Blast disruption using 3D grids/perforated plates for vehicle protection

Thérèse Schunck,Dominique Eckenfels,Laurent Sinniger

French-German Research Institute of Saint-Louis, ISL, 5 Rue Du G′en′eral Cassagnou, 68300, Saint-Louis, France

Keywords:Blast Mitigation Perforated plates 3D grids Vehicle protection

ABSTRACT In this work,blast disruption and mitigation using 3D grids/perforated plates were tested for underbelly and side protection of vehicles.Two vehicle simulants were used: a small-scale one for side vehicle protection assessment and a true-to-scale simulant for underbelly protection testing.The deformation of target plates was assessed.These were either unprotected or protected by three different types of disruptors.The first disruptor was made of a sandwich structure of two perforated plates filled with a thin aluminum structure allowing the air to pass through.The two other disruptors were made of pieces of cast metallic foam.Two different kinds of foams were used:one with large cells and the second one with small cells.Beforehand,the mitigation efficiency of the disruptors was evaluated using an explosivedriven shock tube (EDST).The experiments showed that blast disruption/mitigation by 3D grid/perforated plate structures was not suitable for vehicle side protection.However,3D grids/perforated structures proved to be relatively effective for underbelly protection compared to an equivalent mass of steel.? 2022 China Ordnance Society.Publishing services by Elsevier B.V.on behalf of KeAi Communications

1.Introduction

The present study deals with blast disruption and mitigation using 3D grids/perforated plates within the context of vehicle protection.The main objective is to assess the operational capability of this type of disruptors for underbelly and side protection of vehicles.

One of the most important requirements for combat vehicles is the protection against mines (anti-personnel or anti-tank mines)and improvised explosive devices(IEDs).IEDs are complex because there are many variations.Whereas some IEDs are made of military explosives,others can contain home-made explosives.In addition,they can be hidden in various places,e.g.the device may be buried in the soil or placed in a vehicle for roadside attacks.Blast vehicle protection follows guidelines such as blast protection (blast deflection and mitigation) as well as roll prevention.

The general principle of blast protection is to place a “system”(material,structure,etc.) between the explosive charge and the target.This system serves either to mitigate the detonation of the explosive,to disturb the blast wave propagation,or to ensure passive protection of the target.Methods commonly considered to mitigate explosion are the use of bulk water [1] or mist [2-4] and aqueous foam [5].Multi-layered materials rely on the impedance mismatch between each layer to scatter the blast waves across the system[6].Specific geometries,such as V-shape plates or arrays of cylindrical pipes,are generally used to deflect/disturb the incoming blast wave [7,8].The use of sacrificial claddings is a passive protective solution which allows to dissipate the blast wave energy and improves the target’s resistance against blast load [9].A sacrificial cladding is made of three components: a crushable core,sandwiched between a front plate(attack side) and a rear plate.When submitted to a blast wave,the front plate is set in motion and crushes the core.Elastic,plastic and brittle deformation of the core leads to energy dissipation and to the transmission of a lower,quasi-constant loading over a longer timespan.

