Compressive response of open cell foams Part II: Initiation and evolution of crushing

Part II of this study is concerned with the understanding and modeling of the nonlinear aspects of the compressive response and crushing of open cell foam. The modeling is based on the anisotropic Kelvin foam developed in Part I assigned the same general geometric characteristics. It is demonstrated that the first knee observed in measured responses is associated with the onset of ligament buckling. Models involving either single or stacks of fully periodic characteristic cells are used to establish the critical stresses in the rise and transverse foam directions. In the rise direction the critical state involves a long wavelength mode whereas in the transverse direction the mode is local to the cell. Postbuckling calculations involving these modes showed the rise direction response to exhibit a limit load which is shown to be imperfection sensitive. The response in the transverse direction is monotonically increasing as observed in the experiments. The crushing response is evaluated by considering finite size microsections which allow localized deformation to develop. Localized crushing is arrested by contact between the ligaments of the buckled cells. Contact is approximated by limiting the amount a cell can collapse in the direction of the applied load. This arrests local collapse and causes it to spread to neighboring material at a nearly constant stress level as in the experiments. The stress picks up when the whole domain has crushed.