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Artificial foam structures are used in all kinds of applications, for example, in filters, where non‐metallic inclusions are filtered out of the molten metal. The flow‐through of the fluid leads to a mechanical loading, which is influenced by the flow velocity, the viscosity of the fluid, the foam morphology, and the shape of the filter. Analytical and numerical approaches are being used to study the influence of different parameters on the mechanical response and the impact on local stresses at the foam struts. Finite element models of the foams are used to evaluate the homogenized stiffness tensor and to determine maximal local stresses in dependence of the macroscopic strain. On the macroscopic filter scale, an orthotropic Mindlin plate model is deployed. The results are compared with a FE2‐simulation. [ABSTRACT FROM AUTHOR]