13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A new macroscopic model based on non-local interactions to predict damage and failure in quasibrittle materials Laura B. Rojas-Solano1, David Grégoire1,*, Gilles Pijaudier-Cabot1 1 Univ Pau & Pays Adour, LFC-R, UMR5150, 64600 Anglet, France * Corresponding author: email@address.aa.b.cc Abstract The purpose of this paper is to propose a new macroscopic approach to describe the evolving non-local interactions during damage and failure in quasi-brittle materials. A new integral-type non-local model is proposed where the weight function is directly built from these interactions. The structure is considered as an assembly of inclusions, which are successively elastically dilated in order to characterize the transfer of information inside the material. By this way, the new macroscale weight function takes into account intrinsically the interactions evolution during the material failure similarly as a mesoscale model does. This new model is first validated on simple 1D cases and its performances are compared with the performances of other models proposed in the literature. It is shown that the new model is able to describe the continuous/discrete transition during the dynamic failure of a rod. It is also shown that the new model is able to describe boundary effect during a spalling test. Finally, the model is used to predict damage and failure during 3 points bending fracture tests on notched and unnotched concrete beams. Keywords Non-local model, interactions, damage, quasi-brittle materials 1. Introduction Classical failure constitutive models involve strain softening due to progressive cracking and a regularization technique for avoiding spurious strain and damage localization. Different approaches have been promoted in the literature such as integral-type non-local models (e.g. [1]), gradient damage formulations (e.g. [2]), cohesive cracks models (e.g. [3] with classical finite elements and e.g. [4] with extended finite elements), or strong discontinuity approaches (e.g. [5]). Such macroscale failure models have been applied on a wide range of problems, including the description of damage and failure in strain softening quasi-brittle materials [1], softening plasticity [6–8], creep [9] or composite degradation [10]. They may exhibit, however, some inconsistencies such as (i) incorrect crack initiation, ahead of the crack tip; (ii) propagating damage fronts after failure due to non-local averaging, (iii) incorrect shielding effect with non-zero non-local interactions across a crack surface; (iv) deficiencies at capturing spalling properly in dynamics, with spalls of zero thickness when the expected spall size is below the internal length of the model (see e.g. [11–14]). Moreover changing geometry, e.g. from tensile to bending loads or from unnotched to notched specimens, results generally in the loss of predictive capabilities of the macro-scale non-local models [15, 16]. On the contrary, it has been shown recently [15, 17] that meso-scale models gave good prospect in the prediction of failure and size effect for notched and unnotched concrete beams. Indeed meso-scale results have been compared to a new experimental database [16] consisting in 3 point bending failure tests for similar notched and unnotched concrete specimens of four different sizes but made from the same formulation. Not only the different peak loads for all geometries are recovered but also the failure softening phase is well predicted which is a more challenging issue. It means that the meso-scale models intrinsically contain relevant information leading to a good description of the size effect, the boundary effect and the whole failure process. At the macro-scale, the prediction of failure in quasi-brittle materials needs enhancement of existing non-local damage models and the way the non-locality is taken into account in the macro-scale models has to be redefined. Non-locality finds its origin in the interaction between material points
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