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a b s t r a c tA comparative study is carried out on the mechanical behavior of a Representative Structural Volume of a prestressed concrete structure, using the state of the art of the numerical tools for engineers (and not the most recent developments of the academic research). The structural effect due to the presence of the tendons is carefully studied by comparing a classical truss finite element computation with a more sophisticated approach where the tendons are explicitly represented using a solid meshing. The classical approach based on truss elements appears to be poor to reliably represent the failure mode of concrete. Therefore, in some cases, it is essential to take into account both material (difference between steel and concrete stiffness) and geometrical heterogeneities through the effect of the inclusions. The well-known mesh dependency problem is also studied in this paper. For the truss simulations, contrary to the usual conclusions on bending beams for example, the mesh dependency does not only affect the position of the localized bands but also the global failure mode, questioning once again, for this particular application, the representativity of local simulations with truss elements. Finally, nonlocal calculations are carried out using the integral approach. Contrary to the well-documented simulations on bending beams, the value of the characteristic length does not only affect the width of the localized bands but also the global failure mode.

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International audienceIn the methods used for determination of the hydraulic behaviour at large scale of fractured rock masses, based on the simulation of flow in a fracture network, the mean flux and mean pressure gradient in the network are not rigorously determined. A method is given for deriving these quantities, in a heterogeneous permeable block, from pressure and flux values on the boundary of the block. A block conductivity tensor is then defined based on the condition of linear variation of the pressure on the boundary of the block. It is shown that this conductivity tensor is symmetric and positive definite. An example of application to a model of fractured medium is given