Isotropic and Anisotropic Damage Variables in Continuum Damage Mechanics

Abstract

The present work analyzes the implication and limitation of some scalar damage models. In particular, the elastic‐damage thermodynamic potential and the effective stress concept are reexamined. It is demonstrated that isotropic damage does not necessarily imply scalar damage representation in general. The notion of isotropic and anisotropic damage variables in continuum damage mechanics is then discussed. In addition, some results from micromechanical analyses are applied to show the direct relationship between the fourth‐order damage tensor and the damage‐induced compliance tensor characteristic of microcrack‐weakened brittle materials. It is shown that even for isotropic damage one should employ an isotropic fourth‐order damage tensor (not a scalar damage variable) to characterize the state of damage in materials, in accordance with the effective stress concept. In general, however, a damage tensor is anisotropic and should be derived from micromechanical analysis when possible.