13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- more general cases, numerous fracture and damage models were proposed in the literature. When the stress concentration presents a singularity weaker than the crack one, such a singularity can be found in the cases of sharp notches, interface cracking or cracks in ductile materials, criteria based on finite fracture mechanics were developed and reported in the literature. In simple words, these criteria are kinds of combinations of (1) and (2). [1-5]. Another class of fracture criteria was issued from the so-called cohesive models [6-10]. In all these criteria and models, one can distinguish a length scale parameter, such as the critical distance from the crack tip in finite fracture mechanics or the maximum separation distance in cohesive models. The finite fracture concept can also be found in damage analyses. A wide variety of damage models have been proposed on the basis of continuum damage mechanics by introducing a length parameter [11-15]. The nonlocal models in a continuum damage setting, the gradient theory based damage models, the damage gradient models are some of the principal advances in this direction. In this work, we have constructed a damage model by associating the maximal stress criterion with a non-local formalism. Moreover, equivalence has been illustrated between this non-local model and the Griffith-Irwin fracture criterion for crack propagation. Using the established non-local damage model, we carried out detailed numerical simulations on different specimens in order to study the efficiency and accuracy of the present approach. The numerical results show that the proposed damage model is capable to simulate the crack initiation as well as the crack growth in brittle composites with highly realistic description. 2: Non-local damage model Numerous continuous damage models exist in the literature. In this work, we will use a simple failure criterion for brittle materials, i.e. the instantaneous damage model on the basis of the maximum stress criterion, namely: ⎩ ⎨ ⎧ ≥ < = c c D σ σ σ σ 1 1 1 0 (3) where 1σis the maximal principal stress and cσis the ultimate tensile stress of the material. It is clear that other more elaborate damage evolution laws exist and may be more efficient and physically more realistic for this class of materials. In the present work, (3) is adopted for simplicity. Even though this strength criterion is commonly used in failure assessment of a non-cracked structure, however, it is not suitable to describe fracture due to cracks because of the stress singularity near the crack tips. In order to overcome this shortcoming, various methods have been proposed. Among these, the so-called non-local approaches are widely used. The basic idea of this approach consists in replacing the local damage driving force, i.e. 1σ in the present case, by its
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