A homogenized formulation to account for sliding of non-meshed reinforcements during the cracking of brittle matrix composites: Application to reinforced concrete

Non-linear finite element modelling of complex structures made of composites, such as reinforced concrete, remains a challenge because, until now, the only way to consider the important phenomenon of sliding between the reinforcements and the brittle matrix of the composite has been to mesh the reinforcements and their interfaces explicitly. This method is accurate but so expensive in terms of computational resources that only critical small elements of composites structures are modelled using it. To get around this limit, a method avoiding the meshing of composite reinforcements is proposed. It consists in treating the sliding between reinforcements and matrix with a differential formula of reinforcements directly as a continuous field superimposed to the displacement field of the matrix. The method needs a minor modification of the finite element code, which can take advantage of its analogy with the anisotropic thermal formulation. After the analytical presentation of the method, two theoretical cases of study are given to confront the results obtained with this method without meshing of reinforcements, with reference results obtained using a complete mesh of the matrix, reinforcements and interfaces. (authors)