An experimental facility for detailed studies on energy absorbing components subjected to blast loading

Deformable components such as sandwich structures possess promising properties for use in protection systems. Detailed studies on energy absorption and fluid–structure interaction effects are necessary for the application of deformable sandwich structures in blast resistant design. In this paper, an existing shock tube facility has been extended with a transparent section to observe and measure fluid flow and the structural response of deformable components during transient dynamic loading. The extension was instrumented with pressure sensors and load cells to measure the pressure and force transmitted through the component during testing. The transparent design allows the use of optical measurement techniques. Here, high‐speed cameras were used both for digital image correlation and background‐oriented schlieren imaging. Tests with free‐standing plates and sandwich components were performed. A strong dependency was observed between the plate mass, and thus the velocity of the plates, and the pressure measured upstream and downstream of the components. The tests were simulated with a one‐dimensional numerical model for compressible shock flow with fluid–structure interaction. The numerical model accurately reproduced the shock flow and component displacements measured experimentally. Overall, the experimental set‐up presented in this study proved to be suitable for the detailed examination of deformable components subjected to airblast loading.

dependency was observed between the plate mass, and thus the velocity of the plates, and the pressure measured upstream and downstream of the components.The tests were simulated with a one-dimensional numerical model for compressible shock flow with fluid-structure interaction.The numerical model accurately reproduced the shock flow and component displacements measured experimentally.Overall, the experimental set-up presented in this study proved to be suitable for the detailed examination of deformable components subjected to airblast loading.

K E Y W O R D S
airblast loading, fluid-structure interaction, free-standing plates, sandwich components, shock tube

| INTRODUCTION
The use of sandwich structures to attenuate blast loads is a concept that has been studied extensively for decades.The principle of a protective sandwich system is to introduce a deformable sacrificial layer, usually comprising two skins separated by a lightweight cellular core, to the side of the structure exposed to an incoming shock wave.The load experienced by the structure is attenuated as a result of two main mechanisms.[3] Second, as the sandwich deforms, the skin facing the incoming shock is accelerated.[6] This second mechanism is defined as a fluid-structure interaction (FSI) effect.
Several studies have been conducted to address the FSI effects between shock waves and single-degree-of-freedom (SDOF) structures.Taylor [7] is considered to have pioneered the study of the interaction between acoustic (incompressible) waves and free-standing plates (FPs), documenting an observed decrease in momentum transfer with decreasing mass of a structure.Taylor's work was later expanded upon by Kaboutchev et al [4,8,9] to account for nonlinear compressibility, that is, strong shocks in air.The research showed that accounting for compressibility results in a larger reduction in the transferred momentum than in the linear case, implying that for sufficiently strong shocks and structural displacements the load attenuation by FSI effects is greater in air than in water, for example.The theory established by Kambouchev et al. was further studied by Hutchinson [5] with the inclusion of ambient air behind the plate and considering the stand-off distance from the compressed gas to the plate.Hutchinson's contribution provided further evidence for the beneficial effects of FSI on load attenuation.In parallel to the work of Kambouchev et al., Subramaniam et al [10] developed a somewhat similar and extended numerical model to study one-dimensional FSI effects between a shock wave and an elastic structure.The extended model gave a reduced displacement of the structure when considering FSI; however, the effect was found to be dependent on the ratio between the velocity of the structure and the fluid.Once the structure-fluid velocity ratio fell below a certain threshold, the transmitted impulse became independent of FSI.This solution was later expanded to study one-dimensional dynamic compaction of foam considering FSI effects. [11]The main findings were that the influence of FSI was most significant during the initial phase of the applied blast pressure and that low-strength foams absorb more energy while requiring a larger length of compaction.In addition to the studies mentioned above, extensive work has been carried out on sandwich beams [2,[12][13][14] and sandwich plates [3,[15][16][17][18] with various core materials subjected to shock and blast loading.In general, the results demonstrated the favourable capabilities of sandwich structures for blast load attenuation in comparison to monolithic structures.The behaviour of a sandwich core may often be approximated as a SDOF system (see Main and Gazonas [15] and Deshpande and Fleck, [19] for example), and the results obtained for the one-dimensional behaviour may be transferable to sandwich beams and plates.
Numerical tools can provide valuable insight when considering the design of protective structures.To validate numerical models such that they may be implemented as tools in blast resistant design, it must be ensured with controlled and repeatable experimental studies that the underlying physics is represented in the simulations.An early experimental work on foam components was performed by Hanssen et al, [1] where aluminium foam panels were subjected to a blast load generated by free-field detonations of live explosives and the impulse transferred to the supporting structure was measured using a pendulum.Here, the foam panels were found to increase the impulse transmitted to the pendulum backing.It was assumed that the shape of the panel surface during deformation was the reason for the added impulse to the system.Langdon et al [20] presented a smaller scale experimental set-up where an explosive-driven shock tube was used to generate the blast load and the impulse transferred to the target was again measured using a pendulum.Aluminium foam panels were tested, and it was shown that the numerous compaction wave reflections occurring inside the core were the main source of energy dissipation.Theobald et al [21] used the same set-up as Langdon et al [20] to study aluminium foam and honeycomb core sandwich panels.It was established that a thinner front skin would crush the core at a higher velocity, thus transmitting more energy to the foam.In conclusion, a thicker front skin with a thinner core seemed to be the best solution in terms of energy control.Ousji et al [22] carried out similar studies on polymer foam core sandwich panels but with a simplified experimental set-up; the impulse transmitted to the target was measured using a load sensor rather than a pendulum.Based on the approach by Hanssen et al., [1] Ousji et al [22] proposed an analytical model to account for the FSI effect; however, the accuracy of this model worsened as the shock intensity increased and the core strength decreased.
Recently, works on the blast loading of FPs and plates backed by aluminium honeycombs, polymer foam and brittle materials have been published by Blanc et al. [23][24][25] In these studies, the blast load was generated by an explosive-driven shock tube, similar to that of Ousji et al, [22] and the transmitted impulse was measured with a load cell.The experimental results were compared to the analytical expressions presented by Hanssen et al., [1] Kambouchev et al [9] and Ousji et al. [22] In order to accurately reproduce the results, slight modifications were made to the pressure-time curve which provided valuable verification and development of the analytical expressions.However, the modifications by Blanc et al [23] do not address the accuracy of the numerical solution proposed by Kambouchev et al., which forms the foundation for the analytical expressions.Moreover, the experimental set-up used by Blanc et al [23,24] deviates from the ideal case as there is an opening at the interface between the test components and the end of the shock tube.This opening could have potentially introduced leakage around the specimen, allowing parts of the blast pressure to move in the parallel direction of the reflecting surface.
The literature review highlights a lack of existing experimental set-ups with the capacity for detailed studies on energy absorption and FSI effects during the blast loading of sandwich structures.There is a need for more detailed experimental studies and an evaluation of the performance of current computational models.The main objectives of this study are to (1) establish a controlled and repeatable experimental set-up for testing free-standing and foam-backed plates where the transmitted force and impulse, pressure and air density can be measured during shock impact and (2) validate the numerical model proposed by Kambouchev et al [4,8] by conducting detailed tests on plates that can be described by SDOF models.
To achieve the outlined objectives, an existing compressed air driven shock tube (see Aune et al. [26] ) was modified with a transparent extension.The modification provided an increased field of view such that both the front facing the incoming shock wave and the sides of the test component are visible and accessible for high-speed imaging.Displacements during the component tests were determined using high-speed videos with two-dimensional digital image correlation (2D-DIC).Pressure sensors were used to measure pressure upstream and downstream of the test component and the incoming and reflected shock waves were visualised with background-oriented schlieren (BOS) imaging.Load cell washers were used to measure forces transferred through the test component.Experimental results were compared to numerical results calculated with the model proposed by Kambouchev et al. [4,8] The numerical model was able to accurately predict the shock flow in the RB experiments and the measured pressure and plate displacement for FPs, although with decreasing accuracy as the plate mass increased for the latter.Plate displacements and forces from tests with foam-backed plates were reproduced less accurately than for the FPs.The experimental set-up presented in this study proved to be well suited for detailed examinations of deformable components subjected to airblast loading.Such detailed examinations are crucial for proper validation of numerical methods.

