In this chapter we study the stress and deformation in materials loaded beyond the elastic limit such that plastic yielding occurs. When the stress-strain law is independent of the rate of deformation but is dependent on the history of deformation, this area of study is called rate-independent plasticity, classical plasticity, or simply plasticity. Although constitutive laws for plasticity are not fully developed, we shall nevertheless present relations that are useful under certain conditions. We have already introduced the one-dimensional elastic, perfectly plastic model and the rigid, perfectly plastic model in Chapter 4. The concept of strain hardening was discussed in Section 4.3; we also call this phenomenon work hardening. Recall that on unloading from a point B (see Fig. 8.1) in the nonlinear zone, we find linear elastic behavior with a modulus of elasticity equal to that experienced on initial loading of the specimen. On reloading as shown in the diagram, we find that the yield point has been raised. Such complex behavior is indicative of a basic difference between elasticity and plasticity. In the latter it is clear that the strain is a historydependent function of the stress. This greatly increases the difficulty encountered in the application of plasticity theory.