Non-local model and global-local cracking analysis for the study of size effect

The problematic of size effect for quasi-brittle materials and more particularly for concrete has been widely studied during the last decades. Several approaches have been proposed to describe and explain why the strength decreases as the size increases. Indeed, the capacity of a model to describe the size effect matters greatly when dealing with the modelling of structures. A study of size effect is proposed in this article by considering several notched concrete beams submitted to a three points bending test. To describe the nonlinear behavior of concrete, two different nonlocal regularization methods (the original method and a method proposed recently by one of the authors) are compared to analytical model and to experimental results available in the literature in order to assess their capacity to describe size effect at the global scale as well as at the local scale. More particularly, a quantification of the crack field is obtained by using a discrete elements reanalysis method proposed recently by two of the authors. This last analysis brings an additional element to discriminate or not model capacity to describe size effect of quasi-brittle materials.