Ideal Flow in Plasticity

Ideal plastic flows constitute a class of solutions in the classical theory of plasticity based on, especially for bulk forming cases, Tresca’s yield criterion without hardening and its associated flow rule. They are defined by the condition that all material elements follow the minimum plastic work path, a condition which is believed to be advantageous for forming processes. Thus, the ideal flow theory has been proposed as the basis of procedures for the direct preliminary design of forming processes, which mainly involve plastic deformation. The aim of the present review is to provide a summary of both the theory of ideal flows and its applications. The theory includes steady and nonsteady flows, which are divided into three sections, respectively: plane-strain flows, axisymmetric flows, and three-dimensional flows. The role of the method of characteristics, including the computational aspect, is emphasized. The theory of ideal membrane flows is also included but separately because of its advanced applications based on finite element numerical codes. For membrane flows, restrictions on the constitutive behavior of materials are significantly relaxed so that more sophisticated anisotropic constitutive laws with hardening are accounted for. In applications, the ideal plastic flow theory provides not only process design guidelines for current forming processes under realistic tool constraints, but also proposes new ultimate optimum process information for futuristic processes.