| EXPERIMENTAL SET-UP
The SIMLab Shock Tube Facility (SSTF) was installed at NTNU in 2014 for the study of structures exposed to blast loading.The capability to consistently generate a loading similar to that of an unconfined far-field air blast in the SSTF was demonstrated in the work of Aune et al, [26] where a detailed description of the facility can be found.Successful tests on different materials subjected to blast-like loading conditions have been conducted using the SSTF; see, for example, Brekken et al., [18] Kristoffersen et al., [27] Osnes et al., [28] Elveli et al [29] and Aune et al. [30] One disadvantage of the preexisting SSTF, however, is that only the side of the component facing away from the shock wave is visible during testing (see, e.g., Kaufmann et al. [31] ).Another disadvantage is that it is not possible to measure the load transmitted to the underlying structure from the blast exposed side.In this study, the SSTF has been modified with a transparent extension to achieve an increased field of view such that the front facing the incoming shock wave and the sides of the tested component are visible and accessible for high-speed imaging.The experimental set-up is presented in two parts: First the extension of the shock tube is described followed by the additional instrumentation implemented.

| Extension of the SSTF
The SSTF consists of a driver and a driven section connected by a firing section, as shown in Figure 1.The cylindrical driver section has an internal diameter of 331 mm where the internal length can be altered between 0.27 and 2.02 m in 0.25 m intervals.The driven section is 16.2-m-long and tapers from a 331 mm diameter cross section where it is connected to the firing section (left in Figure 1) to a 300 mm Â 300 mm square cross section at the end flange (right in Figure 1).The driver and driven sections are connected by a 140-mm-long multi-chamber firing section where mylar membranes of different thickness can be inserted to vary the driver firing pressure and thus control the blast intensity.A requirement of any modification to the SSTF is that the load applied at the end of the driven section should not be affected such that the previous validation is invalidated. [26]The 300 mm Â 300 mm square section at the end of the driven section therefore governs the internal dimensions of the extension, while the placement of the windows in the tank surrounding the end flange of the driven section limits the total length of the extension to 600 mm.The extension is made of four 20-mm-thick double-laminated float glass panes glued together to form a rectangular box with an internal open cross section of 300 mm Â 300 mm and a length of 580 mm.The glass box is surrounded by a 30-mm-thick steel frame bolted to end flanges with the same dimensions as the end flange of the shock tube.The placement of the transparent extension is shown to the right in Figure 1, while Figure 2a,b shows images of the glass extension (grey) attached to the end flange of the shock tube (blue).
Figure 3a depicts a section drawing of the extension with the main components highlighted; a steel frame encapsulating a glass box with open ends and internal dimensions of 300 mm Â 300 mm Â 580 mm.At each end of the frame, there is a flange to connect the extension to the end flange of the existing shock tube and to attach a mounting plate to the extension, shown to the left and right in Figure 3a, respectively.Figure 3b displays the assembly of an aluminium reaction plate, load cells (not visible) and a steel mounting plate.As indicated in Figure 3a, the aluminium reaction plate protrudes 20 mm into the glass extension and provides a flat surface for mounting test specimens or pressure sensors.Eight Kistler 9041a piezoelectric load cells are located between the aluminium reaction plate and the steel mounting plate.The load cells are secured by proprietary bolts provided by the manufacturer which are threaded into the aluminium reaction plate.The reaction plate has a lip that extends 20 mm into the mounting flange around the entire circumference of the glass extension.A 5 mm O-ring is placed between the cut-out in the flange and the lip on the reaction plate seals off the volume containing the load cells from the driven section, see the enlarged detail in Figure 3a.The placement of the O-ring is indicated in Figure 3a,b.

