Fundamental Consequences of a New Intrinsic Time Measure. Plasticity as a Limit of the Endochronic Theory

Abstract

Abstract : A new measure of intrinsic time is introduced which broadens the endochronic theory and lends it a wider predictive scope. Idealized plastic models are shown to be constitutive subsets of the general theory and the phenomenon of yield is proved to be a consequence of a particular definition of the intrinsic time measure in terms of the plastic strain tensor. Various versions of the classical plasticity theory are shown to be asymptotic cases of the endochronic theory. In particular the kinematic hardening model, the isotropic hardening model as well as their combinations, are derivable directly from the general theory. In addition, the translation vector of the yield surface in stress space is found to be a constitutive property given by a linear functional of the history of the plastic strain. The Prager and Ziegler rules are immediately obtainable as special cases. It is also shown that the essential features of plastic response under conditions of 'stress reversals', are contained in the constitutive equation whose form remains invariant of the deformation history. It is believed that this is the first time that one single constitutive equation has been shown to predict correctly the essential features of plastic response under conditions of loading, unloading and reloading. However, when the intrinsic time measure is precisely equal to the norm of the increment of the plastic strain tensor, the constitutive unity, spoken of above, no longer exists.