Oblique Impact Research Articles

Numerical Analysis of Dual Droplet Simultaneous Oblique Impact on a Water Film

The simultaneous oblique impact of multiple droplets on a liquid film is an intricate phenomenon prevalent in diverse natural and industrial processes. However, previous studies have primarily focused on single droplet impact, while an in-depth understanding of the more complex multi-droplet scenario remains lacking. The current study aims to numerically investigate the simultaneous oblique impact of two droplets on a water film using a three-dimensional Volume of Fluid (VOF) model. The effects of the Weber number and the impact angle on the crown behavior are carefully analyzed. The results demonstrate that increasing the Weber number enhances the central uprising sheet height but has minor influences on the upstream crown radius and central sheet radius. In contrast, the increase in the impact angle leads to a decreased upstream crown radius and an increased central sheet radius, while the central sheet height remains relatively unaffected. In addition, the splashing threshold for the dual droplet impact cases is significantly lower than that of the single droplet impact cases due to the interactions between the adjacent crowns. The present results provide novel insights into the underlying physics and useful supports in developing predictive models for the intricate multi-droplet impact phenomenon.

Numerical modelling of impact seismic sources using the stress glut theory

SUMMARY Meteorite impacts have proved to be a significant source of seismic signal on the Moon, and have now been recorded on Mars by InSight seismometers. Understanding how impacts produce seismic signal is key to the interpretation of this unique data, and to improve their identification in continuous seismic records. Here, we use the seismic Representation Theorem, and particularly the stress glut theory, to model the seismic motion resulting from impact cratering. The source is described by equivalent forces, some resulting from the impactor momentum transfer, and others from the stress glut, which represents the mechanical effect of plasticity and non linear processes in the source region. We condense these equivalent forces into a point-source with a time-varying single force and nine-component moment tensor. This analytical representation bridges the gap between the complex dynamics of crater formation, and the linear point-source representation classically used in seismology. Using the multiphysics modelling software HOSS, we develop a method to compute the stress glut of an impact, and the associated point-source from hypervelocity impact simulations. For a vertical and an oblique impact at 1000 m s−1, we show that the moment tensor presents a significant deviatoric component. Hence, the source is not an ideal isotropic explosion contrary to previous assumptions, and draws closer to a double couple for the oblique impact. The contribution of the point force to the seismic signal appears negligible. We verify this model by comparing two signals: (1) HOSS is coupled to SPECFEM3D to propagate the near-source signal elastically to remote seismic stations; (2) the point-source model derived from the stress-glut theory is used to generate displacements at the same distance. The comparison shows that the point-source model is accurately simulating the low-frequency impact seismic waveform, and its seismic moment is in trend with Lunar and Martian impact data. High-frequencies discrepancies exist, which are partly related to finite-source effects, but might be further explained by the difference in mathematical framework between classical seismology and HOSS’ numerical modelling.

Computational simulation of impact perforation of polymeric-foam core sandwiched composites with different skin–face configurations

The normal and oblique impact perforation responses of composite sandwich panels based on a Rohacell polymeric-foam core are numerically investigated at high impact energies (>60 J). A cylindrical form factor with a diameter of 140 mm and a thickness of 15 mm is selected for the sandwich specimens. Four different stacking sequences of 1 mm carbon/epoxy face sheets are considered (i.e., quasi-isotropic, cross-ply, angle-ply, and unidirectional stacking). A computational model was constructed using LS-DYNA finite element software and an inverse perforation testing scheme adapted with a split Hopkinson bar and confirmed by comparing these results with those obtained using the free shooting projectile-target testing schemes published in the literature. The effects of impact energy, failure modes, impact angles, and damage key parameters are analyzed. The results reveal the contact force versus displacement curves are highly influenced by the impact energy increases. The stacking sequence of the face sheets does not influence the energy absorption capacity. However, the maximum absorbed energy increases with an increasing impact angle up to 20°. Using Hopkinson bars in conjunction with the virtual inverse perforation testing approach is effective for examining the response of sandwich composites at high impact energies.