| Instrumentation
The SSTF accommodates 20 Kistler 603B piezoelectric pressure sensors mounted in pairs along the entire length of the driven section.For the test set-up in this study, the two sensors closest to the end of the driven section are of primary interest, annotated as Sensors 1 and 2 in Figure 1.Sensors 1 and 2 are placed 0.245 and 0.345 m from the end of the shock tube, that is, 0.825 and 0.925 m from the reaction plate, respectively.The placement of Sensors 1 and 2 is such that accurate measurements of the reflected blast load at the reaction plate cannot be obtained.However, as the shock tube has been shown to provide excellent repeatability, the incoming shock velocity and pressure curve provide a strong indication of the variations in the load experienced at the end of the extension.To measure the pressure at the reaction plate, five of the same Kistler 603B pressure sensors, annotated as Sensors 3 to 7, were mounted on the reaction plate in positions shown by Figure 3d.
Eight Kistler 9041a load cell washers mounted between the reaction and mounting plate were used to measure the reaction force.The positioning of the load cells are shown in Figure 3c.The load cells are designed to measure static and dynamic loads in the normal direction of the cell with a threshold of 0.01 N. The high rigidity (7.5 kN/μm) and thus high natural frequency (62 kHz) of the load cells ensure a minimal contribution to the dynamic system consisting of the aluminium reaction plate, the load cells and the steel mounting plate.With eight load cells and a reaction plate mass of 18.5 kg, the natural frequency of the load sensing system is approximately 340 kHz which is sufficient to capture the load histories expected in the extension accurately.The load cells are mounted with a pre-tension force of 10 kN which shunts the force applied to the load cell assembly through the mounting screws.The extent to which the force is shunted by the mounting screws is dependent on the measuring set-up.Thus, the entire set-up must be calibrated with the load cells already installed and pre-tensioned.Calibration was performed on the load cells individually and for the whole assembly with eight load cells installed.The set-up for calibrating the load cell assembly is shown in Figure 4a.The eight load cells are mounted between the 70-mm-thick aluminium pressure plate and the 30-mm-thick steel mounting plate, and all eight load cells were mounted with a pre-tension load of 10 kN.The entire assembly was placed in an Instron 5985 Universal Testing System fitted with a 200 kN load cell.A medium-density fibreboard plate was placed between the Instron crosshead and the aluminium pressure plate to avoid damage to either the test machine or the Kistler load cells.As the system is in force equilibrium, the fibreboard only serves to control the forces transferred and did not affect the calibration results.The calibration test was repeated three times, with the load cell assembly rotated 90 between each test.A maximum load of 200 kN was used in all orientations.Results from one of the three calibration tests is shown in Figure 4b.The sum of the measured load in all eight load cells, shown by the solid black line in Figure 4b, was linear with respect to the applied load.The total force measured in all eight load cells was 9% lower than the applied load due to force shunting.A correction factor of 1.09 was therefore applied to the sum of the force measured in the load cells, and the corrected force is shown as the red line in Figure 4b.The corrected force was within 0.7% of the applied force for all orientations of the load cell assembly.The load cell manufacturer states that quasi-static calibration of the load cell assembly is sufficient to account for the force shunt by the mounting bolts.It is thus assumed that the corrected force measurements also are applicable in the dynamic shock tube tests.
BOS is an optical imaging technique for visualising density gradients in fluids. [32]In the present study, the BOS setup consisted of a high-speed camera, a light source and a cross-hatched grid which was used as background pattern.As illustrated in Figure 5, placing the camera on the one side of the fluid flow in the shock tube and the background pattern on the opposite side of the fluid flow, the density fluctuation caused by the shock can be measured as apparent displacements in the background pattern.In this study, these apparent displacements are quantified using a phase detection algorithm. [33]The measured apparent displacements allow a qualitative investigation of the position and intensities of the density fluctuations.In principle, density information can be reconstructed from the measured displacements through relations with the density-dependent refractive index, but in the present case, no meaningful density information could be extracted because of vibrations during the test.Thus, quantitative measurements from BOS is still work in progress and is outside the scope of this study.
High-speed imaging of the test components enables measurements of surface displacements and strains by using digital image correlation (DIC).All DIC results in this study were obtained with the in-house DIC software eCorr. [34]oint displacements were measured by tracking single subsets on the test components, and surface strains were extracted by using the subset-based element-DIC module in eCorr.

| EXPERIMENTAL PROGRAMME
The experimental programme in this study is divided into two parts.First, to validate the performance of the shock tube extension, a series of tests without components was performed.In these tests, the incoming shock wave was reflected at the RB of the extension, in a similar way to the tests presented by Aune et al. [26] Second, a series of component tests was performed with plates of different masses, both free-standing and backed with a polymer foam.

| Rigid boundary (RB)
When no test component is installed in the extension, the shock wave travelling through the driven section arrives unimpeded at the end of the extension where it is reflected at the RB.To record the pressure, the reaction plate was instrumented with five Kistler 603B pressure sensors on the side facing the incoming shock, with placements as shown in Figure 3d.Three repetitions of the same test with a nominal driver firing pressure of 20 bar were performed.
Table 1 shows the measured blast parameters 825 mm upstream of the RB at Sensor 1, see Figure 1, and in the centre of the RB at Sensor 3, see Figure 3d.Here, p so;max is the maximum side-on pressure at Sensor 1, found by a least- T A B L E 1 Measured blast parameters for test with a rigid boundary.

