A variational view of partial brittle damage evolution

Under time-dependent loading an elastic material undergoes the simplest form of damage in which it passes from its original state to a weaker elastic state. Elaborating on prior work [14], we establish the 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.