OBJECTIVE LOCALIZATION CRITERION AND BEHAVIOR FOR FINITE DEFORMATION PLASTICITY - A LAGRANGIAN FORMULATION

In this paper, the condition for strain localization bifurcation is st udied using Lagrangian description. The localization criterion with re spect to the reference configuration is obtained by relating the rate of the second Piola-Kirchoff stress to the rate of Cauchy-Green deform ation tenser. When transferred to the present configuration, it is equ ivalent to the one which is obtained when Truesdell rate of Cauchy str ess is used in the rate problem. An example for the localization respo nse for a set of triaxial extensions is presented using a specific fin ite-deformation thermo-elastic-plastic model. When a small-deformation based localization criterion is used, i.e. when some terms in the loc alization criterion are neglected, the localization response, at some loading paths, becomes significantly different from that obtained in t he presence of these terms. It is therefore concluded that finite defo rmation tools should be employed when localization analysis is perform ed even when the small deformation hypothesis is otherwise considered as valid.