Some remarks on damage theory

Abstract To date, damage theory suffers from both the lack of uniformity in its approach and the lack of rigor in its developments. It is one of the aims of this paper to somewhat remedy the second inconvenience and to show that, in turn, rigor greatly helps selecting prevailing points of view. This programme is carried out for the broad problem of anisotropic damage, and general directions for future research in various areas are indicated. In addition, in the case of isotropic damage, we have been able to establish a model that does not exhibit the weaknesses of the usual generalization of Kachanov's theory. In particular, softening of the material is translated by the modifications of both Young's modulus and Poisson's ratio, the change in volume due to voids expansion is properly accounted for, and the need for empirically determined thresholds for failure is eliminated. The model is valid for both the quasi-static and dynamic cases, in the assumption of small elasto-plastic deformations but without restriction to small damage. For simplicity, attention is confined to isothermal processes. The model is well suited for the mathematical treatment of PDEs. The final section is indeed devoted to some theoretical existence and uniqueness results.