Fundamental requirements and formulation of elastoplastic constitutive equations with tangential plasticity

Abstract

In order to extend an elastoplastic constitutive equation to describe the dependency of a plastic stretching on a stress rate component tangential to the yield surface, two fundamental requirements are first formulated, which have to be fulfilled in elastoplastic constitutive equations. One of them is the work rate or stiffness relaxation. The other is the continuity condition of stress rate. The elastoplastic constitutive equation with a “single, smooth” yield surface is formulated to fulfill these requirements, in which a plastic stretching (its magnitude and direction) depends on a stress rate component tangential to the yield surface; thus it is called a tangential plasticity. Based on this, a concrete constitutive equation of metals with isotropic-kinematic hardening and tangential plasticity is formulated, which, among existing concrete constitutive equations with a tangential plasticity, is capable of describing the general loading behavior including nonproportional, reverse loading, and reloading. Its mechanical response is shown in comparison with the traditional J2 flow theory with the associated flow rule.