On uniqueness in the theory of plasticity

The fundamental definitions of work-hardening and perfect plasticity have far reaching implications with respect to uniqueness of solution for elastic-plastic bodies. Satisfaction of the basic postulate, that in a cycle work cannot be extracted from the material and the system of forces acting upon it, guarantees an existing solution to be stable but not necessarily unique. Uniqueness follows for the usual linear relation between the increments or rates of stress and strain and also for combinations of such linear forms. Conversely, lack of uniqueness results for an elastic-perfectly plastic body when, for example, the maximum shearing stress criterion of yield is employed with the Mises flow rule.