Elastic behavior of multi-scale, open-cell foams

The mechanical properties of cellular materials are still subject to numerous theoretical and experimental investigations. In particular, the impact of cell size on the foam’s elastic response has not been studied systematically mainly due to the lack of experimental techniques with which the cell size and relative density of materials can be varied independently. This paper presents the results of a study of the elastic behavior of open-cell foams as a function of relative density and the size of the interconnected, spherical pores. First, the chemical procedure allowed us to produce polystyrene open-cell foams in which the relative density and the average cell diameters were varied independently. The results of compression tests performed on these foams showed an unexpected influence of the cell diameter (at constant relative density) on the elastic response. The analysis of the microstructure of the foam revealed the presence of a complex nanostructure in the edge of the cells that appeared during the synthesis procedure. An analytical model (an extension of the Gibson–Ashby model) is presented, which takes into account the complex multi-scale structure of the foam and accurately describes the observed dependence of the measured Young’s moduli on cell size. This approach was confirmed further by a finite element numerical simulation. We concluded that the observed dependence of elastic modulus on cell size was due to the heterogeneous nature of the material that constitutes the walls of the cells.