抄録
The constitutive equations of a plastic material with isotropic work-hardening are proposed. The plastic potential is assumed to be a function of the stress and the scalar internal state variables. Here four restrictions are taken into consideration, that is, (1) linear elasticity, (2) pressure-insensitivity, (3) no generalized Bauschinger effect, and (4) grade two for stress. A rate-type mechanical constitutive equation is derived which relates the stress rate to the stretching and has a coefficient depending on the internal state variables. Evolutional equations, which govern the temporal variations of the internal state variables, are also derived. From a point of view of the theory of ordinary differential equation the number of the variables is reduced to one. From the constitutive equation the yield criterion and the flow rule are naturally specified, and a generalized Huber-von Mises yield criterion with isotropic work-hardening and the Lévy-St. Venant flow rule are obtained.
