Multi-scale modelling approach to homogenise the mechanical properties of polymeric closed-cell bead foams

The complex mechanical deformation behaviour of closed-cell foams is governed by morphological and physical properties such as cell structure and crystallinity. In this study, the micro-, meso- and macroscopic scale of commercially available bead foam was analysed. Statistical distribution of the cell structure including cell size, wall thickness and shape was determined using optical microscopy and micro computed-tomography. Local crystallinity was investigated by DSC scans and X-ray scattering. The results confirm the important influence of the multi-step manufacturing process on the physical properties of bead foams. Mesoscopic and macroscopic numerical analyses of the mechanical behaviour of polymeric closed-cell bead foams are performed. With regard to the manufacturing influence on local physical properties of bead foams, the suggested approach takes into account the density and crystallinity-specific material properties and the generation of associated material cards, using virtual test methods. To represent the mesoscopic foam morphology considered here, statistical volume elements (SVE) are generated using the Laguerre tessellation method. Crystallinity-dependent base material properties are used in SVE material cards to investigate tensile and compressive behaviour. For validation of the suggested approach, four-point bending tests are conducted on macroscopic scale and compared with the numerically predicted results. The paper shows the advanced forecast capability of locally resolved modelling of closed-cell bead foam structures and underlines the huge potential of the multi-scale modelling approach.