Towards hierarchical micropolar composites: A computational homogenization model of heterogeneous Cosserat media

Size effects play a fundamental role in the mechanical analysis of complex materials such as bone. While micropolar theory can capture these effects, a major gap exists in modeling hierarchical materials, where the meso-scale itself is a heterogeneous composite of micropolar phases. Frameworks to homogenize these heterogeneous micropolar continua into an effective micropolar continuum have received limited attention in the literature, particularly for the general three-dimensional case under finite strains. In this work, we bridge this gap by developing a general, 3D homogenization framework. The model is systematically derived from the Principle of Multiscale Virtual Power (PMVP), accounts for large displacements, and is validated against direct numerical simulations (DNS). The results demonstrate that the meso-scale RVE accurately reproduces the DNS-predicted kinematics and corresponding homogenized stress responses across a range of macro-scale loading conditions and multiscale kinematic constraints, including linear, periodic, and minimally constrained cases. This confirms that the framework is well-suited for analyzing materials with non-classical, hierarchical behavior. • Three-dimensional finite-strain micropolar-to-micropolar homogenization framework. • Variationally consistent scale transition via Multiscale Virtual Power. • Couples large deformations with small macro/meso-microrotations. • Open-source FEniCS implementation of mixed finite element Cosserat formulations.