The Dynamic Compressive Response of Open-Cell Foam Impregnated With a Newtonian Fluid

This analysis considers the flow of a highly viscous Newtonian fluid in a reticulated, elastomeric foam undergoing dynamic compression. A comprehensive model for the additional contribution of viscous Newtonian flow to the dynamic response of a reticulated, fluid-filled, elastomeric foam under dynamic loading is developed. For highly viscous Newtonian fluids, the flow in the reticulated foam is assumed to be dominated by viscous forces for nearly all achievable strain rates; Darcy’s law is assumed to govern the flow. The model is applicable for strains up to the densified strain for all grades of low-density, open-cell, elastomeric foam. Low-density, reticulated foam is known to deform linear elastically and uniformly up to the elastic buckling strain. For strains greater than the elastic buckling strain but less than the densified strain, the foam exhibits bimodal behavior with both linear-elastic and densified regimes. The model presented in this analysis is applicable for all strains up to the densified strain. In the bimodal regime, the model is developed by formulating a boundary value problem for the appropriate Laplace problem that is obtained directly from Darcy’s law. The resulting analytical model is more tractable than previous models. The model is compared with experimental results for the stress-strain response of low-density polyurethane foam filled with glycerol under dynamic compression. The model describes the data for foam grades varying from $70ppito90ppi$ and strain rates varying from $2.5×10−3to101s−1$ well. The full model can also be well approximated by a simpler model, based on the lubrication approximation, which is applicable to analyses where the dimension of the foam in the direction of fluid flow (radial) is much greater than the dimension of the foam in the direction of loading (axial). The boundary value model is found to rapidly converge to the lubrication model in the limit of increasing aspect ratio given by the ratio of the radius $R$⁠, to the height $h$⁠, of the foam specimen with negligible error for aspect ratios greater than $R∕h∼4$⁠.