On Alternative Approaches for Graded Damage Modelling

To prevent problem of spurious localization in damage mechanics, the introduction of a quadratic terms in gradient of damage has been used to govern the amplitude of the spatial gradient of damage. In more recent papers based on definition of Thick-Level-Set, the regularization is obtained considering that damage is function of a level-set, then the gradient of damage is bounded in zone where the level-set becomes a signed distance function. Here we consider classical damage modelling with introduction of an internal constraint on the spatial gradient of damage. This point of view produces a new regularization without the introduction of a level-set and signed distance.