The present study focuses on blast deflection and mitigation and especially on the use of 3D grids/perforated plates for underbelly and side protection of vehicles.Grids and perforated plates were used to disrupt blast waves.The description of the interaction of a shock wave with grid-like obstacles started in the 1950s[10].It has been shown that grids or perforated plates modify the flow field by introducing new shock waves,regions of vortices and considerable turbulences in which the energy of the incident shock wave can be dissipated[8,11].It has been demonstrated that when a shock wave collides with a perforated plate,a part of the incident shock wave is reflected by the plate and the other part is transmitted through it,generating a non-steady flow behind the plate.The flow located immediately behind the grid is highly unsteady and non-uniform.It becomes steady and uniform further downstream.The transmitted wave is mostly attenuated in the region where the flow is highly turbulent.The pressure development on a wall placed behind rigid porous samples was also investigated using a shock tube [12].The porous samples were made of ceramic foams having three different porosities(10 PPI,20 PPI and 30 PPI,PPI stands for pores per inch).The results indicated that lower porosity reduces the time required for the pressure to build-up on the end-wall.This phenomenon was due to the higher flow resistance through porous samples of low porosity (larger PPI).Configurations of several perforated plates were also investigated.It has been reported that shock wave trapping between several plates enhanced the shock wave attenuation downstream from the plates[13-15].The initial shock wave reflected several times and was strongly disturbed.It has been shown that the grid porosity and the shape of the open spaces are the major factors to reduce the overpressure,whereas the geometry had practically no influence.The shape of holes could potentially have an impact in case the plate is thick and the holes beveled thus enhancing the reflection of the shock wave.For this reason we tested in the present work the capability of perforated 3D structures with regard to blast disruption and mitigation.This type of structures offers both effects:a reflection of the blast wave as well as strong perturbations of blast wave on its path.To the best of our knowledge,perforated 3D structures have not yet been tested for vehicle blast protection.As far as ballistic protection is concerned,it has been shown that they could destabilize a threat and reduce its penetration capability before it reaches the main armor [16].Impact tests have proven that perforated plates offer a high protection level against the impact of 7.62 × 51 0.308 WIN P80 hardcore armor piercing projectiles.A rigid slatted metal grid (Slat armor)fitted around key sections of the vehicle has also been used to disrupt shaped charges of a warhead by either crushing it,preventing optimal detonation from occurring,or by damaging the fusing mechanism,preventing detonation outright [17].Consequently,perforated plates could have a dual use as add-on armors.In the present work,three types of blast disruptors were tested.The first disruptor was made of a sandwich of two perforated plates filled with a thin aluminum structure allowing the air to pass through.A disruptor designed in this way will reflect the shock wave two times and the perforated structure will strongly disturb the wave between the two plates.The two other disruptors were made of pieces of cast metallic foam.Two different kinds of foams were used:one with large cells and the second one with small cells.The cast metallic foam is an interesting 3D structure:since the cells are open,they allow the shock wave to pass through but the air flow inside will be strongly perturbed.Moreover,the round shape of open cells will increase the shock wave reflection.Two sizes of cells were tested in order to assess the cell size on blast mitigation efficiency.

The French-German Research Institute of Saint-Louis(ISL)owns two vehicle simulants which were both used in the course of this work:a small-scale vehicle simulant developed to investigate side vehicle protection and a true-to-scale vehicle simulant that has been extensively used to investigate side and underbelly protection.First,experiments with the small-scale vehicle simulant were carried out in order to evaluate the effectiveness of the principle for side vehicle protection.Then,experiments with the true-to-scale vehicle simulant were carried out in order to evaluate the effectiveness of the principle for underbelly protection.The deformation of target plates was assessed.These were either unprotected(reference) or protected by the three different types of disruptors.Beforehand,the mitigation efficiency of the disruptors was evaluated using an explosive-driven shock tube (EDST).

2.Experiment

2.1.Explosive-driven shock tube (EDST)

The design of our EDST was based on previously published works [18,19].The shock tube has a 100 mm square external and 80 mm square internal section,with a total length of 1750 mm(Fig.1).A pressure sensor(Kulite HKS 375)was used to measure the reflected overpressure on a wall behind the disruptor.Spherical charges of composition C-4 were used (m=15 g) to produce a planar blast wave.All the charges were hand-packed and detonated in a distance of 50 mm from the shock tube inlet without any container(Fig.1).The distance between the outlet of the EDST and the wall was 180 mm.The blast disruptor was positioned 50 mm in front of the wall.

Fig.1.Schematic view of the explosive-driven shock tube and positioning of the blast disruptor.

2.2.Small-scale vehicle simulant

The small-scale vehicle simulant is composed of a 1 m3cubic metallic structure equipped with a removable sample plate (the free surface of the sample is a square of 800 mm edge) (Fig.2(a)).The maximum dynamic deformation of the sample was measured by squeezing a hexagonal 150 mm long aluminum tube (Fig.2(b))located at the rear face of the plate.

Fig.2.(a)Experimental setup:the charge was positioned in front of the small-scale vehicle simulant at a distance of 1.5 m.The side-on pressure gauge was located near the vehicle simulant at the same distance;(b) Hexagonal aluminum tube for maximum deformation measurement.

One pressure sensor(PCB137A23)was used to measure the blast generated by the explosive charge in order to control the reproducibility of blast loading across experiments.It was placed 30 cm above the ground and located 1.5 m from the charge,the same distance as from the charge to the test plate,and at a right angle to the charge-vehicle simulant line (Fig.2(a)).Hand-packed spherical charges of C-4 with a mass of 400 g were used.The explosive charges were positioned 7 cm above the ground.

