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The article is devoted to the development of methods for solving the problem of external ballistics using a more complete system of motion equation taken into account the rotation and oscillation about the mass center and using aerodynamic coefficients of forces and moments which are calculated on the basis of modeling the hydrodynamics of flow around the projectile. Developed methods allows to study the basic ways of increasing the shooting range or artillery. [ABSTRACT FROM AUTHOR]

The contribution describes the concept and numerical simulation of a ballistic protective layer which is able to actively resist projectiles or smaller colliding fragments flying at high speed. The principle of the layer was designed on the basis of the action/reaction system of reactive armour which is used for the protection of armoured vehicles. As the designed ballistic layer consists of steel plates simultaneously combined with explosive material - primary explosive and secondary explosive - the technique of coupling the Finite Element Method with Smoothed Particle Hydrodynamics was used for the simulations. Certain standard situations which the ballistic layer should resist were simulated. The contribution describes the principles for the successful execution of numerical simulations, their results, and an evaluation of the functionality of the ballistic layer. [ABSTRACT FROM AUTHOR]

We are developing a new diagnostic useful for the non-invasive detection of projectile passage in the launch tube of a gas gun. The sensing element consists of one or more turns of single-mode optical fiber that is epoxy-bonded around the external circumference of the launch tube. The hoop strain induced in the launch tube by the passage of the projectile causes a momentary expansion of the fiber loop. This transient change in path length is detected with high sensitivity using a fiber optic-based interferometer developed by the NSTec Special Technologies Laboratory. We have fielded this new diagnostic, along with fiber optic Bragg grating (FBG) strain gauges we previously used for this purpose, on a variety of gas guns used for shock compression studies at Los Alamos and Sandia National Laboratories.We anticipate that, when coupled with a broad-range analog demodulator circuit, the fiber optic interferometer will have improved dynamic range over that of the FBG strain gauge approach. Moreover, in contrast to the FBG strain gauge which is somewhat temperature sensitive, the interferometric approach requires no alignment immediately prior to the experiment and is therefore easier to implement. Both approaches provide early, pre-event signals useful for triggering high-latency diagnostics. [ABSTRACT FROM AUTHOR]

The investigation on free-surface impact of projectiles has last for more than one hundred years due to its noticeable significance on improving defensive weapon technology. Laboratory-scaled water entry experiments for trajectory stability had been performed with four kinds of projectiles at a speed range of 20~200 m/s. The nose shapes of the cylindrical projectiles were designed into flat, ogive, hemi-sphere and cone to make comparisons on the trajectory deviation when they were launched into water at a certain angle of 0~20°. Two high-speed cameras positioned orthogonal to each other and normal to the water tank were employed to capture the entire process of projectiles' penetration. From the experimental results, the consecutive images in two planes were presented to display the general process of the trajectory deviation. Compared with the effect of impact velocities and nose shape on trajectory deviation, it merited conclude that flat projectiles had a better trajectory stability, while ogival projectiles experienced the largest attitude change. The characteristics of pressure waves were also investigated. [ABSTRACT FROM AUTHOR]

The investigation on ballistic stability of high-speed projectile in granular materials is important to study the EPW (earth-penetrating weapon). Laboratory-scaled sand entry experiments for the trajectory in the sand have been performed at a range of velocities from 30 m/s to 150 m/s. In addition, pressure sensor was embedded in the sand to record the sand stress which reflects the penetration performance of projectile during the impact. The slender projectiles were designed into flat nose shape with three kinds of L/D (length-diameter ratio) to make comparisons on the trajectory when those projectiles were launched at normal and oblique impact angles (0~25deg) along a view window. A high-speed camera beside window was employed to capture the entire process of projectiles' penetration. Basing on the comparison of different tests, theoretical analysis is carried out on the relationship between ballistic stability and associated conditions. By utilizing DIC technique, the vector field of sand velocity was acquired, and the spreading direction of the impacting energy was observed. It can be concluded that the sand stress is the function of penetrating velocity, L/D and the shot angle. It increases with the growing of penetrating velocity and L/D, decreases with the shot angle. To a certain extent, the biggest initial velocity leads to the highest stress. [ABSTRACT FROM AUTHOR]

