Multiscale homogenization is a widely used framework for predicting the effective behavior of heterogeneous materials in both linear and nonlinear regimes [1]. In this contribution, a generalized Hill-type macrohomogeneity condition is proposed for the multiscale modeling of heterogeneous micropolar continua with microstructure [2-4]. The formulation is based on an explicit separation of symmetric and skew-symmetric components of strain and stress, allowing a consistent energetic coupling with curvature and couple-stress measures. Energetically consistent Dirichlet and Neumann boundary conditions are derived from power equivalence within a unified tensorial framework, ensuring scale-consistent energy balance. Finite element analyses on homogeneous and heterogeneous media with periodic microstructures confirm the robustness and energetic consistency of the proposed approach [5]. Future work will address applications to composite materials with random microstructures. Acknowledgements: This work is supported by MIUR, project: National Center on HPC, Big Data and Quantum Computing (ICSC), PNRR - CN1- Spoke6 (CUP: B83C22002940006), and PROGETTO MUSICS - FISA-2023-00099 (CUP: B83C25000810001). REFERENCES [1] Trovalusci, P. Molecular approaches for multifield continua: origins and current developments. In Multiscale modeling of complex materials: phenomenological, theoretical and computational aspects, 211–278, Springer, 2014. [2] Hill, R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids, 11(5):357–372, 1963. [3] Liu, Q. Hill’s lemma for the average-field theory of Cosserat continuum. Acta Mechanica, 224, 851–866, 2013. [4] Trovalusci, P., Ostoja-Starzewski, M., De Bellis, M.L., Murrali, A. Scale-dependent homogenization of random composites as micropolar continua. European Journal of Mechanics-A/Solids, 49:396–407, 2015. [5] Trovalusci, P., De Bellis, M.L., Ongaro, G. On a macrohomogeneity condition for micropolar continua: the role of skew-symmetric strain and stress. Under Review, 2026.