Macroscopic multiaxial yield and failure surfaces for light closed-cell foams

Abstract

This article deals with the development of a multiaxial “plasticity” criterion for the simulation of the macroscopic behavior of light closed-cell foams. The paper proposes a numerical methodology for the determination of the mechanical macroscopic properties given the geometry of the cells (whose walls are assumed to be thin) and the properties of the bulk material. The focus is on foams with relative densities ranging from 0.0526 to 0.1525. The bulk material is assumed to be isotropic with perfectly plastic behavior. We consider tetrakaidecahedron cells having three planes of symmetry in three orthogonal directions. As expected for a material having a cubic symmetry, one observes that the elastic homogenized material is fully described by three parameters (E∗,ν∗,G∗) and not only two as for the isotropic bulk material (E,ν). We propose a formula which, starting from only a knowledge of the two elastic properties and density of the bulk material, leads to the three macroscopic elastic properties of the thin-wall regular tetrakaidecahedral foam. Their yield and failure strengths in tension, compression and shear are also calculated. Two types of macroscopic behavior can be clearly identified.The first type characterizes foams made of a high-yield-strength bulk material: the foam’s macroscopic behavior is determined mainly by buckling of the cell walls.The second type applies when the bulk material has a low yield strength. In that case, yielding of the cell walls is the main failure mechanism. A loading surface of the Wang and Pan form is proposed for all these cases, both in the early nonlinear stage and at ultimate failure. Lastly the effect of irregularity of the geometries on the load surface is presented for the two previous extreme cases. It is observed that these irregularities play a crucial role in tensile case for the lightest foams having the highest yield strength.It is interesting to note that such a loading surface also leads to a good approximation of the “yield” strength obtained experimentally for both open-cell foams Combaz et al. (2010, 2011) and closed-cell foams Wang and Pan (2006).