28 Crystal Plasticity
This chapter develops the mathematical framework for the physical theory of plasticity outlined in the previous chapter. Examples of the use of the theory are given in subsequent chapters, including the chapter devoted to the development of a special form of the theory developed herein as applied to laminates. In the derivations that follows, the summation convention is used but augmented by the stipulation that a subscript enclosed in (·) is not to be included in a summation; for instance, s(α)mα is simply the dyadic product of the two vectors, sα and mα, not summed over the index α.
28.1 Basic Kinematics
In a crystalline solid an increment of deformation is imagined to occur in two steps. The first, starting from the reference ...