Anisotropy in Buckling Behavior of Kelvin Open-Cell Foams Subject to Uniaxial Compression

This paper describes buckling modes and stresses of elastic Kelvin open-cell foams subjected to [001], [011] and [111] uniaxial compressions. Cubic unit cells and cell aggregates in model foams are analyzed using a homogenization theory of the updated Lagrangian type. The analysis is performed on the assumption that the struts in foams have a non-uniform distribution of cross-sectional areas its observed experimentally. The relative density is changed to range from 0.005 to 0.05. It is thus found that long wavelength buckling and macroscopic instability primarily occur under [001] and [011] compressions, with only short wavelength buckling under [111] compression. The primary buckling stresses under the three compressions are fairly close to one another and almost satisfy the Gibson-Ashby relation established to fit experiments. By also performing the analysis based on the uniformity of strut cross-sectional areas, it is shown that the non-uniformity or cross-sectional areas is an important factor for the buckling behavior of open-cell foams.