastic Deformation in Annealed 1100 Aluminum During Proportional and Non-proportional Biaxial Compression" Int. J. Plasticity, 6, 485) are suitably described by the theory demonstrated from a comparison with the theoretical prediction according to rigid-plastic and elastic-plastic models employed by Huang and Khan . "An Analysis of Finite Elastic-Plastic Deformation under Biaxial Compression", Int. J. Plasticity, 7, 219).
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