Abstract
The Jaumann stress rate of the Cauchy stress is usually used to represent hypoelasticity. Since this stress rate takes into account only the effect of finite rotation; i.e. spin during motion, we here examined the effects of deformation rate terms which can be included in the definitions of the stress rates. First we have shown that the Truesdell stress rate can be defined as a rate of the 2nd Piola-Kirchhoff stress with the current state as reference; i.e. an updated Lagrangian measure. In order to compare the characteristics of the stress rates, localization of deformation was predicted by using the Truesdell stress rate and the convected stress rate, and the results were compared with those by the Jaumann stress rate of the Cauchy stress. All rates predicted the localization at the softening state which is far after the peak of the load-deformation diagram in 3D axisymmetric stress state. However, in plane strain state, the predicted stresses of incipience of the localization by the Truesdell stress rate become close to the experimental critical stresses, Also, the orientations of the localized deformation obtained by the Truesdell stress rate showed consistency with those by the infinitesimal deformation theory, when the stress levels of the localization were in practical order.
