On the Crushing Stress of Open Cell Foams

The compressive response of many foams is characterized by an initial linearly elastic regime which is terminated by instability. For open cell foams instability leads to localized buckling and collapse of zones of cells. Local collapse in these zones is terminated by contact between cell ligaments. In the process collapse spreads to neighboring cells hitherto intact. The spreading of collapse occurs at a well-defined load plateau and continues until most of the cells are thus affected when the material response regains stiffness once more. This type of three-regime compressive response was reproduced numerically by idealizing such foams to be assemblages of space-filling Kelvin cells. The onset of instability involves a long wavelength mode. It has been established by considering a fully periodic column of cells tall enough to accommodate this mode. The crushing response has been evaluated by considering finite size microsections which allow localized deformation to develop. This paper shows that the crushing stress can also be established from the local response of the fully periodic column of cells through an energy argument leading to a Maxwell-type construction.