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The analysis was performed on six commonly used 5.56 x 45 mm projectile types (M193, M855, M855A1, L31A1, M995, and AP45). The projectile's impact velocity (chosen as 900 m/s) was the same in the examination process. This made it possible to assess how the projectile's design has affected its performance against a hard steel target. These evaluations included numerical simulations (Ansys Autodyn) of projectile impacts. Using the available experimental data, the materials in the computational model were first validated. A short description and CAD model of projectiles is also given. Relevant conclusions were reported. [ABSTRACT FROM AUTHOR]

In contrast to cranial gunshot trauma, diagnosis and interpretation of gunshot trauma to long bones remains difficult and controversial. The aim of this study is to review the published literature on fracture patterns resulting from gunshot trauma in human long bones, and to use the described characteristics to provide practical guidance for the forensic anthropologist. In order to achieve this, medical and forensic publications on this topic were reviewed. Several types of fractures, such as linear, oblique, comminuted and butterfly fractures, have been observed in either the shaft or the ends of long bones. Indirect fractures that are not caused by bullets striking bone directly but by bullet-induced forces to the surrounding soft tissue have been found as well. Some of these fractures are related to a specific context or mechanism which might help in the forensic reconstruction of events. It is recommended that future research should focus on available medical data to provide more detailed descriptions on fracture patterns for forensic purposes. Experimentation with bone surrogates and computer modelling might also provide better and more realistic reconstructions of gunshot trauma in the future and provide valuable insights for its diagnosis and interpretation in forensic anthropology. [ABSTRACT FROM AUTHOR]

Due to the complexity of impact-induced reaction, it is difficult to predict and evaluate the ignition and safety of explosives under low velocity impact. Plastic deformation is very important to explosive ignition under impact loading. At low strain rates, plastic deformation can be treated as an isothermal process. The deformation under high-strain-rate is usually seen as an adiabatic process, and the deformation work is transformed into heat with the attendant temperature increase of the explosive. In this paper, we proposed an ignition criterion in terms of effective plastic work and specific plastic power to predict the ignition of explosives under low velocity impact. The plastic work begins to accumulate, when the specific plastic power (i.e., the plastic strain rate) in a local region meets a threshold value; and when the plastic work is sufficient enough, the ignition occurs. The criterion parameters are determined by numerical simulation using LS-DYNA. Numerical simulation is compared with experimental data in order to calibrate the numerical model. The threshold values of this ignition criterion for different configurations are determined. In order to evaluate the validity of the criterion, the predictions of the ignition time, ignition zone, threshold velocities in Steven test with different PBX size designs and various projectiles, as well as the ignition threshold conditions in a modified drop weight test, Susan test, and Spigot test, are carried out. The predicted results show a good agreement with experimental results, and the errors of the ignition threshold are less than 15% for all the experimental configurations. [ABSTRACT FROM AUTHOR]

Highlights • Ballistic impact tests on 4 mm thick Weldox 700 E steel plates struck by blunt rigid projectiles were conducted and a failure mode of shear plugging was identified in the tests. • The strength and fracture models of the steel were calibrated using a hybrid experimental-numerical method. • FE simulations were carried out by using either a modified version of the Johnson-Cook (MJC) fracture criterion or the Lode dependent Modified Mohr–Coulomb (MMC) fracture criterion. • FE simulations using the MJC and MMC fracture criteria predicted almost the same ballistic performance of the targets. • For targets of Lode dependent fracture, FE simulations showed that the Lode dependent fracture criterion would predict a much lower ballistic limit for less ductile targets. However, for targets with high ductility, introducing the Lode angle into the fracture criterion would not obviously alter the ballistic limit prediction. Abstract The necessity of incorporating the Lode angle into a fracture criterion in predicting ballistic resistance of ductile metal plates has not been well elucidated so far although the ductility of a metal may be Lode dependent. In this paper, 4.0 mm thick Weldox 700 E steel plates were fired by 5.95 mm diameter blunt rigid projectiles in a one-stage gas gun in the impact velocity range of 141.2 m/s∼275.7 m/s. A failure mode of shear plugging was observed in the test and the ballistic limit was obtained by fitting the initial-residual velocity data. An axisymmetric finite element (FE) model corresponding to the test was built in ABAQUS and then was utilized to predict the ballistic resistance and fracture behavior of the targets. In the FE model, a slightly modified Johnson-Cook constitutive relation was companied by either a Lode independent modified Johnson-Cook (MJC) or the Lode dependent modified Mohr–Coulomb (MMC) fracture criterion. The plasticity and fracture of the metal were fully calibrated by a series of mechanical tests under varying stress states, strain rates and temperatures. According to the tests and parallel FE simulations, it was found that the fracture of Weldox 700 E is obviously Lode dependent. However, ballistic simulations using the MMC and MJC fracture criterion predicted very close ballistic limit velocity and similar shear plugging failure mode when compared with the test results. The dominant stress state of the material failed in the process of shear plugging was revealed by detailed FE analysis and it was found that the ductility of the metal is quite different on the dominant stress state according to the two fracture criteria. To interpret the current simulation results, further FE simulations were carried out on fictitious metals and it was found that for less ductile metallic plates the MMC fracture criterion predicts a much lower ballistic limit velocity (as much as 22%) when compared with the simulation result from the MJC fracture criterion. In contrast, for metal plates with high ductility, the simulations from the two different fracture criteria would produce quite close ballistic limit velocity predictions. [ABSTRACT FROM AUTHOR]

The viability of numerical simulations to design a solid propellant rocket motor, as opposed to static testing, is discussed in this paper. The results demonstrate that an objectively more detailed insight into the processes taking place within the motor in active combustion can be gained by employing computer simulations. The abundance of readily available computing power allows complex simulations to be run on personal desktop computers, thus, saving money by eliminating the need for static testing during the design phase of the motor. The computer simulation results are validated by a comparison with test data gathered during static tests on the motor. In this study, an RM-12K solid propellant rocket motor is designed and developed, which is currently used in real-world air defence training applications, and therefore, sufficient empirical data are available. The numerical method, based on computer simulations using personal computers, is sufficiently accurate to allow for motor design decisions and an adequate substitute for static testing. Even though a single simulation can take up to 715 h on an 8-core personal machine, it is still an effective solution. [ABSTRACT FROM AUTHOR]