2.3.True-to-scale vehicle simulant

The true-to-scale vehicle simulant has overall dimensions(Length×Width×Height)of 2.8×2.6×3.6 m3(Fig.3).A 1×1 m2sample plate is attached to the floor through a circular flange with an inner diameter of 0.8 m and an outer diameter of 1 m.The screws are regularly disposed along a circle with a diameter of 0.92 m.Consequently,the free surface of the sample is a disc with a diameter of 0.8 m(Fig.3).The sample plate was placed at 1 m above the ground.Thick discs of C-4 were used,hand-packed inside a mold.After removing the discs out of the mold,the charge has the following dimensions: height of 66 mm and diameter of 100 mm.The explosive mass,positioned 20 cm above the ground surface,was 730 g.Consequently,the charge was centered at 80 cm from the sample plate.The maximum dynamic deformation of the plate was measured by squeezing a hexagonal 150 mm long aluminum tube located at the rear face of the plate(Fig.4).The deformationtime history was also assessed by digital image correlation (DIC)[20].DIC uses two high-speed video cameras(VEO 710L,Phantom)to track the movement of the sample.It allows to compute 3D coordinates from the image series recorded by the two cameras.Measurement results for displacements were derived.The two cameras were attached via a ball heads to an aluminum profile.The profile was attached to the vehicle simulant structure using silent blocks(Fig.3).To perform the DIC measurements,the surface of the sample was prepared with an adequate black and white pattern.To this purpose,paint spray cans were used.Before performing a test,the DIC system was set up to the desired field of view and calibrated.The relative angle between the cameras was computed additionally by the software (GOM).Before starting the test,socalled reference images were captured by the left-side and the right-side stereo cameras.These images served as displacement reference for all further evaluations.During the test,image acquisition was carried out depending on the test requirements.Image acquisition parameters were the following:a frame rate of 9500 fps with a resolution of 1024 × 768 pixels.The exposure time ranged from 20 to 30 μs.A matrix of facets (subsets) with an applicationdependent size and distance was overlaid on the initial reference image of the left-hand camera.This matrix consisted of thousands of facets.The facets were used to compute 3D coordinates by evaluating the grey value distribution in each facet and reidentifying it in the reference image of the right-side camera.From the centers of the facets in the left-side camera images and in the right-side camera images,3D coordinates were triangulated with the help of the calibration data from the DIC sensor.The identification of corresponding facets in the left-side and the rightside camera images and through all images over time was done in the sub-pixel range,thus,leading to a much higher accuracy compared to pixel scaling alone.The initial results from DIC were 3D coordinates from the plate’s surface over time.Subtracting the 3D coordinates from all recorded stages over time from the 3D coordinates of the reference stage led to 3D displacement values.In addition,using the time derivatives of the displacement values,3D velocities and 3D accelerations could be calculated.

Fig.3.(a) True-to-scale vehicle simulant;(b) Sample plate and circular flange bolted onto the floor;(c) Hexagonal aluminum tube for maximum deformation measurement.

Fig.4.High-speed camera positioning in the vehicle simulant for DIC measurements.

2.4.Samples

2.4.1.Blast disruptors

2.4.1.1.Home-made sandwich.The first disruptor was made of two steel (S235-steel) perforated plates with “small” round holes(Fig.5(a)).The plate has the following characteristics:a porosity of 48%,a hole size of 10 mm,a distance of 14 mm between the holes and a thickness of 1.5 mm.The plates were distanced 50 mm apart from each other and the space between was filled with pieces of drilled aluminum honeycomb (Fig.5(b) and Fig.5(c)).The orientation of the honeycomb cells in the sandwich was parallel to the perforated plates.

Fig.5.(a)Steel perforated plate with“small”round holes,a porosity of 48%,a hole size of 10 mm and a distance of 14 mm between the holes,and a thickness of 1.5 mm;(b)piece of drilled aluminum honeycomb,foil thickness of 70 μm,diameter of 19 mm,two holes of 7 mm on each side;(c) structure of the home-made sandwich.

