Abstract: High-velocity deformation process of material is usually accompanied with interior damage evolution in different forms. Experimental observations for different materials show that damage evolution is dependent on strain, strain rate and temperature, and a certain equivalency exists between the strain rate effect and the temperature effect. Thus, based on the thermo-activation mechanism, a strain and strain-rate dependent damage evolution law and the corresponding rate-dependent constitutive relation taking account of damage evolution are proposed. As an example, the ZWT nonlinear viscoelastic constitutive relation taking account of damage-weakening effect is further studied, particularly the constitutive response and the response due to damage evolution can be distinguished.