Initial defects are the main cause of the failure of structures made of brittle or quasi-brittle materials. The aim of this paper is to model within the framework of continuum damage mechanics these defects and their influence on the mechanical behavior of the structure they lie in by using a strain localization criterion. The microscopic and mesoscopic conditions for localization are studied by utilizing isotropic or anisotropic damage variables. A representative volume element (RVE) containing one defect is defined and the failure criterion of such an RVE is derived. The initial defect is modeled by an initial damage parameter. The evolution law of this damage value depends upon the nature of induced damage. Finally, an extension of this study to the case of high-cycle fatigue is proposed.
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