Basic Formulations for Elastoplastic Constitutive Equations

Abstract

As described in Chapter 5, the elastic deformation is induced microscopically by the deformations of the material particles themselves, which returns to the initial state if the applied stress is removed. Therefore, it has a one-to-one correspondence to the stress. On the other hand, when the stress reaches the yield stress, slippage between material particles is induced and they do not return to the initial state even if the stress is removed, which leads macroscopically to the plastic deformation. For that reason, one-to-one correspondence between the stress and the strain, i.e. the stress-strain relation, observed in the elastic deformation does not hold in the elastoplastic deformation process. Therefore, one must formulate the constitutive equation as a relation between the stress rate and the strain rate in that process. This chapter presents a description of the basic concept and formulation for elastoplastic constitutive equations within the framework of conventional plasticity (Drucker, 1988) premised on the assumption that the inside of the yield surface is a purely elastic domain for the introductory to elastoplasticity. The unconventional plasticity describing the plastic strain rate induced by the rate of stress inside the yield surface will be described in subsequent chapters.