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Research Papers

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

[+] Author and Article Information
M. A. Dawson, G. H. McKinley

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

L. J. Gibson

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

J. Appl. Mech 76(6), 061011 (Jul 23, 2009) (8 pages) doi:10.1115/1.3130825 History: Received March 06, 2008; Revised March 23, 2009; Published July 23, 2009

## Abstract

The response of a reticulated, elastomeric foam filled with colloidal silica under dynamic compression is studied. Under compression beyond local strain rates on the order of $1 s−1$, the non-Newtonian, colloidal silica-based fluid undergoes dramatic shear thickening and then proceeds to shear thinning. In this regime, the viscosity of the fluid is large enough that the contribution of the foam and the fluid-structure interaction to the stress response of the fluid-filled foam can be neglected. An analytically tractable lubrication model for the stress-strain response of a non-Newtonian fluid-filled, reticulated, elastomeric foam under dynamic compression between two parallel plates at varying instantaneous strain rates is developed. The resulting lubrication model is applicable when the dimension of the foam in the direction of fluid flow (radial) is much greater than that in the direction of loading (axial). The model is found to describe experimental data well for a range of radius to height ratios $(∼1–4)$ and instantaneous strain rates of the foam ($1 s−1$ to $4×102 s−1$). The applicability of this model is discussed and the range of instantaneous strain rates of the foam over which it is valid is presented. Furthermore, the utility of this model is discussed with respect to the design and development of energy absorption and blast wave protection equipment.

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## Figures

Figure 3

Model of rectangular channel flow

Figure 4

Lubrication fluid flow model assuming the absence of foam. (a) At 0 strain and (b) at any given strain ε.

Figure 5

Scanning electron microscope images of silica particles

Figure 1

Images of a 70 pores/in. foam filled with 61% volume fraction silica-based non-Newtonian fluid loaded in axial compression at 250 mm/s. (a) ε=0 strain, (b) ε=0.1 strain, (c) ε=0.2 strain, and (d) ε=0.3 strain.

Figure 2

Optical micrograph of a NNF-filled foam. (a) ε=0 strain and (b) ε=0.4 strain.

Figure 6

Steady shear viscosity plotted against shear stress for 48% volume fraction of silica-based non-Newtonian fluid. Gap thickness: 500 μm (▲) and 250 μm (◇).

Figure 7

Steady shear viscosity plotted against shear stress for 50% volume fraction silica-based non-Newtonian fluid

Figure 8

Steady shear viscosity plotted against shear stress for 61% volume fraction silica-based non-Newtonian fluid

Figure 9

(a) True stress plotted against strain for a 70 pores/in. foam filled with 61% volume fraction silica-based non-Newtonian fluid. −Ḣ=31.25 mm/s (●), 62.5 mm/s (▲), 125 mm/s (◆), and 250 mm/s (◼), corresponding to instantaneous strain rates of 2.5 s−1, 5 s−1, 10 s−1, and 20 s−1 at ε=0.0 strain, respectively. (b) True stress plotted against instantaneous strain rate for a 70 pores/in. foam filled with 61% volume fraction silica-based non-Newtonian fluid. Regimes R1–R4 correspond to fluid behavior regimes.

Figure 10

True stress plotted against instantaneous strain rate for a 70 pores/in. foam filled with 61% volume fraction silica-based non-Newtonian fluid, ranging from 0.10 to 0.40 strain. The model corresponds to regimes R3 and R4 of the fluid given by Eq. 10.

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