Abstract：A direct numerical simulation (DNS) of porous materials with complex microstructures requires extremely detailed meshes, is thus very expensive in terms of modeling and computational costs. The multiscale method can greatly improve the computational efficiency for those problems by transforming a complex single-scale problem into simpler problems at multiple scales. In a conventional first-order multiscale framework, a macroscopic strain tensor characterizes the average deformation within the RVE. First-order frameworks can be used only for problems with a clear scale separation. However, in many porous materials (such as metal foams), the characteristic length of the scale of the heterogeneities is in the order of that of the macroscale. For those problems without scale separation, the micromorphic multiscale computational homogenization framework introduces an additional macroscopic kinematical field to characterize the average strain of inclusions within the RVE. This additional field, along with its higher-order terms, provides a more detailed description of the RVE. The displacement field is only required to be C0 continuous. This paper proposes a micromorphic multiscale approach for porous materials based on the multiscale micromorphic theory. The framework is numerically implemented in MATLAB. A kinematical field decomposition is introduced. The energy equivalence between microscopic and macroscopic scale is naturally guaranteed via the generalized Hill-Mandel condition. The macroscopic governing equations and boundary conditions are derived. The effectiveness of the resulting micromorphic multiscale analysis framework for porous materials is shown via two numerical examples. Compared to the conventional first-order multiscale method, the proposed method is able to accurately characterize macroscopic responses and microscopic field information of porous materials, and accounts for size effects in the considered material to a certain extent. In comparison to DNSs, the computational efficiency is significantly improved. The software developed in this paper has a good generality, and can provide a powerful tool for the design and practical engineering application of porous materials.
2023, Vol. 44 