The research is focused on the simulation and experimental investigation of high-strain rate loading to study the mechanisms of plastic flow localization in metals (AlMg6) using a ballistic installation. Unique results of experiments are given in the paper. Numerical simulation using wide-range constitutive equations is done. The paper also shows the results of structural studies. [ABSTRACT FROM AUTHOR]

This paper presents the terminal ballistic of 3 mm thickness aluminium plate impacted by fragment simulating projectile (FSP). Up to days, not many researchers are keen into terminal ballistic. They are more focus towards ballistic limit. Therefore, there is a need to highlight terminal ballistic as such in this study. The experiment was conducted at the Science and Technology Research Institute for Defence (STRIDE) Batu Arang, Selangor. For recording purpose, digital high speed camera with the capability of 250,000 frames per second (max) and the highest resolution 1024x1024 was used. For the data acquisition and processing, Photron Fastcam Viewer (PFV) software was used. For numerical simulation purpose, commercial software code Hyperworks was employed. Results showed that there were four main failure stages, which were first contact between FSP and the plate, partial perforation, full perforation with FSP and plug still intact and lastly separation of FSP and plug. Good agreement was observed between experiment and numerical simulation. [ABSTRACT FROM AUTHOR]

The work presents opportunities of hydroballistic complex for studying the characteristics of movement supercavitation model (SCM) on the length of waterway to 10 m. Gunfire of SCM implemented by this complex allows to study movement and collision of the different masses of SCM with underwater obstacles at subsonic, transonic and supersonic velocities in water. During the movement of SCM different masses the behavior supercavity was investigated. [ABSTRACT FROM AUTHOR]

The problem of launchers used in civil applications is a topical issue. The role of a launcher is to launch objects with a certain speed towards certain goals like for example dangerous fire outbreaks (drilling areas, fires in buildings). This paper is aiming to present the theoretical aspects and results regarding the launching objects, in this case spheres that contains firefighting substance, during the launching stage, the ballistic stage and the impact stage with a solid surface. [ABSTRACT FROM AUTHOR]

The process of high-speed impact of projectiles against targets of finite thickness is experimentally investigated. Medium-hard steel plates are used as targets. The objective of this research is to carry out a comparative analysis of dynamic effects of interaction of various types of projectiles with targets, such as characteristics of destruction of the target, the state of the projectile behind the target, and particularities of the after-penetration stream of fragments after the target has been pierced. The projectiles are made of composites on the basis of tungsten carbide obtained by caking and the SHS-technology. To compare effectiveness of composite projectiles steel projectiles are used. Their effectiveness was estimated in terms of the ballistic limit. High density projectiles obtained by means of the SHS-technology are shown to produce results comparable in terms of the ballistic limit with high-strength projectiles that contain tungsten received by caking. [ABSTRACT FROM AUTHOR]

The paper presents a calculation-experimental study on high-speed interaction of the metal projectile with a combined barrier made of porous corundum-based ceramics filled with chemically active composition (sulfur, nitrate of potash) in the wide range of speeds. A mathematical behavior model of porous corundum-based ceramics with chemically active filler is developed within the scope of mechanics of continuous media taking into account the energy embedding from a possible chemical reaction between a projectile metal and filler at high-speed impact. Essential embedding of inlet heat is not observed in the considered range of impact speeds (2.5 ... 8 km/s). [ABSTRACT FROM AUTHOR]

Graphene is a new material of a single or multiple layer carbon structure with impressive properties. A brief introduction is initially presented. Graphene does not have a bandwidth and is a semimetal with charge carriers of zero mass. A bandgap can be formed by confining the graphene width in nanoribbon or nanoconstricition structures. For example, the induced bandgap by a 20 nm wide nanoribbon is about 50 meV. The charge carrier mass then increases, but is still very small. This material can especially be employed for various Terahertz applications. Here several examples are to be described, namely a) a THz transistor, b) the opportunities of ballistic electron resonances for THz signal generation, c) the simultaneous optical transmission and electrical conduction up to THz frequencies and d) Cascaded THz emitters. The optical advantages of multilayer graphene can be compared to ITO (Indium Tin Oxide). [ABSTRACT FROM AUTHOR]

We explore using GERBS, a blending-type spline construction, to represent deform able thin-plates and model terminal ballistics. Strategies to construct geometry for different scenarios of terminal ballistics are proposed. [ABSTRACT FROM AUTHOR]

