Transient Dynamics of Elastic Hele-Shaw Cell Due to External Forces with Application to Impulse Mitigation

TL;DR

This paper analyzes the transient behavior of a viscous fluid in an elastic Hele-Shaw cell under external forces, deriving solutions that suggest potential for impact mitigation through elasticity-viscosity interactions.

Contribution

It provides a self-similar solution for the pressure and deformation fields in an elastic Hele-Shaw cell under external forces, highlighting their potential for impact mitigation.

Findings

Pressure reduction by elastic effects suggests impact mitigation potential.

Closed-form expressions for pressure and deformation fields are derived.

Elastic-viscous interaction significantly decreases pressure within the cell.

Abstract

We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation, and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed form expressions. We examine a uniform external pressure acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.