Comparison between two theories of plasticity

Among numerous large strain elasto-plasticity theories, Green-Naghdi's theory and E. H. Lee's theory are distinguished and distinctive. In Green-Naghdi's theory, the Green-Lagrange strain tensor is decomposed into the elastic and the plastic parts. On the other hand, E. H. Lee started with a decomposition of the deformation gradient into a product of two parts: elastic and plastic. In the case of simple tension, the essential differences arc found between these two theories. In E. H. Lee's theory, the unloading curves are parallel on the plots of Cauchy stress vs natural strain. However, this parallel relation does not exist on the plots of Piola-Kirchhoff stress vs Green-Lagrange strain. In Green-Naghdi's theory, the results are reversed. The unloading curves are not parallel on the plots of Cauchy stress vs natural strain, but parallel on the plots of Piola-Kirchhoff stress vs Green-Lagrange strain. The significance of this finding is further discussed.