Because the damage in a solid results from microscopic movements, we d
ecided to include the power of these microscopic movements in the powe
r of the internal forces. The microscopic velocities are related to th
e damage rate. The power of the internal forces that we choose depends
on the damage velocity and its gradient to take into account the inte
ractions. Models from this theory are presented. They are coherent fro
m the mechanical and mathematical points of view. The numerical comput
ations show no mesh sensitivity. They describe with good agreement the
main experimental properties. Concrete is chosen as an example to ill
ustrate the theory. A model using two damage quantities is also presen
ted. It gives a description of the unilateral phenomenon observed in c
oncrete.