Incoming shock parameters (Sensors 1 and 2)
Friedlander parameters (Sensor 3) squares fitting of the experimental pressure curves between the arrival at the sensor until the reflected blast wave arrives back at the sensor to the Friedlander equation given in Equation (1) with p r;max representing p so;max in this case.
The Mach number M s was found by calculating the difference in arrival time of the shock between Sensors 1 and 2. The blast parameters for the reflected shock were found by a least-squares fitting of the experimental pressure curve from Sensor 3 to Equation (1), p r;max is the maximum reflected overpressure, t dþ is the positive phase duration, b is the exponential decay coefficient, p 1 is the atmospheric pressure and t a is the arrival time.For further reference, the atmospheric pressure, p 1 , is assumed constant and only the overpressure is referenced, t a is set to zero.The reflected specific impulse i rþ was found from Equation ( 2).The Mach number and side-on pressure measured upstream of the RB have little variation between the tests, which is also the case for the reflected pressure at Sensor 3 on the RB.This shows that the tests have a high degree of repeatability, both in terms of the incoming and reflected shock.
Figure 6 shows the measured overpressure in all five sensors on the reaction plate for the three RB tests.The pressure curves from all three tests show that the shock wave was planar as it impacted the reaction plate.There were only minor variations in the pressure-time histories in each test.An initial spike in the measured pressure as the shock wave impacted the reaction plate was present in all tests.As these results are very similar to those obtained by Aune et al, [26] the conclusion can be drawn that the addition of the extension does not adversely affect the flow of the shock wave.The overpressure measured at the centre of the rigid plate (Sensor 3) and in Sensor 1 is shown Figure 7a,b, respectively, for all three RB tests.Little variation can be observed between the three tests.For all further analysis, test R_P20_03 was chosen as a reference for the tests with a RB, as the total reflected impulse in this test is closest to the average of all three.
The force measured in the load cells is compared with the measurement from Sensor 3 in Figure 8.For comparison, the overpressure was multiplied by the exposed area of the reaction plate, that is, 300 mm Â 300 mm.Overall, the total force measured by all eight load cells is in good agreement with the force measured by the pressure sensor in the centre of the reaction plate.For all three tests, there was a delay between the first peak of the pressure measurement to the first peak of the load cell measurement.The delay in the first peak is attributed to inertia effects as a result of the mass of the reaction plate undergoing acceleration when the shock wave impacted.There were larger oscillations in the load cell measurements than in the pressure-sensor measurements.When the most severe oscillations in force from the load cells settled after approximately 10 ms, the load magnitude measured by the load cells was higher than the measured pressure.It was suspected that the difference between the load measured with the pressure sensors and the load cells was caused by dynamic oscillations of the load sensing assembly.To clarify how the measured force from the load cells F I G U R E 6 Pressure-time curves for tests with a rigid wall.
was affected by oscillations in the load cell and reaction plate assembly, a SDOF model of the load cells and reaction plate was used.In this SDOF model, the reaction plate was represented by a point mass of 18.5 kg and the eight load cells by a single spring with a spring stiffness of k LC ¼ 7:5 kN/μm Â 8.A force represented by Equation (1) with parameters from Table 1 multiplied with the exposed frontal area of the reaction plate was applied to the point mass.In this SDOF model, the force measured in the load cells was represented by the displacement of the mass x multiplied with the spring stiffness k LC .The SDOF model was able to represent the initial oscillations found experimentally but did not capture the drift between the applied load and the measured load.The exact reason for the difference between the load cell and pressure-sensor measurements has not been fully determined and will therefore be a subject for further studies.For the results presented in this paper, the load cell measurements are consistent for the tests with a RB and are thus deemed accurate for comparison between subsequent test series.

| Component tests
Three sets of component tests were performed on 3-mm-thick plates with a frontal area of 298 mm Â 298 mm, made of polycarbonate, aluminium and steel.The plates were either allowed to move freely along the length of the shock tube extension or backed by a 200-mm-thick polypropylene foam slab.A total of 12 tests were performed with three repetitions for each of the plate materials without foam backing and one test for each plate material backed with EPP.The same load level was used for all tests.The component tests were performed with almost the same experimental set-up as used for the RB tests, presented in Section 3.1, with the only difference being four 14 mm diameter guide rods with countersunk heads fitted to the aluminium reaction plate, shown in Figure 9a.The guide rods held the test component in place and ensured that the front plate was only allowed to move along the length of the extension.Three-millimetre-thick front plates made of polycarbonate, aluminium and steel were used.An aluminium plate mounted inside the extension before testing is shown in Figure 9a.In all tests, the plates were mounted 200 mm from the reaction plate.Table 2 shows the three material densities, and the corresponding plate mass.As the plates were expected to move as rigid bodies with minimal deformations no detailed material characterisation was performed for the materials in this study.
In three of the tests, the plates were backed by a 200-mm-thick slab of polymer foam.The foam slabs were made up of four 50-mm-thick sections and sandwiched between the front plate and the reaction plate with holes drilled to accommodate the guide rods.No adhesive was used between the 50-mm-thick slabs when mounting the 200-mm-thick foam backing.Figure 9b shows a component with an aluminium plate backed by polypropylene foam installed in the extension before testing.The foam used in this study was EPP-5122, a closed cell expanded polypropylene (EPP) foam with a nominal relative density of 30 kg=m 3 .This foam has been studied and characterised in detail by Reyes and Børvik, [35,36] from which the material properties listed in Table 3 for the EPP-5122 are taken.Before testing, a speckle pattern was applied to the foam slabs to accommodate 2D-DIC measurements.
Two synchronised Phantom v2511 high-speed cameras were set up to record one side of the component tests at a frame rate of 50 kHz as shown in Figure 10a.Camera 1 was centred on the test specimens while Camera 2 was centred on the shock tube extension.The field of view of the two cameras is indicated in Figure 10a, where Camera 1 records the immediate vicinity of the test component, and Camera 2 records the entire windowed area of the shock tube extension.An image of the camera placement during testing is shown in Figure 10b.T A B L E 3 Material parameters for EPP-5122, from Reyes and Børvik. [35,36]terial Density (kg=m