The insufficient recognition of injuries by the BB-gun (regarded as toys for children) has led to its increasing misuse without permission, which has caused many public safety issues. Aiming to enhance the understanding of the injuries by the BB-gun, the experimental and numerical study of BB-Gun pellet penetrating "cowhide + gelatine" composite target was comprehensively carried out. It was confirmed from the experiment that BB-Gun is capable of inflicting severe or fatal wounds to important organs, and perforating the skin or not could be employed to evaluate the safety of BB-guns. Moreover, three forms of ballistic limit (including: velocity, kinetic energy and specific kinetic energy) of typical BB were calculated and analyzed by reasonably validated numerical simulation method. Additionally, a formulation was acquired by dimensional analysis based on the simulation results and was verified to accurately predict the ballistic limit velocity of BB with different mechanical properties. The method may help to improve the understanding on the minimal velocity needed to perforate skin and may be advised as the determination of the safety of BB-gun. [ABSTRACT FROM AUTHOR]

A description of a pistol (rifle) cartridge often involves two ballistic coefficients that characterize its ballistic qualities with respect to various air resistance laws (ARLs). How close are the obtained ballistic trajectories with varied ARL specifications and what are the differences between them? How to evaluate ballistics if the ARLs are to be expressed in various mathematical forms? In this paper, the evaluation of external ballistics trajectories is given for two ARLs (the law brought in 1943 and the Siacci law). All the obtained results relate to the TT pistol with 7.62 × 25mm Tokarev cartridge.The paper also presents the answer to the question: how to calculate the ballistic trajectory if the ARL is expressed as a rational function, piecewise function or spline. For the 1943 ARL, a graphical interpretation of the function Cd (i, v) in the form of a surface is shown. This paper shows that, due to the selection of ballistic coefficients, it is possible to obtain sufficiently similar form of ballistic trajectories. A method of graphical comparison of external ballistic parameters is presented as well as the mathematical tools for quantitative analysis of a shape of ballistic curves.The difference between the two trajectories is proposed to be estimated using a relative error in regard to а selected ballistic parameter. Computer simulation considered for the 1943 and Siacci ARLs for the 7.62×25mm Tokarev cartridge indicates that the profiles of the function of instantaneous projectile velocity vs time of flight (TOF) had the greatest non-coincidence in relation to other ballistic parameters (e.g. horizontal range, height of the trajectory, etc.) The obtained maximum of the relative error was 0.8%. Its magnitude localizes at the point of impact. [ABSTRACT FROM AUTHOR]

The paper presents mathematical modeling and computer simulation (MM&CS) in the area of numerical solving of the basic problem of external ballistics for tubed artillery. Five-stage MM&CS scheme for conducting a ballistic simulation is developed. It is shown that a formal mathematical procedure allowing to solve the basic problem of external ballistics is a numerical solution of the Cauchy problem for a system of ballistic differential equations. The trajectory of a projectile flight for the 57-mm ZIS-2 anti-tank cannon is estimated. A solving algorithm and the Mathcad program code are given.The numerical solution for a system of four first order ballistic differential equations is a five-dimensional space.The possibility of visual presentation for a numerical solution was proposed in the form of a square matrix. The boundaries of each subspace are determined. A procedure based on spline functions is developed for checking the correctness of the numerical solution. As a result of such verification, the effects of a light increase in the error at the edges of the integration interval are observed. A comparison of the numerical solution of the basic ballistics problem is conducted by means of “soft“ and “stiff“ solver-functions.The trajectory parameters estimated by “soft“ and “stiff“ methods are the same up to the fifth decimal place. [ABSTRACT FROM AUTHOR]

In this paper, the effect of soft-hard plate and rubber thickness as absorbent impact against on ballistic resistance with 5.56 x 45 mm caliber deformable projectile is investigated. The characteristic of ballistic impact for each configuration target is obtained and compared based on the investigation of the hardness effect of the front plate and the thickness of rubber. The experimental results approached by simulation with finite element method were used to know several characters due to the ballistic impact. The experiment and simulation results showed that the projectile is able to perforate front plate and the impact on the back plate form a bulge on every configuration. The configuration of hard plate as front plate reveals minimum ballistic impact due to the projectile rate. The simulation shows that the maximum stress concentration occurs only on the front plate, so the front plate fails. [ABSTRACT FROM AUTHOR]

Although many aspects of the fracturing process of concrete are now well understood and successfully simulated with various models, it is still very difficult to properly simulate the different failure mechanisms observed in a concrete structure induced by ballistic impact. In this paper, an enhanced version of the effective-rate-dependent nonlocal damage model [Eng. Fracture Mechanics, 176 (2017)] is proposed to simulate the response of concrete in such events. Hydrostatic damage has been added to the formulation in order to take the damage of the material matrix observed while porosity reduces during compaction into account. Besides controlling the evolution of the nonlinear volumetric response of the material, this new damage variable contributes to the deterioration of the material stiffness upon confinement. It is demonstrated that the description of the nonlinear volumetric response of concrete by an equation of state (EOS) as a plasticity phenomenon, as it is commonly done in hydrodynamic constitutive modeling, is unrealistic for concrete. Such formulations fail to represent the effect of the loss of cohesion observed during compaction on the deviatoric response of the material. By taking this phenomenon into consideration, the proposed model systematically predicts the relevant failure modes (cratering, tunneling, radial cracking and spalling) observed during ballistic impact on a concrete plate as a function of the projectile velocity and plate thickness. [ABSTRACT FROM AUTHOR]

