The overall elastic moduli of orthotropic composite and description of orthotropic damage of materials

This paper presents a model of orthotropic damage of materials that combines macroscopic mechanical properties with microstructure parameters of the material. This model proposes nine elastic constants as the damage variables to describe the quantity and orientation of the damage. Based on Eshelbyʹs equivalent principle, a simpli®ed approach to obtaining the overall moduli for a multiphase, anisotropic composite is developed. The overall elastic compliance tensor of an orthotropic composite reinforced with three mutually perpendicular families of ellipsoidal inclusions is then derived. As special cases, explicit expressions of the overall elastic compliance tensor of a damaged material with three mutually perpendicular families of penny voids, needle voids or cracks, respectively, are presented. The relation of stress and strain with microstructure parameters is given. Moreover, the e€ect of microstructure parameters on damage of materials is analyze