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

Dawson, M., McKinley, G.H. and Gibson, L.J.

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
70 ppi to 90 ppi and strain rates varying from 2.5e-3 to 10 1/s 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 around 4.