In order to design hybrid rocket engines, we have developed a numerical prediction approach to the internal ballistics. The key point is its cost performance. Therefore simple but efficient models are required. Fluid phenomenon and thermal conduction phenomenon in a solid fuel should be treated time-dependently, because characteristic times of these phenomena are longer than those of other phenomena. Besides, they are solved with the energy-flux balance equation at the solid fuel surface to determine the regression rate. It is confirmed that numerical evaluation of time- and space-averaged regression rate is the same order of magnitude as that in experiments. However, the factors n in [formula] differ between calculations and experiments. [ABSTRACT FROM AUTHOR]

We study the density decay profile of energetic particles in the upstream region of an interplanetary shock on 14 Dec 2006 observed by the ACE spacecraft at 1 AU. The spatial decay profile of the energetic particle flux does not exhibit an exponential behavior as expected for the standard diffusive shock acceleration process but a power-law behavior in anomalous or superdiffusive transport. The power-law profiles are observed for not only the energetic ions reported in Sugiyama & Shiota (2011) but also heavier ions of He2+, CNO, and Fe. We observe the relation <Δx2> ∝ tα for α ~ 1.24-1.72, where Δx is the particle displacement within the time scale t, and the bracket denotes an ensemble average. This implies that particle propagation around a near-earth orbit can be intermediate between normal diffusion (α = 1) and ballistic motion (α equals 2). [ABSTRACT FROM AUTHOR]

In this study a number of experiments were performed by taking high-speed footage of the firing spherical steel bullets at different speeds into Perma-Gel, a new synthetic thermoplastic material touted to exhibit similar properties to ordnance ballistic gelatin. We found that the gel undergoes very large and recoverable elastic deformations, which could strongly affect the dynamics of the temporary cavity formed behind the projectile. As with ordnance ballistic gelatin, the diameter of the temporary cavity can be many times the diameter of the projectile, in contrast with that of the permanent cavity which is several times smaller. We also observed that the closure of the cavity chokes the air inside, which could affect its dynamics in noticeable ways. Finally, one of the experiments suggest that the precise model of material failure may not be important to determine the dynamics of the temporary cavity. [ABSTRACT FROM AUTHOR]

In the event of high-energy penetrator impact, people involved in battlefield scenarios are exposed to the additional hazard stemming from ultrafine metallic particles, i.e. exposure, inhalation, and respiration of aerolized metals. In order to have reliable quantitative measurement of the aerosol particles generated under controlled impact conditions, an experimental set-up was designed to perform impact tests with light gas-gun in chamber. During the impact events, aerosol particle size distributions and total concentrations were measured with a one-second time resolution. In this study preliminary results relative to high purity copper projectile impact at different velocities are presented. [ABSTRACT FROM AUTHOR]

Porous-ceramic, thermal protection systems are used heavily in current reentry vehicles like the Orbiter, and they are currently being proposed for the next generation of US manned spacecraft, Orion. These systems insulate reentry critical components of a spacecraft against the intense thermal environments of atmospheric reentry. Additionally, these materials are highly exposed to space environment hazards like solid particle impacts. This paper discusses impact studies up to 10 km/s on 8 lb/ft³ alumina-fiber-enhanced-thermal-barrier (AETB8) tiles coated with a toughened-unipiece-fibrous-insulation/reaction-cured-glass layer (TUFI/RCG). A semi-empirical, first principles impact model that describes projectile dispersion is described that provides excellent agreement with observations over a broad range of impact velocities, obliquities and projectile materials. Model extensions to look at the implications of greater than 10 GPa equation of state is also discussed. Predicted penetration probabilities for a vehicle visiting the International Space Station is 60% lower for orbital debris and 95% lower for meteoroids with this model compared to an energy scaled approach. [ABSTRACT FROM AUTHOR]

Scaled, reverse ballistic, long-rod experiments were performed at an impact velocity of ~700 m s-1. The targets were tungsten alloy rods and the projectiles either 3 or 6 mm thick rolled homogeneous armour (RHA) plates. The plate was inclined at 60° to the direction of travel and the interaction was recorded using high-speed photography, strain gauges and laser velocimetry. The pitch of the rod was varied in steps of 3° over a total range of 15°. In this range the rod deformation changed dramatically the bending process moved from a flexing of the tip away from the plate, to a marked motion into the surface. Cross comparison of the diagnostic outputs reveals the time windows for these process and also the varying sensitivity of the measurement system to that process. Post-impact recovery was also performed. [ABSTRACT FROM AUTHOR]