Numerical investigation on the behaviour of concrete barriers subjected to vehicle impacts using modified K&C material model

Full-scale experimental crash tests are important to determine the occupant risk factors and understand barrier system behaviour in vehicle-barrier impacts. Due to the expensive and time-consuming nature of such crash tests, finite element simulations of full-scale crash tests to analyse and design road safety structures have gained popularity as a more practical method of assessment. In this research, a simplified simulation technique was employed by dividing the barrier system into two sections called the Impact Zone and the Rigid Zone, which was adopted for concrete crash barriers for the first time. A previously performed experimental crash test was used to successfully validate the numerical model. The numerical crash model accurately predicted the critical parameters of the barrier performance. The numerical simulation was further used to extract otherwise difficult or impossible results from the experimental crash test, such as internal energies and exit angles. The importance of the use of optimised Karagozian and Case concrete material parameters was demonstrated through a parametric study carried out with autogenerated parameters. A parametric study performed with impact speed and angle proved that increased speed is more harmful for occupants than a more oblique impact angle. The potential benefits of replacing traditional concrete with improved energy absorbing concrete to reduce occupant risks were also investigated. The comparison of results between the numerical models and experimental crash test confirms the trustworthiness of the developed models to simulate the vehicle-barrier crashes for analysing existing barrier designs and further developing new barrier designs to increase road safety.

Enhanced solid particle erosion resistance of nanocrystalline Ni-W coatings through multilayer approach

Electrodeposited nanocrystalline Ni-W alloy coatings are projected as potential alternatives for hard chrome (HCr) coatings owing to their comparable hardness and superior corrosion resistance. However, the limited strain hardening ability of the nanocrystalline Ni-W coatings manifests in their poor resistance towards solid particle erosion involving a high strain-rate (>103 s−1) deformation. In the present study, a novel microstructural engineering strategy has been implemented to enhance the strain hardening ability of the nanocrystalline Ni-W coatings without compromising on their strength/hardness. Ni-W multilayer coatings composed of alternatively stacked soft (2.6 GPa) and hard (8.5 GPa) Ni-W layers were developed using the pulse reverse electrodeposition technique. Further, to investigate the effect of individual layer thickness (λ), multilayer coatings with different λ were deposited. Solid particle erosion testing using the angular SiO2 particles showed that the multilayer coatings (irrespective of λ) exhibit superior erosion resistance compared to the homogeneous nanocrystalline Ni-15W at both oblique (θ = 30°) and normal (θ = 90°) impact conditions. The post-erosion microstructural analysis of the multilayer coatings revealed that the hard Ni-W layers undergo uniform strain (ε > 50 %) without cracking due to the constrained co-deformation imposed by the surrounding soft Ni-W layers. Therefore, the enhanced erosion resistance of the multilayer coatings is attributed to the effective dissipation of impact energy through co-deformation of the individual hard and soft Ni-W layers.

Asymmetric water entry of a wedged grillage structure investigated by CFD-FEM co-simulation

When a ship sails in ocean waves the relative movement between ship and wave is very complex. Slamming of bow or stern structures usually occurs in a manner of asymmetric oblique water entry. This implies that both the deflection angle θ and velocity angle α will likely grow to a large value at the same time. In this study, the hydrodynamics problem associated with the asymmetric and oblique water impact of a three-dimensional wedge is investigated using a partitioned CFD-FEM two-way coupled numerical tool by coupling the commercial software STAR-CCM+ and Abaqus within the framework of SIMULIA co-simulation engine. The hydrodynamic problem is solved by the CFD software using overset grid technique while the structural dynamic response is solved by the FEM software. Validation of the numerical results is conducted by using existing test results of symmetric water entry of the wedge first. Then the behaviours of movements, slamming pressure and structural response of the wedge structure during asymmetric water entry by varying the deflection angle θ or the velocity angle α or both are systematically and comparatively investigated. This research shows that the present numerical simulation well predicts both the fluid and structural dynamic characteristics such as fluid cavity and structural stress concentration of asymmetric impact problems, which has potential engineering application value in the field of ship design and slamming loads evaluation.

