## 1 Introduction
They further showed that the presence of an air gap (of the order of 106 mm) between the granular filter and the protected surface prevents direct contact between the particles composing the granular medium and the protected surface, which eliminates unsteady peak pressures/stresses on the protected surface that are seen in the absence of the air gap. [PERSON] et al. [10] studied the shock wave interaction with materials having different acoustic impedances. They found that an underwater shock wave, which was expected to reflect totally as an unloading wave at the water-air interface due to acoustic impedance mismatch, was observed transmitting across the interface to air. [PERSON] et al. [11] carried out full-scale field explosion tests on concrete slabs, with and without aluminum foam cover. They studied the dynamic response of an elementary concrete structure to blast wave loads, and the ability of aluminum foams to mitigate the blast loads. They reported that the aluminum foam could modify the response of the slab to the blast load but stated that further investigation would be required to predict its efficiency for practical purposes. [PERSON] et al. [12] showed that the reflected shock pressure measured in front of simply supported aluminum foams placed at the end of a shock tube cavity was higher (2.9\(\times\) the incident pressure) than that produced by a rigid aluminum plate (2\(\times\) the incident pressure). The shock speed used was greater than Mach 2 while the incident pressure was 3.5 bar, which gives reflected pressures of about 10 bar. [PERSON] et al. [13] showed that, for higher values of reflected pressure (52 and 69 bar), radial cracks and core crushing occurred in simply supported closed cell aluminum foams. [PERSON] et al. [14] studied interactions between shock and open porous aluminum foam in the elastic loading range (with -3.5 bar incident shock pressure) and showed shock attenuation in foams. They attributed shock dispersal to subsonic gas flow inside the aluminum foam where drag forces become the dominant factor in the solid-fluid interaction. [PERSON] et al. [15] conducted comparative studies on blast attenuation by mild steel plates versus sandwich materials with mild steel face plates and aluminum foam core. They found that the peak transmitted load reduced by more than 50% for the sandwich compared to mild steel plates. Foam cracking and multiple reflections in the foam cavities were cited as mechanisms of shock attenuation. [PERSON] et al. [16] carried out full-scale field tests to investigate the behavior of aluminum foam panels in the density range 0.15-0.35 g/cc subjected to blast loading. It was observed that the energy and impulse transfer to the pendulum increased by adding a foam panel. [PERSON] et al. [17] experimentally demonstrated the occurrence of shock attenuation in two-layer graded density foam-core sandwich structures exposed to blasts. They showed by numerical modeling that the deformations in the low and high density layers were different between the positive and negative density gradient configurations, but that the compaction wave propagation always progressed from the blast side to the distal side. They further showed that the energy absorbed as well as the impulse of the force acting on the protected structure increased with increasing density gradient, which are conflicting requirements of protective structures, and hence a balance needs to be achieved by selecting an optimum density gradient. Although there is a reasonable amount of literature on shock attenuation/amplification and gas filtration through open pore foams of high density, there are no reports on low-density closed cell aluminum foam mediated shock attenuation in cavities in high impedance materials exposed to shocks. Similarly, there have not been adequate studies examining modes of deformation and failure in closed cell aluminum foams under shock loading, and their influence on shock attenuation and gas filtration.