Characterization of isotropic damage using double scalar variables

In this study, double scalar damage variables have been used to characterize the state of isotropic damage. The damage influence tensor relating to the double scalar damage variables of damaged material is thus formulated based on the hypothesis of stress equivalence for this model. The specific damage energy release rate is adopted to represent the thermodynamics force conjugating to the double damage variables. Based on the irreversibility laws of thermodynamics, these forces have been formulated directly from the degradation of effective engineering elastic coefficients in stress space. The contribution of both dilatation and distortion of material to the specific damage energy density release rate in loading process has been explained. The double scalar damage variables of isotropic solid material with penny-shape cracks and spherical voids randomly distributed have been determined on the basis of the micro-mechanics theory, respectively. In addition, the damage influence tensor and the specific damage energy release rate were obtained by using the experimental results of pre-strained aluminum alloy 2024T3 specimens under uni-axial tension tests.