Mechanisms of projectile defeat and ballistic resistance of thin targets impacted by tip-deformable conical projectiles have been discussed in the context of the influence of apex angle of the projectile. Transition in target local failure modes occurred as the projectile apex angle was altered. The effect on projectile deformation and ballistic properties has also been discussed. A brief discussion on projectile deformation mechanism and projectile defeat near ballistic limit velocities with supporting experimental evidence is included. Numerical simulation using ABAQUS/Explicit has been able to effectively predict the projectile deformation and associated target behavior. [ABSTRACT FROM AUTHOR]

Knitted fabrics are constructed from interlocking loops of yarn. Curvature in the yarn provides stretchability, making them well suited for garments that will cover areas of the body that require large relative motion. Although most current soft armors are composed of woven textiles, knitted fabrics made of aramid fibers such as Kevlar may have application for use in soft armor to provide a larger range of motion in addition to protection. However, their ballistic performance has not been well characterized. The goal of this work is to develop a computational framework to simulate a single jersey knit under ballistic loading. The path and shape of the yarn in the knit fabric is defined with parametric equations calibrated to CT images of a sample fabric. Results of finite element simulations demonstrate the unique mechanical response of knit soft armor, and show qualitative agreement with ballistic experiments. [ABSTRACT FROM AUTHOR]

Ballistics is the study of a projectiles motion and can be broken down into four stages: internal, intermediate, external and terminal ballistics. The study of the effects a projectile has on a living tissue is referred to as wound ballistics and falls within terminal ballistics. To understand the effects a projectile has on living tissues the mechanisms of wounding need to be understood. These include the permanent and temporary cavities, energy, yawing, tumbling and fragmenting. Much ballistics research has been conducted including using cadavers, animal models and simulants such as ballistics ordnance gelatine. Further research is being conducted into developing anatomical, 3D, experimental and computational models. However, these models need to accurately represent the human body and its heterogeneous nature which involves understanding the biomechanical properties of the different tissues and organs. Further research is needed to accurately represent the human tissues with simulants and is slowly being conducted. [ABSTRACT FROM AUTHOR]

The paper deals with a possibility of the local repairing of damaged composite armours. The proposed repairs can be performed directly in the field, allowing thus to recover the full ballistic protection in a short time. Several solutions (temporary or permanent) were designed and tested both experimentally and using numerical simulations. Overlapping of the damaged area with patch from armour steel after filling the hole with ceramic balls showed to be optimal as a temporary repair. The calculation clearly showed that the depth of penetration of the projectile is reduced in all cases of designed permanent repairs in comparison to original armour configuration. The experiments confirmed supposed enhancing of ballistic resistance, but only some repair techniques met the requirements of multi-hit testing. However, the reason of failure after multi-hit could be clearly explained with the help of used numerical simulations. [ABSTRACT FROM AUTHOR]

The teleost fish scales, such as Grass Carp and Cyprinoid, characterize hierarchical structure which usually consists of a hard bony outer layer and a soft inner cross-ply of collagen fibrils. Each scale overlaps with other neighboring scales, thus fish skin can effectively disperse external loadings with superior flexibility. Inspired by the two-layer structure and overlapping pattern of fish scales, bio-inspired composite scale, and scale-like protection system are designed in this study. Silicon carbide (SiC) ceramic and aluminum are selected as the outer and inner layers of the bio-inspired composite scale, respectively. In this study, the optimal thickness ratio of SiC/Al is chosen as 3:2 through numerical simulation on penetration test and residual velocity analysis of bio-inspired composite scale with LS-DYNA. Compared with pure SiC scales, the area density of bio-inspired composite scale can be reduced by 12.5% with the same ballistic performance at the impact velocity of 878 m/s. Further, a comparative simulation analysis among different overlapping ratios of scale-like protection systems, which consists of overlapped bio-inspired composite scales, is conducted and an optimal overlapping ratio of 0.40 is found. The present numerical study on scale-like protection system enables pathways to design a lightweight and flexible protective system. [ABSTRACT FROM AUTHOR]

The 2014 Mount Ontake eruption started just before noon on September 27, 2014. It killed 58 people, and five are still missing (as of January 1, 2016). The casualties were mainly caused by the impact of ballistic blocks around the summit area. It is necessary to know the magnitude of the block velocity and energy to construct a hazard map of ballistic projectiles and design effective shelters and mountain huts. The ejection velocities of the ballistic projectiles were estimated by comparing the observed distribution of the ballistic impact craters on the ground with simulated distributions of landing positions under various sets of conditions. A three-dimensional numerical multiparticle ballistic model adapted to account for topographic effect was used to estimate the ejection angles. From these simulations, we have obtained an ejection angle of γ = 20° from vertical to horizontal and α = 20° from north to east. With these ejection angle conditions, the ejection speed was estimated to be between 145 and 185 m/s for a previously obtained range of drag coefficients of 0.62-1.01. The order of magnitude of the mean landing energy obtained using our numerical simulation was 10 J. [ABSTRACT FROM AUTHOR]

The subject of the paper is a description of a simple test from the field of terminal ballistics and the handling of issues arising during its simulation using the numerical techniques of the finite element method. With regard to the possible excessive reshaping of the finite element mesh there is a danger that problems will arise such as the locking of elements or the appearance of negative volumes. It is often necessary to introduce numerical extensions so that the simulations can be carried out at all. When examining local damage to structures, such as the penetration of the outer shell or its perforation, it is almost essential to introduce the numerical erosion of elements into the simulations. However, when using numerical erosion, the dissipation of matter and energy from the computational model occurs in the mathematical background to the calculation. It is a phenomenon which can reveal itself in the final result when a discrepancy appears between the simulations and the experiments. This issue can be solved by transforming the eroded elements into smoothed particle hydrodynamics particles. These newly created particles can then assume the characteristics of the original elements and preserve the matter and energy of the numerical model. [ABSTRACT FROM AUTHOR]

