Basic formulations for elastoplastic constitutive equations

Elastic deformation is induced microscopically by the elastic deformations of the material particles themselves, exhibiting a one-to-one correspondence to the stress. However, when the stress reaches an yield stress, slippages between material particles are induced, which do not disappear even if the stress is removed, leading to macroscopically to the plastic deformation. Then, the one-to-one correspondence between the stress and the strain, i.e. the stress-strain relation does not hold in the elastoplastic deformation process. Therefore, onemust formulate the elastoplastic constitutive equation as a relation between the stress rate and the strain rate. This chapter addresses 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 as the introduction to elastoplasticity. The unconventional plasticity describing the plastic strain rate induced by the rate of stress inside the yield surface will be described in the subsequent chapters. © Springer-Verlag Berlin Heidelberg 2014.