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Woven composite materials are receiving particular attention in a wide range of specialized aeronautical applications. Reliable numerical prediction tools based on computational modeling are required to quantitatively characterize the role of the microstructure and damage mechanisms at the mesoscale. In this paper, such a computational strategy is illustrated on a generic SiC/SiC plain weave composite with chemical vapor infiltrated matrix. Matrix and tows damage mechanisms are respectively introduced through the use of an anisotropic damage model, and an homogenized model based on a micromechanical model on the fiber scale. The latter is presented in this paper for the first time. Particular attention is paid to the generation of accurate hexahedral meshes, compatible at the tow–tow and tow–matrix interfaces. The mesh quality is analyzed using an error estimator variable based on the strain energy …