On the stability of Kelvin cell foams under compressive loads

It has been previously shown that the nonlinearity exhibited in the compressive response of open cell foams is governed by cell ligament buckling. Significant insight into this behavior can be gained by idealizing such foams as periodic, space-filling Kelvin cells assigned several of the geometric characteristics of actual foams. The cells are elongated in the rise direction; the ligaments are assumed to be straight, to have Plateau border cross sections, and nonuniform cross sectional area distribution. The mechanical response of such foams can be established using models of a characteristic cell assigned appropriate periodicity conditions. The ligaments are modeled as shear deformable beams. The periodicity of this microstructure allows the use of Bloch wave theory to conduct the search for the critical state efficiently. The method tailored to the present microstructure is outlined. It is subsequently used to establish the critical states for uniaxial and a set of triaxial loadings. A rich variety of buckling modes are identified which are affected by the anisotropy and the mutliaxiality of the applied loads. Under some loadings the critical modes have long wavelengths which are shown to lead to unstable postbuckling behavior involving localization. Under other loading conditions the modes are either local to the characteristic cell or involve an assemblage of a few such cells. For the cases analyzed local modes were found to have a stable postbuckling response.