| Experimental results
Experimental results from the component tests are presented below.For the FPs, key results are given in Table 4.For all nine tests, little variation in the incoming shock velocity M s and the incoming side-on pressure p so;max was identified.This indicates that the shock load applied to the plates was consistent for all tests.In all tests, the maximum plate displacement x max was lower than the initial distance of 200 mm from the FPs to the reaction plate, that is, the plates stopped prior to impacting the reaction plate due to the pressure build-up behind the plates.For all three plate materials, the maximum displacement x max and the maximum velocity V max were consistent with small variations within each of the three repetitions.The reflected specific impulse at maximum displacement i r,x max was found by numerical integration of the pressure history from Sensor 3 for each test from t ¼ 0 until the time of maximum displacement of the plate in the respective test.i rþ was found by numerical integration of the pressure history from Sensor 3 for each test from t ¼ 0 until the time at which the overpressure measured in Sensor 3 was zero.As the results were consistent, only one test for each plate material was chosen for further analysis.The selected tests are FP_PC_01, FP_AL_02 and FP_ST_03 as these displayed maximum displacements and velocities closest to the average for each plate material.
Figure 11 shows results for the first 10 ms of the three chosen tests with FPs. Figure 11a,b shows the plate displacements and velocities, respectively, while Figure 11c,d shows the pressure measured downstream and upstream of the plates, respectively, compared with the pressure measured in the same locations from one of the RB tests.Note that for all figures, t ¼ 0 ms is set to the time at which the shock wave passes Sensor 1, that is, 625 mm upstream of the FPs.A strong dependency on plate mass can be identified for the plate displacement and velocity from the displacement and velocity histories displayed in Figure 11a,b, respectively.As the plates were accelerated by the incoming shock wave, the volume behind the plates reduced and the pressure increased accordingly for all three plate materials, as seen in Figure 11c.Eventually, the pressure build-up caused the plates to stop accelerating.The pressure behind the two plates with the lowest mass was similar as the maximum displacement was approximately the same.For the heaviest plate made from steel, the maximum displacement was approximately 10 mm (6%) less than for the two other materials.The smaller displacement resulted in a lower maximum pressure behind the steel plate, as seen in Figure 11c.We suspect that the smaller maximum displacement for the steel plate is related to two effects.First, the plates were not perfectly sealed along the perimeter with a 1 mm gap between the plate and the inside of the glass wall.This gap could have enabled a leakage that may have caused the pressure in the volumes in front of and behind the plates to partially equalise.The steel plate moved at a slower velocity than the two lighter plates, allowing more time for the pressure to equalise and thereby inducing a stronger equalisation effect causing a lower pressure difference across the plate.Second, the heaviest plate may have experienced increased friction between the plate and the guide rods, reducing the maximum displacement.The measured specific impulse at maximum displacement i r,x max and the maximum reflected impulse i r;max for all tests are given in the two rightmost columns of Table 4.These values were calculated by integrating the pressure-time curves obtained by the sensor behind the plates; see Figure 11c.The impulse at maximum displacement, i r,x max , increased as the plate mass increased, while the maximum reflected impulse, i rþ , decreased as the F I G U R E 1 1 Comparison of experimental results from selected tests with free-standing plates.plate mass increased.For all tests, both the impulse at maximum displacement and the maximum reflected impulse were lower than the measured reflected impulse from the RB tests, given in Table 1.
The pressure upstream of the plates, shown in Figure 11d, was affected by the plate movement.At t ¼ 0 ms, the incoming shock wave reached Sensor 1 and the pressure began to decay.At t ≈ 3:1 ms, the shock wave reflected at the FPs arrived again at the sensor.The initial peak pressure measured at Sensor 1 was 289, 322 and 344 kPa for the polycarbonate, aluminium and steel plates, respectively.That is, the initial peak reflected pressure measured upstream of the plate was smaller for smaller plate masses.The pressure history after the initial peak declined faster for smaller plate masses.These results indicate that there was a strong FSI effect which was dependent on the velocities and thus the mass of the plates before they came to rest.The maximum linear momentum for the plates was 34.2, 53.2 and 81.8 kgÁm/s for the polycarbonate, aluminium and steel material, respectively.This observation follows the early works of Taylor [7] suggesting that lightweight structures undertake less momentum compared to heavier structures when exposed to the same blast intensity.It also supports the findings of Subramaniam et al. [10] which implies that the effect of reduced pressure is expected to be larger for plates with increased velocities.That is, the polycarbonate and aluminium plates experience a larger velocity due to their light weight and the change of linear momentum is smaller during the FSI.For the polycarbonate and aluminium plates, a second peak in the pressure history at Sensor 1 can be observed which corresponds to the plates coming to rest.For the polycarbonate plate, the second peak pressure of 383 kPa was higher than the initial peak pressure, which was also higher than the initial peak pressure for all three plate masses and higher than the peak achieved with the RB.The second peak pressure for the aluminium plate was approximately the same as the initial peak pressure of 335 kPa.For the steel plate, no distinct second peak pressure was detected.It should be noted that the pressure at Sensor 1 measurements were taken 625 mm upstream of the initial position of the plates and are thus only an indication of the pressure at the plates.
Figure 12 presents the measurements from BOS for the aluminium test plate case.Details for the BOS set-up are given in Table A2.Displacement fields are displayed for relevant events: the approaching and reflected shock, the impact on the test plate and the secondary shocks forming behind the test plate.The visualisations demonstrate the symmetry of the vertical shock fronts and show the test plate interacting with the secondary shocks as it moves downstream.The variation in thickness of the observed shock occurs due to the angle between camera and shock position and is therefore not physical.The test plate does not appear to have rotated significantly as it moved downstream, confirming that the assumptions of one-dimensional plate motion remain valid.The sensitivity of the BOS method was chosen to allow a density reconstruction before and after the shock and to compare with the numerical models.However, the observed vibrations of the background plate together with the rest of the set-up are of the same order of magnitude as the relevant signal amplitude, rendering density reconstructions impossible in the present case.
For the plates backed by the polymer foam, the test results are summarised in Table 5.These results are similar to the results for the FPs, where V max was found to be dependent on the plate mass.When foam backing was applied, the peak velocities were reduced by 39%, 36% and 20% for the polycarbonate, aluminium and steel plates, respectively, while the peak displacements were reduced by 10%, 17% and 13%, respectively, as compared to the FPs.Front plate displacement and velocity for the first 12 ms of the tests are shown in Figure 13a,b, respectively.
The reaction force for the foam-backed plates is compared to the reaction force in one of the RB tests in Figure 13c.A short plateau can be observed at 12 kN during the first millisecond for all the tests on foam-backed plates.This corresponds to a reaction stress of 130 kPa, which is lower than the initial compressive strength of EPP-5122; see Table 6.After this point, an approximately linear increase in the reaction force can be identified for the three plate masses.The  T A B L E 6 Material constants for EPP-5122, from Reyes and Børvik. [35,36]p (MPa) peak force was 78, 63 and 58 kN, for the polycarbonate, aluminium and steel front plates, respectively.The peak force of 48 kN measured in the RB tests, presented in Section 3.1, was considerably lower than for the foam-backed plates.The increase in peak force observed in the tests with the foam-backed plates is likely because the foam reached the compaction strain before the plates were halted.As the compaction strain was reached, the foam stiffness increased, and the plates were rapidly decelerated resulting in an increase of the measured reaction force.There were significantly fewer oscillations in the force measurements for the foam-backed plates than in the RB test, most likely because the addition of the foam damped the vibrations induced by the incoming shock wave.The reflected impulse at maximum displacement, i r,x max , and the total reflected impulse, i rþ for the foam-backed plates are given in Table 5.These values were calculated based on the measurements from the load cells and are therefore not directly comparable to the values given for the FPs in Figure 4.As was shown in Figure 8 in Section 3.1, the force measured by the load cells was higher than the corresponding force calculated from the pressure-sensor measurements.The difference in force increased after the first 10 ms.Although the two impulses are not directly comparable, the trends were the same as for the FPs, that is, that the impulse at maximum displacement increased while the total reflected impulse decreased as the plate mass was increased.The overpressure measured in Sensor 1 for the tests with foam-backed plates is compared to the result from the RB test in Figure 13d.The initial peak reflected pressures were 298, 324 and 344 kPa for the foam-backed polycarbonate, aluminium and steel plates, respectively, which were almost the same as the initial reflected pressures measured with the corresponding FPs.For all three plate masses, the initial reflected pressure was lower than the peak reflected pressure in the RB test.After the initial peak reflection, the decay of the pressure histories was slower than for the corresponding FPs.For the polycarbonate and aluminium plates, there was a secondary peak in the overpressure when the plates halted.This secondary peak was smoother and lower in magnitude than the corresponding peak for the FPs.For the heaviest (steel) plate, there was no secondary peak in the pressure at Sensor 1.
Figure 14 shows the horizontal logarithmic surface strains obtained with 2D-DIC for all three tests with foambacked plates.Details for the DIC set-up according to the iDIC Society Good Practices Guide [37] are given in Table A1.The surface strains were obtained with the in-house DIC-code eCorr. [34]Subset-based DIC with a subset size of 10 pixels and element size of 20 pixels was used.Element-wise grey value normalisation was applied to all images to account for highlights on the surface of the test specimens.As the plates moved at different velocities the tests are compared at four front plate displacements, 4.5, 35, 80 and 120 mm.At 4.5 mm front plate displacement, the measured Foam surface strains in the horizontal direction obtained from 2D-DIC for foam-backed plates.
horizontal surface strains were similar and mostly homogeneous for the three front plates.When the plate displacements increased to 35 mm, there was a localisation of compressive strains behind the front plates.The localisation was strongest for the lightest polycarbonate plate and became less distinct for heavier front plates.At 80 mm front plate displacements, a second band of localised compressive strains is visible in Figure 14 for all three plate materials.The foam with the polycarbonate front plate showed the strongest localisation and the highest compressive strains.The distribution of compressive strains became more homogeneous for increased front plate mass.At 120 mm front plate displacements, the surface strains were similar for all three front plate masses.Overall, the foam compression was not homogeneous and the surface strains obtained from 2D-DIC showed that the foam deformation localised in bands with similar placement, but different magnitude depending on the front plate mass.

