A constitutive equation for elastic-viscoplastic materials is proposed. The condition to have a unique solution of initial, time-dependent boundary value problems is derived. Introducing the definition of stability in terms of the kinetic energy of perturbation velocity, a stability criterion is here suggested. Also the localization phenomenon interpreted as a particular case of instability is dealt with for the elastic-viscoplastic materials. The effect of geometric nonuniformity on the localization is studied here assuming the isothermal deformation process.