In this work a series of experiments were carried out in which right-circular cylinders were launched into sand targets at velocities ranging from 70 to 150 m/s. The projectiles were launched along a view window in order to record the penetration event with high-speed photography. Stress measurements of the transmitted wave forms were simultaneously collected from a piezoelectric load cells buried in the sand. A particle image velocimetry (PIV) technique, which extracted information from the photographic images, was used to resolve transmitted wave profiles. A two wave structure was observed. The first wave, a compaction wave, moves at the bulk sound speed of the sand. The second is an attached fracture wave which is stationary relative to the projectile. Together these experiments further our understanding of high-speed granular penetration events. [ABSTRACT FROM AUTHOR]

Boron Carbide (B4C) is widely used to provide ballistic protection in challenging service environments. This work was carried out to develop non-destructive testing (NDT) for B4C characterization. Deliberate flaws were introduced within the B4C tiles during manufacturing. An experimental program was undertaken to determine the best method to detect defects in ceramic tiles and material characterization. Ultrasonic characterization of the material was found to be able to detect both density variation and defects within the material. [ABSTRACT FROM AUTHOR]

This paper evaluates the ability of wave filtering techniques to identify and quantify defect variations in structures. The proposed techniques are based on the evaluation of reflection, transmission, and conversion of different Lamb wave modes in the presence of damages and of the spatial evaluation of their phases. The structure is excited by an enhanced fundamental symmetric mode, and the damage is initially located by evaluating the phase gradient of the converted Lamb mode. The process relies on mode separation and incident-wave removal procedures implemented in the frequency/wavenumber domain. Such procedures rely on the spatial integration of wave amplitudes in contrast to point-wise estimation previously proposed in the literature, as a way to reduce the effect of noise. Numerical and experimental parametric studies are conducted, where the specific damage geometry is varied to represent common external ballistic impact, from a sharp rectangular notch to a semi-circular depression. Likewise, the techniques are demonstrated on experimental data obtained from a Scanning Laser Doppler Vibrometer setup. [ABSTRACT FROM AUTHOR]

The penetration and fragmentation characteristics of spheres made of pressed aluminum powder are studied via normal impact on thin steel plates at 0.6 to 1.8 km/s. Ultra-high speed photography and flash x-rays are used to monitor the formation and evolution of the debris cloud formed by impact. The mass distribution of debris fragments is measured directly via a soft-catch experiment. Experimental results are compared to simple analytic theories of brittle fragmentation and spall. This data aids in understanding the mechanical properties and potential energy release of porous reactive materials. [ABSTRACT FROM AUTHOR]

Digital Speckle Radiography (DSR) is a technique allowing full field displacement maps in a plan within an opaque material to be determined. The displacements are determined by tracking the motions of small sub-sections of a deforming speckle pattern, produced by seeding an internal layer of lead and taking flash x-ray images. An improved DSR algorithm is discussed which can improve the often poor contrast in DSR images, such that the mean and variance of the speckle pattern is uniform. This considerably improves the correlation success relative to other similar algorithms for DSR experiments. A series of experiments involving the penetration of granular media by long-rod projectiles, and the improved correlation achieved using this new algorithm, are discussed. [ABSTRACT FROM AUTHOR]

Digital Speckle Radiography (DSR), a technique allowing measurement of the full field displacement maps in a plane within an opaque material, is used to follow the temporal progression of a long-rod (100 mm long, 10 mm diameter) penetrating a granular sample at a variety of rates. Quasi-static rates of 1.5 mm/min are achieved using an Instron machine, 5 m/s is achieved using a drop-weight and velocities between 10 and 200 m/s are achieved using a light gas gun. These experiments are carried out using a series of time delayed flash x-ray images analysed with an optimised Digital Image Cross Correlation algorithm (DICC). The subsequent data sheds considerable light on the response of granular materials to penetration at a variety of rates. Particularly, a large difference in the response of the material between quasi-static and dynamic rates is observed. [ABSTRACT FROM AUTHOR]

Tungsten projectiles were shot into sand at velocities between 600 and 2200 m/s. Penetration was maximum at about 775 m/s. Below that velocity, projectiles were apparently stabilized by a fin set. Above that velocity, projectiles were broken by transverse loads. High-speed penetration resulted in comminution of sand particles, reducing their size by about 1000 times. [ABSTRACT FROM AUTHOR]

