On a macrohomogeneity condition for micropolar continua. The role of skew–symmetric strain and stress

The work addresses multiscale modeling of materials with complex microstructures within a micropolar continuum framework. A generalized macrohomogeneity condition of Hill's type is formulated. The proposed formulation explicitly accounts for symmetric and skew-symmetric strain and stress and for their coupling with curvature and couple stress within a unified tensorial framework. This formulation provides a rigorous basis for deriving energetically consistent Dirichlet and Neumann boundary conditions for performing homogenization of heterogeneous materials. Numerical examples illustrate the role of skew-symmetric effects and highlight differences with respect to classical Cauchy-based homogenization approaches.