The ballistic impact response of thermoplastic-based composite armors made from Kevlar ® fabric and polypropylene (PP) matrix has been investigated against ballistic test standard NIJ-STD 0106.01 Type IIIA. Kevlar ® fabrics of different architectures, namely 2D plain woven, 3D orthogonal and 3D angle interlock fabrics, were produced and used as reinforcements to fabricate composite armor panels, using compression molding technology. Interfacial property between PP and Kevlar ® was improved by adding a coupling agent called maleic anhydride grafted PP. Reduced density was observed in Kevlar ® thermoplastic-based composites as compared to that of the thermoset-based laminates. Ballistic impact tests were imparted with 9 mm full metal jacket (FMJ) on armor panels having different fabric architecture. Ballistic test results revealed that 2D armor was 2.4–7% more susceptible to damage than 3D armors. Hydrocode simulations were carried out using ANSYS AUTODYN v. 14.0 to obtain an estimate for the ballistic limit velocity and simulate failure modes. Post-impact damage patterns obtained from the simulations were compared with the experimental results to assess the performance of the simulations. Good correlation between the hydrocode simulations and experiments was found, both in terms of failure modes and damage patterns. 3D composite armors were able to confront the 9 mm FMJ projectile; however, the 2D plain woven armors failed. The increase in the ballistic limit from 2D plain woven armor to 3D orthogonal and 3D angle interlock armors was 16.44% and 20%, respectively, indicating the effect of fabric architecture. [ABSTRACT FROM AUTHOR]

We present an efficient event-driven algorithm for sequential ballistic deposition of complex-shaped rigid particles. Each of the particles is constructed from hard spheres (typically 5 … 1000 ) of variable radii. The sizes and relative positions of the spheres may mutually overlap and can be chosen such that the surface of the resulting particle appears relatively smooth. In the sequential deposition process, by performing steps of rolling and linear motion, the particles move along the steepest descent in a landscape formed by the boundaries and previously deposited particles. The computer time for the simulation of a deposition process depends on the total number of spheres but only weakly on the sizes and shapes of the particles. The proposed algorithm generalizes the Visscher–Bolsterli algorithm [1] which is frequently used for packing of spheres, to non-spherical particles. The proposed event-driven algorithm allows simulations of multi-million particle systems using desktop computers. [ABSTRACT FROM AUTHOR]

In this study, the penetration behaviour of a Mild Steel Cored (MSC) round, 7.62 mm in diameter and 39 mm in length, commonly known as the AK47 round, was studied since it still forms an important part of the threat spectrum for personnel body armour systems. Likewise, boron carbide strike face materials were selected since this armour material is often the material of choice for ultralightweight body armour systems for protection against this particular threat. The presence of two, relatively soft, intermediate materials (the copper jacket and filler material of the bullet, and a fibre-reinforced polymer cladding layer on the ceramic) between the mild steel core and the boron carbide target was examined using reverse ballistics techniques, flash x-radiography and round recovery measurements. This was supported by selective numerical simulations using the computer code ANSYS-AUTODYN. It was found that stripping of the jacket, from the AK47 MSC rounds, makes a difference to its penetrating ability: the mild steel core is significantly reduced in length, and mass, when the jacket is not present. The magnitude of this effect is much greater than previously reported for high-strength steel-cored rounds and for tungsten carbide-cored rounds. The penetration event appears to be a twostage process: mushrooming of the mild steel core on, or near, the surface of the ceramic, followed by a linear erosion process as the core penetrates the ceramic itself. The second step has not been reported previously for MSC rounds. [ABSTRACT FROM AUTHOR]

Hypervelocity impact dynamics is the theoretical support of spacecraft shielding against space debris. The numerical simulation has become an important approach for obtaining the ballistic limits of the spacecraft shields. Currently, the most widely used algorithm for hypervelocity impact is the smoothed particle hydrodynamics (SPH). Although the finite element method (FEM) is widely used in fracture mechanics and low-velocity impacts, the standard FEM can hardly simulate the debris cloud generated by hypervelocity impact. This paper presents a successful application of the node-separation technique for hypervelocity impact debris cloud simulation. The node-separation technique assigns individual/coincident nodes for the adjacent elements, and it applies constraints to the coincident node sets in the modeling step. In the explicit iteration, the cracks are generated by releasing the constrained node sets that meet the fracture criterion. Additionally, the distorted elements are identified from two aspects – self-piercing and phase change – and are deleted so that the constitutive computation can continue. FEM with the node-separation technique is used for thin-wall hypervelocity impact simulations. The internal structures of the debris cloud in the simulation output are compared with that in the test X-ray graphs under different material fracture criteria. It shows that the pressure criterion is more appropriate for hypervelocity impact. The internal structures of the debris cloud are also simulated and compared under different thickness-to-diameter ratios ( t / D ). The simulation outputs show the same spall pattern with the tests. Finally, the triple-plate impact case is simulated with node-separation FEM. [ABSTRACT FROM AUTHOR]

The work is focused to study the mathematical modeling and numerical simulation of solid propellant combustion during internal ballistics cycle. Here, we have used a reduced single phase model from Baer–Nunziato two-phase flow model for gas and solid mixture of propellant. The model consists of balance equations of mass, momentum and energy with constitutive laws. First ORder CEntred (FORCE) scheme is employed to provide an insight of motion of pressure wave in gun chamber during burning of igniter and solid propellant. The study is performed with the constant emission rate of igniter gases. The burning rate of propellant is expressed as a non-linear function of pressure in terms of pressure exponent. Depending on the pressure exponent three cases are evolved: constant, linear and non-linear rate of burning of propellant. FORCE scheme captures the motion of pressure wave with time and space. The local phenomena of pressure, temperature, velocity, density and rate of burning are demonstrated from breech end to the base of the projectile at different time. The effect of discontinuous pressure on burning dimensions of grain are examined. The non-uniform burning of grain dimensions may result into grain fracture. This study helps in designing the system to avoid such situations. [ABSTRACT FROM AUTHOR]

