Abstract

AbstractDespite the increase in computational power, the accurate modelling of crack openings in reinforced concrete remains an open problem for structural elements of complex shapes. Since the national CEOS.fr project dedicated to the control of cracking for large structures, it is accepted that the statistical scaling effect on the tensile strength of concrete and the realism of the concrete steel slip law are two essential ingredients to achieve a good level of accuracy in the prediction of crack spacing and openings. The implementation of these two aspects in finite element codes faces two problems: on the one hand, the statistical scaling effect depends on the dimension of the tensioned zone, which varies with cracking, and on the other hand, the steel-concrete slip is generally longer than the size of the finite elements. In this context, proposing homogenized reinforced concrete finite elements is problematic. The most common methods consist in using random mechanical property fields to integrate the statistical aspect of the tensile strength, and the slip is explicitly modelled by joint elements, preventing the use of homogenized elements. However, it is possible to avoid both random draws and explicit modelling of concrete-steel interfaces. The proposed method generalizes the notion of phase fields to address both problems simultaneously. A first phase field integrates the scale effect, and another one the steel-concrete slip. The FE code Castem (CEA) has been modified to allow such generalizations. After having given the theoretical bases of the methods used, we will comment two implementations.KeywordsFinite elementPhase fieldsReinforced concreteStatistical scale effectRebars sliding

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