The lode angle dependency introduced by anisotropic damage evolution laws is analyzed in detail for initially isotropic materials. Many rupture criteria are obtained, under the proportional loading assumption, by the time integration of different anisotropic damage evolution laws [Formula: see text] among the three existing families: strain governed, stress governed and plastic strain governed. The cross-analysis of path independent rupture criteria and of anisotropic damage evolution laws finally allows us to improve the Lode angle dependency of (fully coupled) anisotropic damage models.