Nanostructured (NS) metals with bimodal grain size distribution, composed of coarse grained (CG) and nanograined (NG)/ultrafine-grained (UFG) regions, not only have high strength and good ductility, but they can also provide excellent ballistic performance. In this work we use numerical simulations to study the influence of microstructural attributes such as the distribution and shape of the CG inclusions on the ballistic performance of bimodal NS Cu. Our formulation is based on the mechanism-based strain gradient plasticity theory and the Johnson–Cook failure model. We also consider the effects of constitutive and failure parameters of the NG phase as well as boundary constraint of the specimen. Our results on the effect of inclusion attributes indicate that microstructures can significantly affect the velocity history of the bullet as well as limit velocity and maximum displacement of the specimen. The analysis also suggests that, to improve the ballistic performance of the bimodal NS metal, the CG inclusions need to have regular distribution and, under the condition of same distribution, they also need to have a longer projection perpendicular to the direction of impact. The simulations show that when the abrasion effect is not considered, the ballistic performance of the microstructures depend heavily on their ductility rather than their strength. The results on the boundary constraint show that when this constraint is released, the ballistic performance is reduced tremendously. It is believed that these results could provide useful insights into the development of advanced NS materials for ballistic protection. [ABSTRACT FROM AUTHOR]

Impact loading is an important process in the transport industry as it causes wear and failure of critical components. Conveyor belts are of particular importance as they are used in practically every industry where large quantities of goods are moved over short (<10 m) or long distances (>1 km). To investigate stress levels inside the material during impact loading, a gas gun was utilized to shoot 9 mm spherical steel balls onto the surface of a rubber conveyor belt. A high speed video recording system was employed in order to determine penetration depth and dissipated energy of the steel ball. Maximal penetration depths of up to 3.9 mm and maximal dissipated energies of up to 86.8 % were measured. Additionally, a numerical simulation using smooth particle applied mechanics was conducted and compared to the experimental results obtained with the gas gun. The calculated von Mises stresses affected the conveyor belts up to a maximum depth of 8.8 mm with at least 20 MPa. Maximum von Mises stresses were calculated to reach 60 MPa. [ABSTRACT FROM AUTHOR]

The ballistic performance of thin aluminium targets and influence thereon of different circumferential fixity conditions were studied both experimentally and by finite element simulations. A pressure gun was employed to carry out the experiments while the numerical simulations were performed on ABAQUS/Explicit finite element code using Johnson–Cook elasto-viscoplastic material model. 1 mm thick 1100-H12 aluminium plates of free span diameter 255 mm were normally impacted by 19 mm diameter ogive and blunt nosed projectiles. The boundary conditions of the plate were varied by varying the region of fixity along its circumference as 100%, 75%, 50% and 25% in experiments and the numerical simulations. Further, simulations were carried out to compare the response of the plates with 50% and 75% continuous fixity with those with two and three symmetrical intermittent regions of 25% fixity respectively. The variation in the boundary condition has been found to have insignificant influence on the failure mode of the target however; it significantly affected the mechanics of target deformation and its energy absorption capacity. The ballistic limit increased with decrease in the region of fixity. It decreased for intermittent fixity in comparison with equivalent continuous fixity. And, it has been found to be higher for the impact with projectile having blunt nose in comparison with the one having ogive nose. [ABSTRACT FROM AUTHOR]

This study aims to investigate the penetration of a projectile into a surrogate human tissue numerically, using Finite Element (FE) simulation. 20% Balistic Gelatin material (BG) is simulated with an elasto-plastic hydrodynamic constitutive law, and then impacted by steel spheres at different velocities. The results from the FE simulations are compared with existing experimental data and other analytical equations from the literature. To our knowledge, this is the first study to investigate a projectile penetration by numerical simulation, and then compare the results with analytical and experimental data from previous studies. This developed model gives encouraging results for further investigations of penetrating impact of projectile in the human body. [ABSTRACT FROM AUTHOR]

Studies of ballistic penetration into metal plates and their numerical simulation currently play a vital role in the defence sector. However, no congruent results have been presented so far, especially when it comes to impact on welded plates. Furthermore, these issues are investigated for normal impacts and very few have made an attempt for oblique impacts. Thus the aim of the present work is to conduct numerical simulation using Abaqus/Explicit in order to evaluate the ballistic performance of similar and dissimilar welded plates subjected to various bullet velocities and impact angles. The effect of post weld residual stresses and associated plastic damage on the ballistic performance of similar (Al6061) and dissimilar (Al 6061- SS 304) welded plates is also determined. The energy absorbed by the welded plates for various configurations was determined and the results are critically evaluated. [ABSTRACT FROM AUTHOR]

Abstract: Experimental, analytical and numerical simulations were performed to study the ballistic resistance of 6061-T6 aluminium plates subjected to a normal impact of small calibre armour piercing bullets. Two types of bullets were used, steel and tungsten carbide core bullets. Three plate thicknesses, 101.6 mm, 76.2 mm and 25 mm, were considered. Bullets were impacted at ordnance velocity thus results range from deep penetration to complete perforation with residual velocity. Ballistic results, deformations of the plates and of the bullets are discussed and reproduced through numerical simulations using both LS-DYNA and ABAQUS solvers; analytical models by means of a cavity expansion approach are also used. Exploiting analytical and numerical models the ballistic behaviour of the two bullets on the three plates is discussed with emphasis on the capability of the models to reproduce the physical features of the phenomena. X-ray diffraction measurements for the residual stress patterns of the plate's surface were also performed on all of the plates both before and after the tests and the experimental measurements are compared with the numerical model results. A specific discussion about tungsten carbide core bullet behaviour is reported highlighting the importance of the sabot in the impact phenomena. Although the work focuses on monolithic plates, the results and discussion can be of interest for the design of optimised multilayer armour shields. [Copyright &y& Elsevier]

