A Directional Damage Model

B. LUCCIONI; S. OLLER

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ELSEVIER SCIENCE SA

Lugar: Amsterdam; Año: 2003 vol. 192 p. 1119 - 1145

0045-7825

Quasi-brittle materials like concrete present a non-linear stress?strain response mainly due to microcracking. In most of the cases these cracks are oriented following the stress history and produce a progressive deterioration of the material elastic stiffness. The initially isotropic material is expected to gradually turn anisotropic.The problem of damage with oriented directions, normally called anisotropic damage or damaged induced anisotropy, has been studied in the last years due to its application to the representation of the behavior of metals and geomaterials in general.The predictive ability of damage models strongly depends on the particular choice of the damage variable that is used as a macroscopic approximation to describe the underlying micro-mechanic process [11]. The scalar damage variable firstly defined by Kachanov [12] is not capable of representing the directional damage phenomenon. A great number of models based on damage vectors [13], second order damage tensors [4?8,14,16,21,23,25,27,30?32,34] and fourth order damage tensors [3,14,24,26,29] have been developed to reproduce anisotropic damage in quasi-brittle materials.Additionally, these models are based on different hypothesis to define the transformation produced by damage [31]: the
strain equivalence hypothesis [10,15] and the
energy equivalence hypothesis  [10,25].In this paper, the problem is presented from a well-known approach [30?32], based on the formulation of the finite strains theory. Although there is no physical relation between these two phenomena, a mathematical comparison can be made at the level of formulation. In the authors opinion, the unification of both formulations results in a considerable advantage at the time of implementation in existent computer programs oriented to the study of finite strains.The bases of the formulation of
directional damage based in the theory of space transformations is presented in this paper along with simple application examples that show the capabilities of the model developed.