Damage, gradient of damage and principle of virtual power

theory of continuum damage mechanics is developed within the framework of the principle of virtual power. Because the damage in a solid results from microscopic movements, we decided to include the power of these microscopic movements in the power of the internal forces. The microscopic velocities are related to the damage rate. The power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions. Models issued from this theory are presented. They are coherent from the mechanical and mathematical points of view. The numerical computations show no mesh sensitivity. They describe with good agreement the main experimental properties. Concrete is chosen as an example to illustrate the theory. A model using two damage quantities is also presented. It yields the correct description of the unilateral phenomenon observed in concrete. Finally, an extension of the existing models is proposed to describe the fatigue damage behaviour.