M. Fremond et D. Nedjar, DAMAGE, GRADIENT OF DAMAGE AND PRINCIPLE OF VIRTUAL POWER, International journal of solids and structures, 33(8), 1996, pp. 1083-1103
A theory of continuum damage mechanics is developed within the framewo
rk of the principle of virtual power. Because the damage in a solid re
sults from microscopic movements, we decided to include the power of t
hese microscopic movements in the power of the internal forces. The mi
croscopic velocities are related to the damage rare. The power of the
internal forces we choose depends on the damage velocity and its gradi
ent to take into account the interactions. Models issued from this the
ory are presented. They are coherent from the mechanical and mathemati
cal points of view. The numerical computations show no mesh sensitivit
y. They describe with good agreement the main experimental properties.
Concrete is chosen as an example to illustrate the theory. A model us
ing two damage quantities is also presented. It yields the correct des
cription of the unilateral phenomenon observed in concrete. Finally, a
n extension of the existing models is proposed to describe the fatigue
damage behaviour.