Response of Open-Cell Foam

Impregnated With a Newtonian

Fluid

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.