2.4.1.2.Cast metallic foam sandwich.The two other disruptors were made of pieces of aluminum cast metallic foam(F.T.B,France).Two types of foam were used,one with“l(fā)arge”cells and the second one with “small” cells (Fig.6).Their characteristics were as follows: a cell diameter of 30 mm and 15 mm,a strand thickness of 4.2 mm and 2.1 mm and a porosity of 93%,respectively.

Fig.6.(a) Aluminum cast metallic foam with “l(fā)arge” cells: cell diameter of 30 mm,strand thickness of 4.2 mm,and a porosity of 93%;(b) Aluminum cast metallic foam with “small”cells: cell diameter of 15 mm,strand thickness of 2.1 mm,and a porosity of 93%.

From a technical point of view,FTB was not able to provide 1 × 1 m2cast metallic foam slices but only pieces of 250×250 mm2.Consequently,several pieces were aggregated and held together with a strap.In order to keep the flatness of the assembly,it was inserted between two thin expanded aluminum plates with the following characteristics:a hole size of 10×5 mm2,a thickness of 0.8 mm,an apparent thickness of 2.1 mm,and a strand of 1 mm.

2.4.1.3.Metallic test plates.The reference test plates for the tests on the small-scale vehicle simulant were 2,4 and 5 mm thick aluminum alloy plates (EN AW-2017A).Each blast disruptor was placed in front of a 2 mm thick aluminum alloy plate.

The reference test plates for the experiments on the true-toscale vehicle simulant were 5,6 and 8 mm thick steel plates(S235).Each blast disruptor was placed in front of a 5 mm thick steel plate.

3.Experimental results and analysis

3.1.Explosive driven shock tube

Six reference tests were conducted without any disruptor,and three experiments were conducted each with one of the three different blast disruptors positioned at the outlet of the EDST.The time-history of reflected overpressure was captured by the sensor inserted into the wall,50 mm behind the disruptor.The impulse,which is the overpressure signal integrated over time,was also computed as a function of time.Fig.7 (a) shows the reflected overpressure as a function of time.The results of a reference test conducted without disruptor were compared to the results of those tests conducted with disruptors.Fig.7 (b) presents the impulse versus time for the same experiments,respectively.The maximum reflected overpressures and the maximum reflected impulses for all the tests are illustrated in Table 1.The attenuation of the maximum reflected overpressure or the maximum reflected impulse,compared to the mean value obtained in the reference tests,is also given.

Table 1 Initial reflected overpressure and maximum impulse obtained with the sensor inserted in the wall located 50 mm downstream from the disruptors.The attenuation is calculated with respect to the mean value from reference tests(no disruptor).

Fig.7.(a) Reflected overpressure and (b) impulse measured on the wall positioned 50 mm behind the disruptor for all types of disruptors.The figure also shows the results of a reference test performed without disruptor (CMF: cast metallic foam).

The maximum reflected overpressure on the wall decreased in a range between 48%and 67%with the cast metallic foams.There was no obvious difference between the two types of cast metallic foam.The attenuation was higher with the home-made sandwich,ranging from 73% to 79%.The maximum reflected impulse decreased in a range between 69% and 86% with the cast metallic foams,and in a range between 77%and 88% with the home-made sandwich.

3.2.Small-scale vehicle simulant

The explosion test matrix is provided in Table 2.Thanks to these tests,the deformation of a 2 mm thick plate protected by a disruptor was compared to the deformation of a 2 mm unprotected plate as well as to the deformation of thicker aluminum plates.

Table 2 Explosion test matrix.

The residual deformation of the metallic plates was difficult to assess as the plates were warped and bent forward after the detonation tests.As expected,the maximum dynamic deformation of the reference plates decreased when the thickness increased.The measurement of the maximum dynamic deformation revealed that the 2 mm thick aluminum plates were less deformed when protected by disruptors(Table 2).

Fig.8 presents the side-on initial overpressure and maximum impulse obtained with the pressure gauge located at a standoff distance of 3 m to the charge for each experiment.The initial overpressure and the maximum impulse were relatively similar across the tests.Thus,the dynamic loading on the vehicle simulant was relatively equivalent.The home-made sandwich has been more efficient to protect the 2 mm thick aluminum plate than both types of cast metallic foam sandwiches.The deformation of the 4 and 5 mm thick aluminum plates has been assessed.They were less deformed than the 2 mm thick target plates protected by the disruptors.An aluminum plate with a smaller mass outperformed the home-made sandwich combined with a 2 mm thick aluminum plate.The two cell sizes of cast metallic foam led approximately to the same results.An aluminum plate having an equivalent mass outperformed both types of cast metallic foam sandwiches combined with a 2 mm thick aluminum plate.

