ISOTROPIC /K INEMATIC-HARDENING THEORY

Abstract-Using Mandel's director concept, the internal time theory for small deformation devia-toric plasticity (as given by Valanls and by Watanabe and Atlurl) is extended to the case of finite elastoplasticity. The introduction of the material director triad together with an isoclinic con-figuration makes possible an integral representation f the induced stress tensor in terms of the deformation history [referred to the relaxed intermediate configuration.] For a class of defor-mations in which elastic strains are small, this leads to rate-type constitutive equations similar to those in the small deformation theory. The model retains the characteristics of the original internal time theory, such as the existence of avon Mises type of yield surface that undergoes translation (nonlinear kinematic hardening), as well as uniform expansion in the stress pace, and of the normality of the tensor of plastic rate of deformation to the yield hypersurface. In modeling finite uniaxial compression and finite torsion test data, the present internal time theory is found to lead to results very similar to those from a phenomenological theory with a priori postulated evolution equation for an arbitrary objective rate (say, the Jaumann rate) of the back stress using the general representation for the symmetric tensor function. This lat-ter phenomenological theory is a slight modification of the one proposed earlier by Reed an