The prime concern is to leverage copious details at the microstructural scale of multi-phase materials—e.g. fiber-reinforced composites and porous materials—in order to enrich a damage model obtained by homogenization. This is achieved using a non-local variationnal framework and tools representing accurately the microstructural morphology. A crucial aspect of this model is the ability to replace tomography images with ”morphologically equivalent” (ME) materials. This streamlines meshing processes : the microstructure description is then the key element of the model. The covariogram and the ”structure tensor field” (STF) serve as instrumental tools in achieving this objective. In essence, the covariogram, or geometrical covariance, provides a description of the heterogeneous medium, encompassing parameters such as volume fraction (Vf), inclusion size, repulsion length (lrep), and the integral range (A) beyond which no addi- tional statistical information is provided[2]. The explicit morphology (shape and orientation) is obtained by the covariogram’s inertia matrix, named as the ”structure tensor” (ST). These tools facilitate the ME materials characterization. Furthermore, the computation of the ST for each point within the medium offers a local description needed for the damage model. This includes local orientation, depicted by the first eigenvalue vector, and local texture, issued through a ratio involving its eigenvalues, called ”coherence factor”. High factors convey high anisotropy, low ones convey domain borders[1]. The resulting local description acts as the ”structure tensor field” (STF) mentioned earlier, as shown in Figure (1) with an example involving ±45° bands (see attached pdf) REFERENCES [1] Jesus Angulo. Structure Tensor Image Filtering using Riemannian L 1 and L ınfty Center-of-Mass. Image Analysis & Stereology, 33(2):95–105, April 2014. Publisher: International Society for Stereology. [2] Bruno Galerne. Computation of the Perimeter of Measurable Sets via their Covariogram. Applications to Random Sets. Image Analysis & Stereology, 30(1):39–51, March 2011. Publisher: International Society for Stereology.