Topological modeling of metallic foams

Abstract Understanding material’s micro- and macrostructure is key to linking inner structure information to large-scale physical properties and function. An improvement of the microstructure during production processes can lead to materials with enhanced physical properties or even to the development of new classes of materials. In this paper, we develop an ‘accurate’ topological model to describe the dual neighborhood structure of foams and other cellular materials (e.g. plant cell clusters or polycrystalline materials like steel, rocks, and ceramics) obtained by x-ray tomography, adhering to Plateau’s rules: four pores meet at a vertex, and three meet along an edge. While the degree of non-convexity in the pores is a priori unknown, our approach is designed for structures without extreme geometric irregularities (e.g. tangled pores). It provides meaningful combinatorial-numerical validation in such cases but may not extend reliably to more complex geometries. To illustrate our method, we analyze a sample of aluminum foam comprising 1911 pores. The resulting abstract combinatorial foam structure partially aligns with that of the associated power diagram—sharing 51.45% of the tetrahedra in the dual complex—but also reveals significant deviations.