Buckling behavior of Kelvin open-cell foams under [0 0 1], [0 1 1] and [1 1 1] compressive loads

This paper describes buckling modes and stresses of elastic Kelvin open-cell foams subjected to [0 0 1], [0 1 1] and [1 1 1] 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 as 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 [0 0 1] and [0 1 1] compressions, with only short wavelength buckling under [1 1 1] 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 of cross-sectional areas is an important factor for the buckling behavior of open-cell foams.