Bridging the macro to mesoscale: Evaluating the fourth

One of the most challenging problems which arises in continuum damage mechanics is the selection of variables to describe the internal damage. Many theories have been proposed and various types of damage variables ranging from scalar to vector to tensor quantities have been used. In this paper we consider anisotropic damage and the most general form for damage by using a fourth-order tensor for the damage variables. We demonstrate how experimentally measured quantities can be related to the internal tensorial damage variables. We apply this analysis to experiments of an initially isotropic solid becoming transverse isotropic under triaxial or uniaxial stress loading