Existence of Nonsteady Planar Ideal Flows in Anisotropic Plasticity

Abstract

Ideal plastic flows are those for which all material elements follow minimum work paths. The general equations for steady and nonsteady planar ideal flows in Tresca solids have been given elsewhere. The present paper focuses on nonsteady planar ideal flows in anisotropic plasticity. In particular, the existence of such flows is proven under a certain assumption concerning the orientation of principal stress trajectories at the initial instant. It is also shown that the system of kinematic equations is hyperbolic. This system can be treated separately from the stress equations. The original ideal flow theory is widely used as the basis for inverse methods for the preliminary design of metal forming processes driven by minimum plastic work. The new theory extends this area of application to anisotropic materials.