| NUMERICAL MODELLING
In this study, the numerical model for compressible shock flow proposed by Kabouchev et al [4] is used to model the experiments.While this model may be considered simple compared to three-dimensional simulations of FSI and shock flow in compressible media, the low computational cost makes it favourable for preliminary design of protective structures.Comparing the experimental results obtained in the previous section with this model serves to justify the relevance of the experimental set-up.In this section, the numerical model is briefly described before the numerical results are compared with the experimental findings presented in the previous section.

| KNR model for FSI in a compressible fluid
The numerical model proposed by Kambouchev, Noels and Radovizky (KNR) [4,8,9] was used to model the shock propagation and FSI.The fluid part of this model is the von Neumann-Richtmeyer model for shock flow in compressible fluids. [38]The authors introduced an artificial viscous dissipation term to the conservation equations to model the shock flow.The viscous term acts to stabilise the numerical solution around discontinuities caused by a propagating shock wave.In effect, the viscous term smooths out the shock to a width coinciding with the grid spacing, thus stabilising the numerical solution.This model was later expanded by Kambouchev et al. to include the interaction between a shock wave and a FP.A detailed description of the KNR model can be found in Kambouchev et al., [8] but the main components of the model are repeated here for completeness.
The kinematic relations for a fluid in a Lagrangian framework are given by the material velocity V and acceleration A in terms of time t and a spatial coordinate x of each fluid particle X: Conservation of momentum in terms of the initial density ρ i , pressure p and the Lagrangian coordinate X of a fluid particle is expressed as The viscous dissipation is introduced to the equation of state (here, the ideal gas law), which takes the form where R is the ideal gas constant, T is the temperature, γ ¼ c p c v is the ratio of the specific heats for the gas, e ¼ c v T is the internal energy of the gas and F ¼ ∂x ∂X is the deformation gradient.The dissipation term Q is defined as where K 1 and K 2 are artificial viscosity constants, Δ is the width of the smeared shock, a ¼ ffiffiffiffiffiffiffiffi ffi γRT p ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi γðγ À 1Þe p is the local speed of sound in the fluid and D ¼ 1 is the deformation rate.The viscous dissipation is also included in the internal energy conservation: where ρ is the current density of the particle.The governing conservation equations, that is, Equations ( 3) to (8), are solved by a central difference scheme as described in Kambouchev et al. [8] and Drumheller. [39]

| Shock tube implementation
The KNR model described in Section 4.1.1 was implemented in Matlab R2022a [40] based on the work of Hjelmeland, [41] following the numerical scheme given in Kambouchev et al. [8] To model the shock tube, a 0.27-m-long driver section was connected to a 16.2 m + 0.58 m driven section.In these sections, the initial conditions of the shock tube when fired were applied, that is, at t ¼ 0 ms, the pressure recorded in the driver section when firing was set as the initial condition, and the ambient pressure and temperature as initial conditions in the driven section.At each end of the model, a RB was applied.A spatial discretisation of 2 mm was applied for the entire length of the model, resulting in N ¼ 8500 grid points.The gas properties for air were assumed throughout: a constant specific heat ratio γ ¼ 1:4 and initial density ρ 0 ¼ 1:225 kg=m 3 .The initial and maximum time steps were dt 0 ¼ 1 Â 10 À8 s and dt max ¼ 1 Â 10 À5 s, respectively.The numerical constants in the dissipation term Q were set to K 1 ¼ 0 and K 2 ¼ 1.The Courant number for calculating the critical time step was set to α ¼ 0:25, ensuring the stability of the numerical scheme.
The model used for simulating the plates was the same as for the shock tube with a RB where the interaction between the shock wave travelling down the driven section and the deformable plates was included.Following Kambouchev et al, [9] the acceleration A p of a FP impacted by a shock wave travelling down the shock tube is found by Newton's second law: where ρ p is the plate density, h p is the plate thickness and p p is the pressure difference across the plate.The plate is modelled as a point mass with areal density m p ¼ ρ p h p , where the fluid domain is extended downstream of the plate.
In the case of a sandwich structure, the plate is backed by a material or structure that, when compressed, imparts a stress σ f on the side of the plate opposite to the incoming shock.This resistance can be included in the acceleration of the plate by substituting the air behind the FP in Equation ( 9) with σ f [41] : where p s is the pressure from the incoming shock wave in front of the plate.The air volume behind the plate is not modelled in this case, and the air pressure in the volume behind the plate is assumed constant and equal to the ambient pressure p a .The reaction stress of the material behind the plate can be modelled in many different ways.Here, the resistance of the foam is assumed to only depend on uniaxial compression.The elastic behaviour of the foam is neglected, and the compressive stress including strain hardening is taken from Brekken et al. [18] Thus, the following expression for the foam stress is used: where σ p is the plateau stress, while γ F , α 2,F and β F are hardening constants determined from quasi-static compression tests.The densification strain ε D ¼ Àln ρ f ρ f0 is found from the relative density of the foam, where ρ f and ρ f0 are the density of the foam and base material, respectively.ε eq ¼ Àln h f Àξ h f is the equivalent plastic strain in the foam, where ξ is the displacement of the front plate and h f is the initial thickness of the foam.As the foam may undergo large strain rates, viscoplasticity is included by addition of the term in the final parentheses.Here, _ ε eq ¼ ∂ε eq ∂t is the plastic strain rate, and _ ε 0 is a reference strain rate.The strain-rate sensitivity constant c F is determined from compression tests at varying strain rates.It is well known that cellular materials subject to impulsive loading often results in stress wave propagation in the material, [42] but the expression for the foam stress in Equation (11) does not account for this phenomenon.
The EPP foam used in this study has been extensively studied and characterised by Reyes and Børvik. [35,36]The hardening and viscoplastic constants in Equation (11) are taken from these studies and given in Table 6.

