by George Z. Voyiadjis and Peter I. Kattan
In this work, various definitions of the damage variables are examined and compared. In particular, special emphasis is given to a new damage variable that is defined in terms of the elastic stiffness of the material. Both the scalar and tensorial cases are investigated. The scalar definition of the new damage variable was used recently by many researchers. However, the generalization to tensors and general states of deformation and damage is new and appears here for the first time. In addition, transformation laws for various elastic constants are derived. Finally, the cases of plane stress, plane strain, and isotropic elasticity are examined in detail. In these cases it is shown that only two independent damage parameters are needed to describe the complete state of damage in the material. In this work, a physical basis is sought for the damage tensor [M] that is used to link the damage state of the material with effective undamaged configuration. The authors and numerous other researchers have used different paths including fabric tensors (Voyiadjis and Kattan, 2006a; Voyiadjis et al., 2007) to connect the two configurations. However, the approach presented here provides for a strong physical basis for this missing link.