Fig.8.Side-on initial overpressure and maximum impulse measured by the pressure gauge located at a distance of 3 m of the charge for each experiment.

After the test,the home-made sandwich was relatively undamaged,the perforated plates were intact but the honeycomb was compressed (Fig.9(a)).The pieces of cast metallic foam were intact after the test (Fig.9(b)).

Fig.9.(a) Home-made sandwich after the test;(b) Large cells of cast metallic foam after the test.

3.3.True-to-scale vehicle simulant

The explosion test matrix is provided in Table 3.With these explosion tests,the deformation parameters of a 5 mm thick steel plate protected by a disruptor could be compared with the unprotected target plate as well as with the deformation parameters of steel plates with a higher or almost equivalent mass.

Table 3 Explosion test matrix,maximum dynamic and residual deformations.

Table 3 indicates,for each experiment,the residual and the maximum dynamic deformations of the metallic plate obtained either by using aluminum tube squeezing or DIC.As expected,the residual and the maximum dynamic deformations of the reference plates decreased when the thickness increased.Both deformations,dynamic as well as residual,showed that the 5 mm thick steel plates were less deformed when they were protected by the disruptors (Table 3).Differences in the protective effect of the three disruptors were not obvious.It could be noted that the two cell sizes of cast metallic foam led approximately to the same results.

Fig.10 plots the decrease of the maximum dynamic deformation compared to the 5 mm thick steel plate as a function of the additional mass of the protective solution for all the tests.The homemade sandwich proved to be relatively efficient.Compared to the 5 mm thick steel plate,it induced an increase of 30% in the floor mass but a decrease of 25%-32% in the maximum dynamic deformation.While a 6 mm thick steel plate increased the floor mass by 20%,when compared to a 5 mm thick steel plate,the maximum dynamic deformation decrease was only 11%-14%.In comparison with an 8 mm thick steel plate,the home-made sandwich was much lighter and caused almost the same maximum dynamic deformation.

Fig.10.Decrease of maximum dynamic deformation compared to the 5 mm thick steel plate as a function of the additional mass of the protection solution.AT: Aluminum tube.DIC: Digital image correlation.

When compared to a 5 mm thick steel plate,the cast metallic foam sandwiches increase the floor mass by 15% but decrease the maximum dynamic deformation by 13%-32%.These disruptors were more effective than a 6 mm thick steel plate.The maximum dynamic deformation decrease was equivalent or higher than that obtained with a 6 mm thick steel plate but these protective solutions had a lower mass.

Fig.11 shows the deformation of the metallic plate at the position of maximum deformation as well as that of the vehicle simulant floor as a function of time for all the tests.The curves were obtained by DIC measurements.The time evolution of the metallic plate deformation was similar for all the tests.In fact the deformation was not delayed in time when the metallic plate was protected by a disruptor.The maximum deformation of the metallic plate occurred between 0.0025 and 0.0030 s while that of the vehicle simulant floor occurred at about 0.01 s.The deformation of the vehicle simulant floor occurred much later and was similar across all the experiments.Obviously the level of deformation was different according to the targets.The metallic plate deformations with respect to the vehicle simulant floor deformations are given in Table 3.It could be noted that the results obtained using the aluminum tube were in good agreement with the DIC measurements.

Fig.11.Deformation of the metallic plate and of the vehicle simulant floor as a function of time for all the tests (DIC measurement).

After the test,the home-made sandwich was damaged,the two perforated plates were bent and the honeycomb was compressed or destroyed (Fig.12).The pieces of cast metallic foam were relatively intact,even if slightly distorted.The deployed aluminum plates were torn(Fig.13).

Fig.12.(a) Home-made sandwich after the test;(b) Details.

Fig.13.(a)Cast metallic foam sandwich after the test;(b) Pieces of cast metallic foam after the test.