| Numerical results
The numerical results are presented below.The results from simulations of the RB tests are first presented to demonstrate that the numerical model represents the shock formation and propagation observed in the SSTF.Secondly, the results from simulations of the free-standing and foam-backed plates are presented and compared with the experimental observations.

| Rigid boundary (RB)
The numerical results with a RB are compared to the experimental results from test R_20_02 in Table 7.For the incoming shock wave, the Mach number is captured accurately by the numerical model, while the incoming side-on pressure p so;max is underestimated by 9.4%.Also the peak reflected pressure p r;max is accurately predicted by the numerical model, while the reflected specific impulse is underestimated by 14%.The reflected impulse is lower numerically than experimentally because the pressure decays faster in the numerical model, resulting in a reduction in t dþ of 18%. Figure 15 shows a comparison between the numerical and experimental results for test R_P20_02.The pressure at Sensor 1, located 825 mm from the end of the extension, is shown in Figure 15a, while the pressure measured at the end of the extension is shown in Figure 15b.The numerical model also accurately captures the reflected shock velocity, which is shown by the time between the incoming and reflected shock wave at Sensor 1, that is, the time between the distinct jumps in the measured pressure in Figure 15a.Overall, considering the low complexity of the numerical model, it is able to suitably predict the shock generated by the shock tube with the parameters used in this study.

| Free-standing plates (FPs)
Selected main results from the numerical models of the FPs are compared with the experimental results from tests FP_PC_01, FP_AL_02 and FP_ST_03 in Table 8.For the polycarbonate and aluminium plate the calculated  16a, are very close, but somewhat higher than the experimental values from initial acceleration to maximum displacement.Note that the curves for the aluminium and steel plates in Figure 16 have been shifted with 10 and 20 ms, respectively, for ease of comparison.For the polycarbonate and aluminium plates, the difference in maximum displacement is 2.6% and 3.1%, respectively.This difference in maximum displacement is within the range of the experimental scatter.For the steel plate, the simulated initial velocity shown in Figure 16b is close to the experimental value, but the maximum displacement is 8.5% larger numerically.This increased difference between experimental and numerical results for heavier plates is most likely caused by leakage from high to low pressure around the plates in the experiments.This is further confirmed when considering the pressure behind the plates, as shown in Figure 16c.The maximum pressure behind the plates is consistently higher in the simulations than in the experiments, which should cause greater deceleration and thus lower displacements than in the experiments.However, in the experiments, a rise in pressure was observed when the shock wave impacted the plates because some of the pressure from the incoming shock wave leaks around the plates.This leakage between the front to the back of the plates presumably lasted until the pressure behind the plates was greater than in front, causing a deceleration of the plates.As the steel plate had a lower velocity because of a larger inertia, the time when the leakage had an effect was longer in this experiment.The increased pressure behind the plates obtained numerically was most likely caused by the reduced final volume.Again, this difference was larger for the heavier plate because the difference between the experiment and simulation increased when the plate mass was increased.Numerical results of the pressure upstream of the plates are compared with the experimental results in Figure 16d.The initial reflection caused by the shock wave impacting the FPs and the subsequent decay in pressure were well captured by the numerical model for all three plate masses.The secondary reflection caused by the plate coming to rest was also well predicted for the polycarbonate plate.For the aluminium plate, there was a larger drop in the pressure before the secondary reflection in the simulations than observed in the experiment.However, the magnitude of the secondary reflection and the subsequent decay were captured.For  the steel plate, the numerical simulation did not capture the secondary reflection accurately as there was a delay in the occurrence of the secondary reflection.The magnitude of the secondary reflection was also lower in the simulation than in the experiment.Overall, a good correlation can be observed between the numerical and the experimental results from the time the shock wave impacted the FPs to the point where the plates began to decelerate.After the onset of plate deceleration, the model accuracy is reduced and worsens for increased plate mass.

| Foam-backed plates
Selected numerical results from the foam-backed plates are compared to the experimental results in Table 9.The numerical model does not account for the rebound of the foam and the air behind the plates; therefore, the results are only given from the time at which the shock wave passed Sensor 1 to peak displacement of the plates.The numerical displacements and velocities are compared to the experimental results in Figure 17a,b, respectively.Note that the curves for the aluminium and steel plates in Figure 17 have been shifted with 7 and 14 ms, respectively, for ease of comparison.In general, the numerical model did not capture the displacements and velocities of the plates as accurately for the foam-backed plates as for the FPs.For all three plate masses, the numerical model overestimated the maximum displacement x max and underestimated the peak velocity V max .The reaction force from the numerical model is compared with the experiments in Figure 17c.The numerical model was partially able to represent the reaction force from the experiments.As the plates started accelerating, a reaction stress was immediately applied to the reaction wall in the numerical model.This happens because the foam behaviour is modelled as homogeneous and rigid plastic with stresses determined by Equation (11).Experimentally, there was a delay between the initial acceleration of the plates and the time until the reaction force started to rise.The shape of the reaction force curve differs between the experimental and numerical results.Experimentally, there was an approximately linear increase in the reaction force with no distinct yield stress and plateau, while in the numerical model, there was a clear yield stress and a plateau followed by an increase in the reaction stress as densification was reached.The transmitted impulse until maximum displacement i r,x max was thus underestimated in the numerical simulations.The results in Figure 17c show that the foam model employed here is not able to accurately represent the experimental behaviour.There appears to be a correlation between the accuracy of the numerical model and the mass and, consequently, the inertia of the front plates.The exact reason for this is not known and is a subject for further investigations.However, considering the simplicity of the numerical model, it is able to capture the experimental trends for displacement and reaction force well.

