Extension of the Flow Rule in Plastic Constitutive Equation

Abstract

The extension of the elastoplastic constitutive equation so as to describe the dependencies of the direction of a plastic stretching on a stress rate or on a stretching and of the magnitude on a stress rate component tangential to the yield surface has been one of the most pressing problems in the elastoplasticity. To this aim, various models have been proposed in the past. However, a pertinent model applicable to a general loading process has not previously been proposed. In this article, keeping a single smooth (regular) yield surface for the steady development of elastoplasticity, an extended flow rule describing the above-mentioned dependencies is proposed by incorporating an additional term of the stretching tensor in degree zero into the associated flow rule. The elastoplastic constitutive equation with this flow rule is thought to be a pertinent one which fulfills the mechanical requirements, i.e. the rate-nonlinearity, the continuity condition and the work rate-stiffness relaxation [1,2] and which is applicable to an arbitrary loading process including unloading, reloading and reverse loading.