September , 2008 , Brno , Czech Republic From Nonlocal Damage to Fracture

Failure of quasibrittle materials such as concrete is characterized by gradual transition from diffuse microcracking to a localized damage process zone and finally to a macroscopic crack. Diffuse damage and its localization into a narrow band of a nonzero thickness are properly described by regularized constitutive models with softening, e.g. by integral-type nonlocal damage models. In this paper, a new nonlocal formulation of the isotropic damage model is proposed, with the damagedriving internal variable dependent on both the local and nonlocal equivalent strain. Localization properties of this model are studied analytically and numerically. It is shown that the localized process zone has initially a certain thickness controled by the nonlocal interaction radius, but later it shrinks and approaches zero thickness. The damage variable grows to 1 only in a very narrow band, which is an improvement over the standard formulation that leads to unrealistically wide bands of fully damaged material. For this reason, the new formulation is more appropriate for the description of transition to a localized crack.