| CONCLUSIONS
In this work, the SSTF was extended with a transparent section to study components subjected to blast-like loading.The purpose of the modification was to create an experimental set-up where deformable components can be studied in greater detail than with the existing SSTF.The transparent extension enabled high-speed imaging of the test component and on the air in the area upstream and downstream of the test object.The high-speed images allowed for measuring displacements and deformations of the components with 2D-DIC.High-speed, full-field imaging was also used for the BOS technique to visualise fluid flow and shock interaction with the test components.Reaction forces from tested components were measured with an assembly made up of eight piezoelectric load cell washers.The pressure upstream and downstream of test components was measured with pressure sensors.The tests were modelled using a one-dimensional numerical model for the shock flow with FSI.The main conclusions of this study are as follows.
• The experimental set-up was first validated with a test series in which the incoming shock wave was reflected at the rigid end of the shock tube extension.From these tests, it was confirmed that the addition of the transparent extension did not adversely affect the shock flow and that both the incoming and reflected shock waves were consistent and planar.F I G U R E 1 7 Comparison between experimental and numerical results for foam-backed plates.
• It was found from the RB tests that the force obtained from the load cell washers was highly consistent between tests with the same blast load, but somewhat inconsistent with the pressure-sensor measurements.The reason for a slightly higher load measurement with the load cell washers than with the pressure sensor was not conclusively determined.However, the force measured with the load cell washers included the 18.5 kg mass of the aluminium reaction plate and possible deflections of the steel backing plate.Therefore, the system including the load cell washers is prone to oscillations which could cause some disturbances in the measurements.• By adding the transparent extension to the shock tube, the area inside the extension was available for recording with high-speed cameras.The BOS technique was used to visualise the shock flow during testing.The results obtained with BOS were suitable for identifying qualitative differences in air density between tests.However, the reconstructed air density from the BOS results requires further work to provide reliable quantitative results for the air density during testing.• The component tests with FPs demonstrated that the experimental set-up can be used to produce results with a high degree of repeatability.This is important for a better understanding of the governing phenomena during FSI.• The displacement and velocity of the FPs were, as expected, dependent on the plate mass, where a lower mass resulted in increased maximum displacements and higher maximum velocities.The pressure upstream and downstream of the FPs was highly dependent on the plate velocity, and the impulse imparted to the reaction plate at maximum plate displacement was dependent on the plate mass.While a lower plate mass resulted in a lower impulse measured at the reaction plate, suggesting a beneficial FSI effect for lighter plates, the peak pressure was significantly higher than the reflected pressure without any plate specimen.The foam-backed plates exhibited similar behaviour to the FPs.• The one-dimensional numerical model used is able to predict the shock flow and plate response observed experimentally with a high degree of accuracy considering the low complexity of the model.The numerical model was able to accurately predict the shock velocity and the reflected pressure measured in the RB tests, but the duration of the positive phase and the reflected impulse was somewhat under-predicted in the numerical model.• The numerical results were in good agreement with the measured response of the FPs but with deteriorating accuracy for larger plate masses.This shows that the numerical model is able to describe the FSI effects both upstream and downstream of the FPs.Numerical results for the foam-backed plates were less accurate compared to the experimental results.Although the numerical model was in good agreement with the measured plate response, the reaction forces were not accurately predicted.Overall, considering the simplicity and low computational cost of the numerical model, it gave reasonable predictions of the experimental results.• The main conclusion of this study is that the extension of the shock tube succeeded in establishing an experimental set-up which is ideal for detailed studies of deformable components subjected to airblast loading.Such investigations are considered important for experimental validation of numerical models for energy absorbing materials and structures.

F I G U R E 1
Overview of shock tube with transparent extension.F I G U R E 2 (a) Transparent extension attached to the end of the shock tube and (b) extension without the end assembly attached to the shock tube.

F
I G U R E 3 (a) Cross section of the shock tube extension consisting of the steel frame and the flanges (black), glass (blue), reaction plate (purple), mounting plate (green) and position of the load cells (red).The fasteners are not shown.(b) Aluminium reaction plate mounted to the steel mounting plate.(c) Back of reaction plate with load cells (inside coloured circles).(d) Front of reaction plate with pressure sensors mounted.
Experimental set-up for load cell calibration.(b) Results from load cell calibration.

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I G U R E 8 Force-time curves comparing results from load cells with pressure sensor for all tests with rigid wall.F I G U R E 7 Comparison of pressure-time curves for tests with a rigid wall.(a) Pressure in Sensor 3 and (b) pressure in Sensor 1 3.2.1 | Materials and component test set-up

F I G U R E 9
Components mounted inside extension.(a) Free-standing plate and (b) foam-backed plate.T A B L E 2 Materials and corresponding masses for plates used in component tests.

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I G U R E 1 0 (a) Schematic showing high-speed camera placement and field of view.(b) Image of experimental set-up showing the setup of high-speed cameras.T A B L E 4 Shock parameters and peak displacements and velocities from tests with free-standing plates (FPs).

F I G U R E 1 3
Comparison of experimental results from tests with foam-backed plates.T A B L E 5 Shock parameters and peak displacement and velocity for tests with foam-backed plates (SW).

F I G U R E 1 5
Numerical results for rigid boundary simulations compared with experimental results.(a) Pressure at Sensor 1 and (b) pressure at end of the extension.

F I G U R E 6
Comparison between experimental and numerical results for free-standing plates.
Comparison between numerical and experimental results for a rigid boundary test.
Comparison between numerical and experimental results for free-standing plates.
T A B L E 8 max (mm)V max (m/s) i r,xmax (kPa ms) i rþ (kPa ms) Comparison between numerical and experimental results for foam-backed plates.materialx max (mm)V max (m/s) i r,xmax (kPa ms) T A B L E 9