# ICME overview of shear thickening fluids in body armor

## Contents |

## Problem description

In order to improve mobility, weight, and cost in body armor applications, shear thickening fluids are being introduced into the protective clothing field. Shear thickening fluids have the ability to increase the material’s elastic modulus and energy dissipation. The shear thickening behavior occurs when the effective viscosity of the material increases as the strain rate increases. This shear thickening phenomenon can be used to improve the ballistic protection of body armor. For example, the velocity required to penetrate a single layer of Kevlar is about 100 m/s, but Kevlar formulated with a colloidal silica shear thickening fluid can stop projectiles up to 250 m/s ^{[1]}.

## Macroscale

At the macroscale, the shear thickening behavior is observed and can be modeled using the Ostwald-de-Waele power law, which needs an effective viscosity parameter and a flow behavior index. This power law approximation can be used in a finite element software to model the non-Newtonian shear thickening phenomenon. For this approximation, the effective viscosity is a function of the stran rate and is determined from experimental data. From the mesoscale, simulations can be used to determine the effective viscosity and flow behavior index.

## Mesoscale

For the colloidal silica, at the meso/micro-scale two different phases can be observed: a solid particulate phase (silica particles) immersed in a fluid (ethylene glycol) ^{[2]}. Simulating the interactions between these two phases is an active area of research with many different methods. For example, Bain et al. ^{[3]} were able to determine the effective viscosity versus shear rate for a simple shear simulation. However, this method averages the particle interactions, not studying the discrete effects of each particle. The elasticity of the particles, the contact interactions, and the density and viscosity of the fluid approximated in these methods and can be simulated at lower length scales.

## Atomistics Scale

From atomistic simulations, the Newtonian viscosity of fluids for high strain rates can be determined using equilibrium molecular dynamics ^{[4]}. Also for the silica particles, high rate mechanisms and mobility properties can be determined using molecular dynamics. However, for these molecular dynamic simulations the elastic modulus and fluid density, must be known from a lower length scale.

## Electronic scale

At the lowest length scale, properties such as elastic modulus and fluid density are determined. Density functional theory (DFT) can be used to determine the elastic modulus for the silica particles. DFT has also been used to simulate the density of classical fluids ^{[5]}.

## References

- ↑ Wagner, Norman J., and John F. Brady. "Shear thickening in colloidal dispersions." Physics Today 62.10 (2009): 27-32.
- ↑ Lee, Young S., Eric D. Wetzel, and Norman J. Wagner. "The ballistic impact characteristics of Kevlar woven fabrics impregnated with a colloidal shear thickening fluid." Journal of materials science 38.13 (2003): 2825-2833.
- ↑ Bian, Xin, et al. "Hydrodynamic shear thickening of particulate suspension under confinement." Journal of Non-Newtonian Fluid Mechanics 213 (2014): 39-49.
- ↑ McCabe, Clare, Charles W. Manke, and Peter T. Cummings. "Predicting the Newtonian viscosity of complex fluids from high strain rate molecular simulations." The Journal of chemical physics 116.8 (2002): 3339-3342.
- ↑ Ebner, C., W. F. Saam, and D. Stroud. "Density-functional theory of simple classical fluids. I. Surfaces." Physical Review A 14.6 (1976): 2264.