The compressive response of open-cell foams
The compressive response of many cellular materials is characterized by a nearly linear elastic regime, which terminates into a limit load. This is followed by an extensive load plateau that is responsible for their excellent energy absorption characteristics. The end of the plateau is usually followed by a second branch of stiff response. This study uses experiment and analysis to illustrate how the cell microstructure and the properties of the base material govern these mechanical characteristics for a class of foams. The experiments are conducted on polyester urethane open-cell foams of several cell sizes. They include: measurement of the compressive response of the foams, characterization of the foam microstructure, and measurement of the mechanical properties of foam ligaments. It was found that for such materials the onset of instability and the subsequent localization occur due to buckling of the microstructure. The foam is idealized to be periodic using the space-filling Kelvin cell assigned the major geometric characteristics found in the foams tested. Several modeling levels are used to analyze the different aspects of this complex mechanical behavior. Beam-type models are used to develop closed form expressions for the initial elastic moduli. The onset of instability is established numerically using models involving either a single or stacks of fully periodic characteristic cells. Large scale models are used to reproduce all aspects of the compressive response including crushing. In the rise direction the prevalent instability exhibits a long wavelength mode that leads to a limit load, an indication that localization is possible. By contrast, in the transverse direction the buckling mode is local to the characteristic cell and has a stable postbuckling response. For more general loadings the Bloch wave method is employed to establish the onset of instability. For such general loadings a rich variety of buckling modes are identified that are affected by the anisotropy and the multiaxiality of the loads. The crushing response is simulated by considering finite size microsections that allow localized deformation to develop. Ligament 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 crushing stress and the extent of the stress plateau can be evaluated by using this pseudo-contact scheme.