Abstract
The constitutive equations of a plastic material with general work-hardening are proposed. Two internal state variables, scalar and tensor, are introduced. The plastic potential is assumed to be a scalar function of the translated stress and the scalar internal state variable. Four constitutive assumptions are taken into cosideration. A mechanical constitutive equation and two evolutional equations are derived, where the former relates the translated stress rate to the stretching, and the latter govern the temporal variation of the internal state variables. These constitutive relations may show the kinematic work-hardening as well as the isotropic work-hardening. A fracture rule is also proposed. It is supposed that the fracture occurs when a scalar function of two internal state variables, called the fracture function, has a critical value.
