An active concept for limiting injuries caused by air blasts
Introduction
Explosions in air create intense shock waves capable of transferring large transient pressures and impulses to the objects they intercept [1], [2], [3]. The traveling shock comprises a strong positive pulse followed by a weaker rarefaction, Fig. 1. The peak overpressure, po, scales as: , with the mass of the explosive and R the distance from the explosion. The pressure-time integral represents the impulse per unit area, I, carried by the shock. The incident wave front is partially reflected at a surface [1], [2], [3], [4], [5], [6] amplifying the disturbance that enters a structure. Upon entering a body, the differential displacements set-up in tissues of differing compliance and density can cause tearing of muscle tissue, blood vessels and neurons [7], [8], [9], [10], [11], [12], [13], [14]. Studies using animal models exposed to explosions have revealed that both the pressure and duration of the shock affect the probability of injury [15], [16], [17]. For detonations of high explosives (with decay time ∼0.1–1 ms), a peak overpressure of 0.3 MPa (three atmospheres) can cause injury to the thorax, while a peak pressure of 1 MPa usually results in death. For the present assessment, we will require that each mitigation concept assures that the transmitted pressure behind a mitigation system never exceeds a threshold, .
A passive strategy for mitigation entails the use of perforated plates [18], cellular media [19], [20] such as polymer, metal or ceramic (pumice granules) foams, and various unconsolidated ballistic fabrics. It will be shown that, for representative loadings, significant mitigation can only be achieved by using excessively bulky or heavy buffer plate systems. For air blasts, these limitations can be overcome through active mitigation concepts in which a cellular material is compressed and then deployed just prior to arrival of the shock disturbance. The key feature of such an active (deployable) strategy is momentum cancellation. Other examples of active concepts can be found the helicopter industry [21], hydraulic actuator based active impact control (or absorption) [22], and sensor-based pedestrian protection systems [23], [24]. A deployable concept based on momentum cancellation utilizing a pre-compressed cellular core sandwich panel is proposed and evaluated by simulations with varying levels of fidelity. To define and support the concept, the basic characteristics of air shocks, and their interactions with static structures, are first summarized. Thereafter, the interactions with moving plates are analyzed and used to chart the velocities of deployable buffers.
Section snippets
Impulses, pressures and arrival times
The free-field pressure–time response from an explosion in air is described by,where p(x,t) is the pressure at a point x and time t, po is the maximum incident overpressure, ti is the wave decay time and a0 is the sound speed in air. In this simplified description, the wave propagates to the right within the domain x ≤ 0 without changing its shape and reaches the plate at time, t = 0. When the (compressed) shock encounters a surface, it is reflected, amplifying the
The passive concept
The use of cellular materials for mitigation is conceptually straightforward. Between the blast and the structure to be protected, an intervening medium is used that reduces the pressure from . This medium must be capable of large volume decrease at essentially constant pressure (Fig. 3). Solids and fluids are not suitable because they are incompressible. The only materials having the appropriate characteristic are low density cellular solids such as reticulated polymers, metal foams [19]
The active concept
Analytic estimates. To explore active mitigation, we note that a shock propagating from a 10 kg TNT charge to an object placed 3 m away arrives in , Fig. 2(c). [At 6 m, the time increases to .] A sensor capable of detecting the electromagnetic emission [34], [35], [36], [37] created at the instant of detonation would thus afford a time delay, tarrive, between detonation and the arrival of the blast wave. This delay provides an opportunity to deploy a buffer by using a
Summary
Explosions in air can cause damage in at least six different ways: (i) by their reaction to the impulse associated with the primary blast wave, (ii) by secondary fragment impact, (iii) by burning upon contact with high temperature gases created during the detonation, (iv) by acceleration into a rigid object, (v) by differential momentum transfer to appendages, and (vi) by the collapse of surrounding structures. The present article addressed the first of these by devising concepts for the
Acknowledgements
The active mitigation concepts discussed in this paper were initially developed during a study conducted by the Defense Science Research Council and we are grateful to Geoffrey Ling, Brett Giroir, Rick Satava and Judith Swain for stimulating discussions of this topic. We are grateful to the Defense Advanced Research Projects Agency for its support of the Council and to the Office of Naval Research for its support of the subsequent analysis of reactive cellular material mitigation concepts under
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