A constitutive model is proposed to simulate the orthotropic stiffness, pre-peak nonlinearity, failure envelopes, and the post-peak softening and fracture of 3D woven composites. Following the microplane model framework, the constitutive laws are formulated in terms of stress and strain vectors acting on planes of several orientations within the material meso-structure. The model exploits the spectral decomposition theorem to define orthogonal strain modes at the microplane level. These are associated to the various types of deformation. Strain-dependent constitutive equations are formulated for each mode, corresponding to different damage mechanisms, to relate the microplane eigenstresses and eigenstrains. Model calibration and verification were performed against the experimental data. The capability of the model capturing the intra-laminar size effect of composite structures was also verified.