Quasistatic evolution of damage in an elastic body

The processes of quasistatic evolution of the mechanical state of an elastic body, and the development of material damage which results from internal compression or tension, are modelled and analyzed. The problem is formulated as an elliptic system for the displacements coupled with a parabolic inclusion for the damage field. The existence of the unique local weak solution is established by using approximate problems, the recent theory of set-valued pseudomonotone operators, and a priori estimates.