Adriana Garroni, Department of Mathematics, University of Rome "La sapienza"
"Quasi-static evolution for a variational model of damage"
We consider a variational model for damage introduced by Francfort and Marigo. In this model the damage process consist in passing from an initial elastic state (undamaged) to a weaker elastic stated (damaged) and the resulting energy density is non quasi convex. For a given time-dependent external loading we establish existence of a relaxed variational evolution where, at each time, the two states of the material combine to form a fine mixture, optimal from the standpoint of the applied load at that time, yet preserving the irreversibility of the damaging process.