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.