Abstract: Whipple shield is widely used on manned spacecraft, numerical simulation is an important way for obtaining the ballistic limit. The large population of particles and the large space span of Whipple shield simulation model restrict the computational efficiency. A fast numerical approach is presented for Whipple shield ballistic limit analysis. First, the critical penetration analysis of the rear walls is converted into specific impulse analysis delivered by the secondary debris cloud, because the maximum of specific impulse is the main determinant of the penetration. The dual plate simulation model is then converted into single plate model and the population of particles is reduced. Second, based on the isotropic expansion theory of secondary debris cloud, the specific impulse analysis is further converted into particle position and velocity analysis when the stable secondary debris formed. The space span of the simulation model is reduced. An example of Whipple shield ballistic limit analysis is provided for the verification of the fast numerical approach, it shows that this approach can significantly increase the computation efficiency with acceptable accuracy. [Copyright &y& Elsevier]

A numerical simulation of heat conduction in a grain aggregate is carried out to determine the packing fraction (the spatial fraction occupied by grains or 1-porosity) dependence of the thermal conductivity of the aggregate. Arrangements of grains are given by random ballistic deposition. It is found that the packing fraction dependence is well approximated by an exponential function. The number of contacts between grains is the crucial quantity in the conduction, and its packing fraction dependence is exponential. Heat conduction is found to be anisotropic, where the conduction along the deposition direction is more efficient than that perpendicular to the deposition direction. [ABSTRACT FROM AUTHOR]

Abstract: Sphere structures for ballistic protection have rarely been studied. In this paper a novel unit cell, called Square Based Pyramid Unit Cell (SBPUC), is created as a fundamental building block of sphere structures for the purpose of ballistic protection. Although it has been proved by the other authors that the arrangement of spheres in a tapered chain is an efficient way for impact energy absorption (Sokolow A, Pfannes JM, Doney RL, Nakagawa M, Agui JH. Absorption of short duration pulses by small, scalable, tapered granular chains. Appl Phys Lett 2005;87:1–3), it is very difficult to convert this 1D concept to 3D application in reality with arbitrary tapering angle. The adoption of SBPUCs may provide a good solution. In this research, the core of a sandwiched sphere structure is build with such SBPUCs and is characterized with increasing sphere diameter, decreasing sphere thickness, and increasing sphere cap thickness. From the numerical simulation results with ABAQUS/Explicit, the sandwiched sphere structure can absorb at least 11.6% more impact energy compared with the monolithic plate with the same area density. This study might provide a potential armor design platform which makes further performance improvement possible by optimizing the large parameter space associated with material selection and structure design. [Copyright &y& Elsevier]

Abstract: Finite element analysis is frequently used in several fields such as automotive simulations or biomechanics. It helps researchers and engineers to understand the mechanical behaviour of complex structures. The development of computer science brought the possibility to develop realistic computational models which can behave like physical ones, avoiding the difficulties and costs of experimental tests. In the framework of biomechanics, lots of FE models have been developed in the last few decades, enabling the investigation of the behaviour of the human body submitted to heavy damage such as in road traffic accidents or in ballistic impact. In both cases, the thorax/abdomen/pelvis system is frequently injured. The understanding of the behaviour of this complex system is of extreme importance. In order to explore the dynamic response of this system to impact loading, a finite element model of the human thorax/abdomen/pelvis system has, therefore, been developed including the main organs: heart, lungs, kidneys, liver, spleen, the skeleton (with vertebrae, intervertebral discs, ribs), stomach, intestines, muscles, and skin. The FE model is based on a 3D reconstruction, which has been made from medical records of anonymous patients, who have had medical scans with no relation to the present study. Several scans have been analyzed, and specific attention has been paid to the anthropometry of the reconstructed model, which can be considered as a 50th percentile male model. The biometric parameters and laws have been implemented in the dynamic FE code (Radioss, Altair Hyperworks 11©) used for dynamic simulations. Then the 50th percentile model was validated against experimental data available in the literature, in terms of deflection, force, whose curve must be in experimental corridors. However, for other anthropometries (small male or large male models) question about the validation and results of numerical accident replications can be raised. [Copyright &y& Elsevier]

Abstract: The paper describes a numerical study on the perforation of sheet steel by a projectile under high impact velocity to predict the ballistic behaviour and, in particular the ballistic limit. The parametric study is performed for several of the important variables in the numerical model using Abaqus/Explicit finite element code and their effects are reported in the paper. The variables considered include the target configuration (thickness), constitutive material model of the target, mass of the projectile, friction between the projectile and the target and shape of the projectile. The effect of the material behaviour was also studied through the use of two constitutive relations and to conclude the ballistic curves were calculated for several different target materials using data from literature. The numerical results were compared with existing data sourced from the literature and an analytical model was used to compare the trend obtained using numerical simulations in terms of ballistic limit. [Copyright &y& Elsevier]

Abstract: This paper presents a semi-analytical approach on the performance of ceramic/metal armor under ballistic impact. Numerical simulations for alumina/aluminum armor impacted by 20 mm APDS in AUTODYN were carried out and verified against the experimental data. Comprehensive numerical simulations were performed using the verified numerical model material parameters providing corroborative data for ensuing discussions. A semi-analytical model relating projectile residual velocity, impact velocity and armor ballistic limit velocity (BLV) is presented for impact of hard projectile against ceramic/metal armor. It is shown that the projectile residual velocity and BLV satisfy the replica scaling laws. Based on the replica scaling laws of projectile residual velocity and BLV, an empirical equation for BLV is obtained and used for armor optimization applications giving reasonable results similar to experiments available in the literature. [Copyright &y& Elsevier]

