Non-Quadratic Pseudo Dual Potentials for Plastic Flow Modeling

Abstract

Abstract The existence of dual flow potentials is well established in mathematical theory of plasticity since the seminal work by Hill in 1987. For a metal undergoing plastic flow, a flow stress potential is used to compute its plastic strain increments when the applied yield stress is known. On the other hand, the corresponding dual flow strain-rate potential is used to compute the stress on the flow surface when the plastic strain increments are given. This work examines some issues associated with plasticity modeling using non-quadratic dual flow potentials. Unlike the quadratic case where flow stress and strain-rate potentials are the exact dual to each other, it is often difficult if not impossible to obtain analytically the dual of a non-quadratic flow stress or strain-rate potential. The study instead focuses on formulating and assessing various non-quadratic pseudo dual flow potentials that approximate the actual flow surfaces in either stress or strain-rate space. The difference and connection between the yield surface and flow surface in non-associated plasticity are also investigated. Although only one of the dual flow potentials is actually needed for their applications in associated and non-associated plasticity modeling, the unique advantage of having both dual flow potentials on hand even in their pseudo forms is pointed out for new computational analyses.