The Johnson-Holmquist ceramic material model has been calibrated and successfully applied to numerically simulate ballistic events using the Lagrangian code EPIC. While the majority of the constants are “physics” based, two of the constants for the failed material response are calibrated using ballistic experiments conducted on a confined cylindrical ceramic target. The maximum strength of the failed ceramic is calibrated by matching the penetration velocity. The second refers to the equivalent plastic strain at failure under constant pressure and is calibrated using the dwell time. Use of these two constants in the CTH Eulerian hydrocode does not predict the ballistic response. This difference may be due to the phenomenological nature of the model and the different numerical schemes used by the codes. This paper determines the aforementioned material constants for SiC suitable for simulating ballistic events using CTH. [ABSTRACT FROM AUTHOR]

The impact behaviour of composites is of great importance in the field of aerospace and vehicle protection. The combination of formability, lightness and strength make composite systems attractive compared to equivalent monolithic systems. However, their use as optical components has been hampered by their lack of transparency. Transparency is strongly affected by refractive index differences in the materials that form the composite. In this study a number of ribbon-based composites were produced. The impact velocity, sample deformation during the impact process and residual impactor velocity were measured. This allowed comparison between the materials ballistic efficiency. The materials are then compared to other transparent systems. [ABSTRACT FROM AUTHOR]

Strength of glass and glass ceramic was measured with a bar impact technique. High-speed movies show regions of tensile and compressive failure. The borosilicate glass had a compressive strength of at least 2.2 GPa, and the glass ceramic at least 4 GPa. However, the BSG was much stronger in tension than GC. In ballistic tests, the BSG was the superior armor. [ABSTRACT FROM AUTHOR]

When a projectile approaches the back surface of a target, complicated mechanics and different failure modes ensue that can lead to perforation. There have been a number of attempts to model these different failure modes, for example models due to Ravid and Bodner [1] and Walker [2]. Of particular interest are analytic models (as opposed to hydrocode models) where the model attempts to explicitly identify relevant failure modes and back surface breakout modes. This paper examines back surface breakout and target failure models with different failure modes to see how they are invoked in specific impact geometries and scenarios. Comparisons are made of thresholds and sensitivities for the different failure modes to gain a greater understanding of their usefulness and applicability. The model results are compared to data to ensure reasonableness of the computations. Good agreement is shown with a relatively simple back-surface-strain target failure mode for predicting ballistic limit velocity for large aspect-ratio projectiles and relatively thick targets as compared to the projectile diameter. [ABSTRACT FROM AUTHOR]

High-velocity impact onto a layered glass target produces a very extensive damage pattern exhibiting many distinct morphologies. High-speed photography reveals failure waves and cracks that move at acoustic velocities. These prompt features evolve into a complex final damage pattern that includes needle fragments around the penetration cavity, radial cracks at mid distance, and dicing cracks near the edges. [ABSTRACT FROM AUTHOR]

Analysis of experimental data using theoretical models reveals that a very small portion of a shaped charge jet particle’s kinetic energy shocking the air in front of it can couple convectively into the particle’s leading surface to soften an already hot material enough to justify hydrodynamic modeling of the air cratering process. [ABSTRACT FROM AUTHOR]

One can understand what velocimetry does and does not measure by understanding a few fundamental experiments. Photon Doppler Velocimetry (PDV) is an interferometer that will produce fringe shifts when the length of one of the legs changes, so we might expect the fringes to change whenever the distance from the probe to the target changes. However, by making PDV measurements of tilted moving surfaces, we have shown that fringe shifts from diffuse surfaces are actually measured only from the changes caused by the component of velocity along the beam. This is an important simplification in the interpretation of PDV results, arising because surface roughness randomizes the scattered phases. [ABSTRACT FROM AUTHOR]

The performance of behaviour of brittle materials depends upon discrete deformation mechanisms operating during the loading process. The critical mechanisms determining the behaviour of armour ceramics have not been isolated using traditional ballistics. It has recently become possible to measure strength histories in materials under shock. The data gained for the failed strength of the armour are shown to relate directly to the penetration measured into tiles. Further the material can be loaded and recovered for post-mortem examination. Failure is by micro-fracture that is a function of the defects and then cracking activated by plasticity mechanisms within the grains and failure at grain boundaries in the amorphous intergranular phase. Thus it is the shock-induced plastic yielding of grains at the impact face that determines the later time penetration through the tile. [ABSTRACT FROM AUTHOR]

