A substructure-based homogenization approach for systems with periodic microstructures of comparable sizes

The classical homogenization method has been widely adopted to capture the effective behaviors of heterogeneous materials. However, when the characteristic length of the microstructure of the heterogeneous material is comparable to the size of the structure, the classical homogenization method is mathematically no longer valid. In this paper, a new substructure-based homogenization approach is proposed to predict the mechanical responses of systems with periodic microstructures of comparable sizes. A substructure element is developed to reconstruct the system with periodic microstructure of comparable size. It is verified that this substructure-based homogenization approach can accurately predict the mechanical responses of the system. Comparing with the full finite element analysis, the computational scale is dramatically decreased. After that, a simplified substructure element is developed by using less surface nodes in the “full” substructure element. The numerical results show that, with further significantly reduced computational cost, the third-order simplified substructure element can provide a good prediction of the responses of the system with periodic microstructure of comparable size.