On the Uniqueness and Stability of Endochronic Theory

Abstract

Several numerical and analytical analyses are described which evaluate the uniqueness and stability of solutions of mechanical models whose material behaviors are governed by the endochronic theory of plasticity. It has been found that the simplest form of this theory does show some “material instability” in the sense it does not satisfy Drucker’s postulate when subjected to certain conditions. In other words, an endochronic material creeps under the action of applied force for dynamic problems. However, this “instability” or “lack of a hysteresis loop” can be circumvented by using more general forms of the endochronic theory when necessary. It is also shown that the endochronic solution is at least as unique as that of the elastoplastic theory. No numerical difficulties particular to this theory are observed even when the simplest form is used.