4.Discussion

The experiments conducted with the EDST have shown that the three types of disruptors were effective in reducing the blast wave impacting a wall located at the back of the disruptor.The homemade sandwich was more effective than the cast metallic foams.The reflected overpressure and impulse on a wall were strongly reduced.This is due to the fact that the disruptors had relatively a low porosity consequently a large part of the incident shock wave was reflected.Moreover,these 3D barriers led to strong disturbances on path of the transmitted shock wave.The air flow was heavily thwarted when passing through the disruptors in which the shock wave energy was dissipated.Following these interesting results,these disruptors were tested for vehicle side and underbelly protection.

The explosion tests performed with the small-scale vehicle simulant have shown that the 2 mm thick aluminum alloy plates were less deformed when protected by the disruptors.The homemade sandwich was more efficient than both types of cast metallic foam sandwiches to protect the 2 mm thick aluminum plate.This is consistent with the results obtained with the EDST.The home-made sandwich was somewhat more efficient than the cast metallic foams.This result is also coherent since the additional mass related to the home-made sandwich was higher.The disruptors had the expected effects: the maximum dynamic deformation of the target plate behind was well decreased.Therefore the incident shock wave was effectively reflected and we can assume that the part of the shock wave passing through has been stronglydisturbed.However,a lighter aluminum plate outperformed the home-made sandwich combined with a 2 mm thick aluminum plate.The two cell sizes of cast metallic foam led approximately to the same results.As both foams had the same density,it could be assumed that the difference of cell size had no effect on blast disruption and mitigation.An aluminum plate with an equivalent mass also outperformed both types of cast metallic foam sandwiches combined with a 2 mm thick aluminum plate.Consequently,the blast disruptors tested in front of an aluminum plate were efficient,but the protection level was not higher than that of an aluminum plate with an equivalent mass.A crucial issue for vehicle protection is the vehicle mass.It is acceptable to increase the protection level while maintaining the mass and even to maintain the protection level while decreasing the mass.To obtain protection solution with equivalent mass,it will be much simpler to increase the metallic plate thickness than to integrate such blast disruptors on vehicles.Accordingly,such disruptors cannot be considered as a valuable option for vehicle side protection.

With regard to the experiments featuring the true-to-scale vehicle simulant,it was observed that both deformations,residual as well as dynamic,of the 5 mm thick steel plate decreased when it was protected by the disruptors.The protective effect of the home-made sandwich seems greater than those of the cast metallic foams,but the mass increase is higher.The three disruptors were relatively effective for underbelly protection compared with an equivalent mass of steel.An effect on the residual deformation was observed.The maximum dynamic deformation was also influenced,and reducing the maximum dynamic deformation is paramount in the area of vehicle protection.With such disruptors,it would be possible to increase the protection level while maintaining the mass or to maintain the protection level while decreasing the mass.

In summary,the blast disruption/mitigation by 3D perforated structures for vehicle side protection cannot be considered as an effective approach.Very good results were obtained with the EDST experiments,however this efficiency could not be achieved for vehicle protection as it is necessary to take into account the total mass of the protection solution.The blast disruptors were not more efficient than metallic plate with an equivalent mass.However,for underbelly protection,the blast mitigation was better.This is probably due to the numerous blast reflections under the vehicle.The blast reduction obtained by the interaction of the blast wave with the disruptor was amplified by the numerous blast reflections.Concerning underbelly protection,it would be possible to increase the protection level while maintaining the mass or to maintain the protection level while decreasing the mass.All things considered,this method seems to be of interest for vehicle underbelly protection purposes but some further work and improvement are still required.More experiments should be conducted and the concept should be tested with higher blast loading.Sturdy and lightweight 3D structures may be interesting solutions for such protection solution.

5.Conclusions

(1) The blast mitigation by 3D grids/perforated structures is due to the fact that:(a)these disruptors has a low porosity and so a large part of the incident shock wave is reflected;(b)these 3D barriers lead to strong disturbances on the path of the transmitted shock wave in which the energy of the shock wave can be dissipated.

(2) The blast disruption by 3D grids/perforated structures for vehicle side protection is not a good protection solution.

(3) 3D grids/perforated structures are relatively effective for underbelly protection compared with an equivalent mass of steel.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge the French Ministry of Defense for its financial support,in the frame of an official subsidy agreement (convention de subvention).

We thank our colleagues Yannick Stehlin and Thierry Ottié who assisted us in our research by providing technical support.