We use the technique of Stimulated Raman adiabatic passage (STIRAP) to affect transport of ultracold atoms between two optical lattices in relative motion. We show, using Floquet analysis and degenerate perturbation theory, that the dynamics of atoms in a particular time-dependent optical lattice system can be reduced to the 3-level STIRAP model, allowing for a simple description of their coherent acceleration. [ABSTRACT FROM AUTHOR]

An analytical model of normal ballistic impact on the ceramic/metal gradient armor, which is based on modified Alekseevskii-Tate equations, has been developed. The process of gradient armour impacted by the long rod can be divided into four stages in this model. First stage is projectile's mass erosion or flowing phase, mushrooming phase and rigid phase; second one is the formation of comminuted ceramic conoid; third one is the penetration of gradient layer and last one is the penetration of metal back-up plate. The equations of third stage have been advanced by assuming the behavior of gradient layer as rigid-plastic and considering the effect of strain rate on the dynamic yield strength. [ABSTRACT FROM AUTHOR]

The failure characterization of brittle materials like glass is of fundamental importance in describing the penetration resistance against projectiles. A critical question is whether this failure front remains “steady” after the driving stress is removed. A test series with short gold rods (D = 1 mm, L/D≈5–11) impacting borosilicate glass at ∼1 to 2 km/s was carried out to investigate this question. The reverse ballistic method was used for the experiments, and the impact and penetration process was observed simultaneously with five flash X-rays and a 16-frame high-speed optical camera. Very high measurement accuracy was established to ensure reliable results. Results show that the failure front induced by rod impact and penetration does arrest (ceases to propagate) after the rod is totally eroded inside the glass. The impact of a second rod after a short time delay reinitiates the failure front at about the same speed. [ABSTRACT FROM AUTHOR]

Accurate predictions of non-eroding penetration are becoming a problem of increasing technological importance. Sandia's Zapotec (a coupling of Pronto3D and CTH) has been the code of choice for design purposes, but there have been some concerns expressed about relying on a single code methodology. Consequently, LLNL's ALE3D (which uses a slide line based approach) is currently being investigated for applicability. As a benchmark, we choose to model the penetration experiments of steel projectiles against aluminum targets to examine the differences between the two methodologies. [ABSTRACT FROM AUTHOR]

Constitutive models for brittle materials such as glass can be very complex as they are dependent on strains, strain rates, pressures, temperatures, damage and other parameters. There may also be significant (pressure-dependent) strength after failure such that the constitutive response is much different for intact material and failed material. A large number of laboratory tests is required to develop a comprehensive constitutive model. Another approach is to develop simple models by using penetration-velocity data obtained from ballistic experiments. Here various functional forms of simple models (with a limited number of constants) can be used to (computationally) match the penetration velocity over a range of impact velocities. This allows for the determination of the most important parameters and it provides an approximation of the stresses that occur during penetration. This article presents several simple computational models for borosilicate glass, including single-state models and dual-state models (that include an intact strength and a failed strength). [ABSTRACT FROM AUTHOR]

A phenomonological elastic-viscoplastic constitutive model is developed that accounts for variations in initial grain morphology and for changes to grain morphology under load. [ABSTRACT FROM AUTHOR]

Structurally weak materials are attractive for explosive blast and fragment mitigation applications because they break up easily into small particles and do not present secondary fragment hazards. Several materials have been investigated under a mitigation research programme aimed at developing a predictive capability. Experiments with 2.5 kg–20 kg charges confirmed earlier small scale results that porosity and particle density are dominant factors in reducing blast. Measurement of incident overpressure however, effectively ignores the momentum acquired by the mitigant which has the potential to cause significant damage. Techniques to measure dynamic particle loading have been investigated and initial results are presented. Fragment mitigation has been studied with and without the presence of explosive blast. Indications are that for some materials, shock loading from the blast may change the fragment retarding performance, but for practical purposes the effect is not significant. It has also been shown that small quantities of a low-density mitigant can significantly influence the effectiveness of ballistic protection materials placed close to an explosive. [ABSTRACT FROM AUTHOR]