Abstract: Several studies, both theoretical and experimental, show that sedimentary rocks have fractal pore–grain interface. The real rocks are 3-d structures with highly tortuous and often fractal pore spaces. Before attempting simulation of this daunting geometry, we present here, as a preliminary study, a simpler 2-d version. In this paper, a computer simulated 2-d sedimentary rock structure is generated by the relaxed bidisperse ballistic deposition model. Grains of two different sizes are dropped ballistically on a linear substrate. By changing the fraction of the two types of particles, the porosity of the rock structure can be tuned. The structure undergoes compaction through the relaxation of possible unstable overhangs. The micro structure of the pore space is investigated. The pore mass and the rock–pore interface show a fractal behaviour with the same fractal dimension indicating that the pore volume is a fractal. Our simulation results indicate that the process of compaction of grains during the deposition process seems to erase the dependency of the fractal dimension on the grain size distribution. The two point density correlation is measured for the pore space. It shows anisotropy which is an outcome of the growth rule. X-ray tomography of two-dimensional sections of real sedimentary rocks obtained from Mallorca Island is subjected to the same study and the results compared with those obtained from simulation. The simulation results agree qualitatively with the real rock sample. We also study diffusion on the pore space. Diffusion is found to be anomalous as is expected in fractal spaces. It also bears the signature of anisotropy of the structure. Diffusion studies on the real rock sample could not yield conclusive results as the system size is not large enough. [Copyright &y& Elsevier]

Abstract: This paper presents results from both experiments and numerical simulations of frontal and lateral ballistic impacts on a Hybrid III headform equipped with Advanced Combat Helmets (ACH) of two different interior cushioning designs, namely the strap-netting system and the Oregon Aero (OA) foam padding. It aims to study the differences between two different impact orientations for these two different interior cushioning systems. The experiments involve frontal and lateral ballistic impacts of a 11.9g spherical steel projectile traveling at speeds of approximately 200m/s, striking on the helmet-cushion-headform assemblies. The dynamic interaction between various components of the helmet-cushion-headform assemblies are investigated with the use of high-speed photography while post-test evaluation of the damaged helmets are performed using visual observation, optical microscopy and computed tomography (CT) scan. A series of ballistic impact simulations with finite element (FE) models of the two assemblies reconstructed from CT images, are performed to correlate with experimental results. The commercial software, Abaqus™, is used for the FE analyses. In general, there is reasonable correlation between numerical and experimental observations and on quantitative parameters, such as head accelerations, helmet damage and deflections. It is also found that softer foams with low stiffness are more effective as shock absorbing cushion against ballistic impacts under certain condition. Additionally, results of the two interior cushioning systems are compared with various injury criteria to assess their acceleration levels. It is found that, for frontal impact, the helmet with strap-netting system fails both the Wayne State Tolerance Curve (WSTC) and Federal Motor Vehicles Safety Standards (FMVSS) 218 criteria while the one with OA foam-padding passes both. [Copyright &y& Elsevier]

One-dimensional discrete element model for the ballistic impact is used to determine the depth of penetration of a bullet on a thick target. Discrete Element Method (DEM) is a numerical tool where a continuum is modelled as a network of masses connected by normal springs. A one-dimensional discrete element model is developed to obtain the displacements and forces associated with the ballistic impact on a thick target. The depth of penetration of the penetrator into the target is calculated from these DEM results. The simulated results of depth of penetration are found to be in reasonable agreement with the simulation results of other numerical approaches that are available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Three-dimensional numerical simulations were carried out with ABAQUS/Explicit finite element code to study the influence of target span and configuration on its ballistic limit. 1 mm thick 1100-H12 aluminum targets of varying span diameter and configuration were impacted by blunt and ogive nosed projectiles of 19 mm diameter and 52.5 g mass. The effect of target span was studied by varying the span diameter of 1 mm thick monolithic target as 50 mm, 100 mm, 204 mm, 255 mm and 500 mm. The effect of configuration was studied by taking the monolithic, double layered in-contact and double layered spaced targets of 1 mm equivalent thickness and 255 mm span diameter. The spacing between the layers was varied as 2 mm, 5 mm, 10 mm, 20 mm and 30 mm. In each case the target was impacted normally by blunt and ogive nosed projectile to obtain the ballistic limit. The highest ballistic limit was observed for monolithic target followed by layered in-contact and spaced targets respectively. The variation of spacing between the layers did not have significant influence on the ballistic limit in the case of ogive projectile but some effect was seen in the case of blunt projectile. The ballistic limit was found to increase with increase in target span diameter for both the projectiles and it was found to be higher for blunt nosed projectile as compared to that of ogive nosed projectile for all the spans considered excepting in the case of 50 mm span for which it was higher for ogive nosed projectile. [Copyright &y& Elsevier]

In previous work, a time-stepped numerical algorithm to compute particle trajectories consisting of lunar soil blown by the engine exhaust of a lunar lander was developed. The time-stepped integration method relies on the gas density, velocity, and temperature fields, calculated by computational fluid dynamics simulations, to compute the forces and accelerations acting on single noninteracting particles. In this paper, a computationally efficient particle ballistics model is presented where the trajectory is estimated by computing the vertical position (axial coordinate x) as a function of the horizontal position (radial coordinate y) using a constant horizontal velocity and a vertical acceleration approximated as a power-law. The unknown parameters of the model are determined by fitting the ballistics trajectory path to a matrix of trajectories generated by the time-step integration method using the rocket exhaust gas properties predicted by computational fluid dynamics software. Also in previous work, a strictly empirical trajectory model was developed to satisfy the need for a computationally efficient method of computing particle trajectories. This new model (like the previous model) is expressed as a time-independent trajectory path function. However, the method of this current work is based on physical laws of motion, unlike the previous empirical model. [ABSTRACT FROM AUTHOR]

