ABSTRACT
In Equation 19.4, Ψi is the yield function. Ψi=0 determines a closed convex surface in stress space called the yield surface. (We will see later that Ψi also serves as a [complementary] dissipation potential.) The stress point remains on the yield surface during plastic flow, and is moving toward its exterior. The plastic strain rate, expressed as a vector, is typically assumed to be normal to the yield surface at the stress point. If the stress point is interior to, or moving tangentially on, the yield surface, only elastic deformation occurs. On all interior paths, for example, due to unloading, the response is only elastic. Plastic deformation induces “hardening,” corresponding to a nonvanishing value of Ci. Finally, k is a history-parameter vector, introduced to represent dependence on the history of plastic strain, for example, through the amount of plastic work.
