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Simple but also accurate models are needed to predict the failure response of concrete structures. Simplicity involves modelling assumptions while accuracy involves objectivity of both the experimentally identified model parameters and the numerica results. For concrete‐like heterogeneous and brittle materials, the modelling assumptions idealizing the material as a homogeneous continuum with classical linear or non‐linear behaviour, leads to some problems at the identification stage, namely the size effect phenomena. A continuum damage model, representing the non‐linear behaviour due to microcracking, is proposed here for predictive computations of structural responses. A Weibull based theory is used to determine, in a statistical sense, the value of the initial damage threshold. The essential influence of material heterogeneity on the damage evolution, is accounted for with a bi‐scale approach which is based on the idea of the non‐local continuum with local strain. It has already established that the non‐local approaches yield realistic failure predictions and the numerical results are convergent for subsequent mesh refinements. The applications presented here show the ability of the approach to predict the failure response of concrete structures without being obscured by size effect problems.

Simplified methods are often employed for the analysis of reinforced concrete beams (R‐C beams). A three‐dimensional problem (3D) is often transformed into a two‐dimensional problem (2D) with some assumptions which are usually established in static. The essential reason for this simplification lies in the fact that the 3D finite element analysis is so expensive that it is impossible to study directly the non‐linear behaviour of R‐C beams in many cases. Our purpose is to present a specific method which allows the direct 3D analysis of R‐C beams with a suitable numerical cost. First, the 3D linear heterogeneous beam theory is briefly recalled as well as the continuum damage model used for concrete. Second, the non‐linear behaviour of concrete is introduced in the 3D beam theory. Several numerical examples illustrate the effectiveness of the method.