The standard Lévy walk is performed by a particle that moves ballistically between randomly occurring collisions when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events, the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present a full analytic evaluation of both models and emphasize the importance of initial conditions. We show that, in the limit of weak velocity fluctuations, the integral diffusion characteristics and the bulk of diffusion profiles are identical to those for the standard Lévy walk. However, the type of underlying velocity fluctuations can be identified by looking at the ballistic regions of the difïiision profiles. Our analytical results are corroborated by numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: This work presents the design of a robust control law, and the related control system architecture, for the Vega launcher ballistic phase, taking into account the complete six degrees of freedom dynamics. To gain robustness a non-linear control approach has been preferred: more specifically the Lyapunov''s second stability theorem has been exploited, being a very powerful tool to guarantee asymptotic stability of the controlled dynamics. The dynamics of Vega''s actuators has also been taken into account. The system performance has been checked and analyzed by numerical simulations run on real mission data for different operational and configuration scenarios, and the effectiveness of the synthesized control highlighted: in particular scenarios including a wide range of composite''s inertial configurations performing various typologies of maneuvers have been run. The robustness of the controlled dynamics has been validated by 100 cases Monte Carlo analysis campaign: the containment of the dispersion for the controlled variables – say the composite roll, yaw and pitch angles – confirmed the wide validity and generality of the proposed control law. This paper will show the theoretical approach and discuss the obtained results. [Copyright &y& Elsevier]

An experimental and numerical study of ballistic impacts on steel plates at various temperatures (700 °C, 400 °C and room temperature) has been carried out. The motivation for this work is the blade-off event that may occur inside a jet engine turbine. However, as a first attempt to understand this complex loading process, a somewhat simpler approach is carried out in the present work. The material used in this study is the FV535 martensitic stainless steel, which is one of the most commonly used materials for turbine casings. Based on material test data, a Modified Johnson-Cook (MJC) model was calibrated for numerical simulations using the LS-DYNA explicit finite element code. To check the mesh size sensitivity, 2D axisymmetric finite element models with three different mesh sizes and configurations were used for the various temperatures. Two fixed meshes with 64 and 128 elements over the 2 mm thick plate and one mesh with 32 elements over the thickness with adaptive remeshing were used in the simulations. Both the formation of adiabatic shear bands in the perforation process and the modeling of the thermal softening effects at high temperatures have been found crucial in order to achieve good results. [ABSTRACT FROM AUTHOR]

In the design and development of solid propellant rocket motors, the use of numerical tools able to predict the behavior of a given motor is particularly important in order to decrease the planning times and costs. This paper is devoted to present the results of the internal ballistics numerical simulation of the NAWC tactical motor n. 6, from ignition to burn-out, by means of a quasi-one-dimensional unsteady numerical simulation model, SPINBALL, coupled with a three-dimensional grain burnback model, GREG. In particular, the attention is focused on the effects on the SRM behavior of the erosive burning, total pressure drops and the cause of the pressure overpeak occurring during the last part of the ignition transient. The final objective is to develop an analysis/simulation capability of SRM internal ballistics for the entire combustion time with simplified physical models, in order to have reduced the computational costs, but ensuring an accuracy greater than the one usually given by zero-dimensional models. The results of the simulations indicate a very good agreement with the experimental data, as no attempt of submodels calibration is made, enforcing the ability of the proposed approach to predict the SRMs internal flow-field conditions. The numerical simulations show that NAWC n. 6 internal ballistics is completely led by the erosive burning, that is the root cause of the pressure peak occurring immediately after the SRM start-up. [ABSTRACT FROM AUTHOR]

Experimental investigation of high velocity perforation of 2/1 and 3/2 GLARE 3 target panels with flat ended projectile was presented. Also, numerical simulations were carried out using explicit nonlinear finite element software, LS-DYNA, considering strain rate hardening effects. The ballistic limit was determined experimentally and numerically. Some GLARE 3/2 laminates with different Aluminium thickness is considered. The Aluminium thickness varies in frontal, medial and distal layers of GLARE, while the thickness of glass/epoxy layers is constant, and the ballistic limit and absorbed energy of each GLARE target is determined numerically. Specific absorbed energy is defined as goal function and should be maximized. The laminate with maximum specific absorbed energy is determined. In addition, energy absorbing portion of each layer is determined. There is a reasonable agreement between numerical and experimental results. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and finite-element investigation of ballistic limit of thin single and layered aluminium target plates. Blunt-, ogive- and hemispherical-nosed steel projectiles of 19 mm diameter were impacted on single and layered aluminium target plates of thicknesses 0.5, 0.71, 1.0, 1.5, 2.0, 2.5 and 3 mm with the help of a pressure gun to obtain the ballistic limit in each case. The ballistic limit of target plate was found to be considerably affected by the projectile nose shape. Thin monolithic target plates as well as layered in-contact plates offered lowest ballistic resistance against the impact of ogive-nosed projectiles. Thicker monolithic plates on the other hand, offered lowest resistance against the impact of blunt-nosed projectiles. The ballistic resistance of the layered targets decreased with increase in the number of layers for constant overall target thickness. Axi-symmetric numerical simulations were performed with ABAQUS/Explicit to compare the numerical predictions with experiments. 3D numerical simulations were also performed for single plate of 1.0 mm thickness and two layered plate of 0.5 mm thickness impacted by blunt-, ogive- and hemispherical-nosed projectiles. Good agreement was found between the numerical simulations and experiments. 3D numerical simulations accurately predicted the failure mode of target plates. [ABSTRACT FROM AUTHOR]

Abstract: The numerical investigations were carried out to determine the ballistic resistance of the carbon nanotube (CNT) fibres reinforced composites. In this paper, the fundamental studies of the reinforcement characteristics are presented. It includes the single fibre mechanical and geometric properties as well as fibres distribution and volume (mass) concentration. The continuum matrix material includes a certain amount of fibres made of CNTs. An impact of the projectile with the sharp nose on the metal matrix composite plate was analysed. The computer simulations were performed with the finite element method implemented in LS-DYNA code. The plane formulation allows analysing extremely dense meshes. The obtained results presented the significant role of the carbon nanotube fibres. [ABSTRACT FROM AUTHOR]

The article presents a study examining the behavior of aluminum plates under ballistic impact. It states that 1,100 one-millimeter (mm)-thick aluminum plate undergone experimental ballistic impact tests with different projectile nose shapes in the Product Safety Laboratory, and finite element method and regression analysis were applied in numerical investigation. Results showed a good correlation between residual velocity in computer simulation and failure modes in the experiment.