The variational approach to damage: I. The foundations

This Note is devoted to the construction of local brittle damage laws. We first justify by the Drucker-Ilyushin postulate to set their formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties of the material. Moreover, the evolution problem can be read as a variational problem which is reinforced so that it finally contains the concepts of stability and of energy conservation. (C) 2010 Academic des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.