This work presents a statistically based computational homogenization framework for the characterization of trabecular bone elastic properties from \(\mu\) CT data. Trabecular bone exhibits a highly heterogeneous, anisotropic, and non-periodic microstructure, whose mechanical response is governed by mesoscale architectural features, posing significant challenges for biomechanical modeling. Starting from segmented \(\mu\) CT images, relevant morphological descriptors, including Euler number, maximum trabecular length, and degree of anisotropy, are extracted to quantitatively characterize the trabecular architecture. A two-dimensional framework based on orthogonal slicing of a three-dimensional \(\mu\) CT dataset is adopted to enable stochastic homogenization under plane strain conditions. The ergodic hypothesis, supported by correlation analyses, together with a principal component analysis–based reduced-order representation, allows for the generation of statistically equivalent microstructural realizations. The effective elastic response is estimated through statistical computational homogenization using finite-size volume elements, and the representative volume element (RVE) size is identified from convergence analyses. The results demonstrate that the proposed approach captures directional mechanical anisotropy and provides stable, reproducible estimates of homogenized elastic properties at the trabecular scale, offering a basis for future extensions toward fully three-dimensional stochastic homogenization and multiscale biomechanical modeling of bone tissue.