Can riot-control water cannon be lethal?

A riot-control water cannon is a large, supposedly nonlethal apparatus that uses pressurized water to control and disperse crowds. However, riot-control water cannons may cause personal injury if directly aimed at the human forehead, for example. Therefore, we systematically analyzed, via a numerical model, the spatio-temporal evolution of the equivalent pressure of a water cannon and its influence on the human body dynamic response, especially considering the head and neck body regions. The simulation results suggest that 10 m is a critically dangerous working distance because the impact of a water cannon can lead to skull, cervical vertebra and brain injuries. In addition, compared to side/back impacts, frontal impacts are much more dangerous due to a more extensive range of head movement. Oblique impact induces rotational movement on the human body, resulting in a significant risk of injury. A quantitative injury risk analysis is presented to provide safety guidance for water cannon usage.

Damage evolution of CFRP laminates by normal and oblique impact erosion of pulsating water jets

Impact direction is one of the critical factors affecting the waterdrop erosion behavior of materials. In this paper, rain erosion damage behavior of a typical carbon fiber reinforced polymer (CFRP) laminate is investigated as a function of the impingement angle (0° as normal impact and 15°, 30°, 45° as oblique impact deviated from the normal) and the relative fiber orientation (parallel PA and perpendicular PE to the fiber direction of the surface layer) under the waterjet velocity of 320 m/s and the impact frequency of 50 Hz via a pulsating waterjet erosion test rig. After continuous impact of multiple waterjets, the typical damage of CFRP laminates is mainly composed of the central erosion crater and the upheaval of the surrounding surface layer. The onset and evolution of damage are mainly driven by the shear action of lateral jetting and stress concentration of hydraulic penetration exerted at the surface irregularities. There is no significant difference in the damage modes between the normal and oblique impacts, except for the asymmetric distributions of matrix cracking in PA-orientation and delamination in PE-orientation caused by the angle inclination. With the impingement angle increasing, the volume loss and erosion depth decrease while the incubation period increases mainly due to the decreases of water hammer pressure and contact area. The PA-orientation can cause lower incubation period and larger erosion mass loss than PE-orientation before the surface ply is penetrated, with the underlying mechanism related to the distinct tensile properties of CFRP laminates along longitudinal and transversal directions and the asymmetric properties of fiber–matrix interface. According to the fitting results of erosion curves, it is possible to describe the incubation period and the erosion rate of CFRP laminates under oblique impact using a two-branch equation, and Springer model can give reasonable prediction for the average incubation period and PA-orientation erosion rate of a certain oblique impact occasion with known 0° impact erosion results.

Vibrational analysis of finite plate on elastic foundation subjected to oblique impact

Vibrational analysis of finite plate on elastic foundation subjected to oblique impact

Nonlinear low-velocity impact analysis of sandwich plates with titanium face sheets and porous aluminum core reinforced by GPLs

This study examines the nonlinear dynamic response of sandwich plates under low-velocity impacts (LVIs), which consist of a porous aluminum foam core with functionally graded (FG) graphene platelets (GPLs) reinforcement and two titanium alloy face sheets. The finite element method is employed to perform the numerical simulations and the Hertz contact theory is used to model the impact behavior. The generic Halpin-Tsai model, which incorporates the porosity effect, is adopted to estimate the mechanical properties of core made of the FG-GPLRC, based on the experimental data of the closed-cell aluminum alloy foam. The simulation results reveal that the FG-X configuration has the highest impact resistance, and that the addition of GPLs improves the impact performance. Moreover, a thicker core can reduce both the first contact time and the vibration period of plates, while a looser boundary condition can prolong the vibration time after the first impact. Additionally, a higher impactor velocity, mass and radius lead to a higher deflection and contact force. The oblique impact decreases the impact energy. This work provides a lighter and stiffer design for structure engineers when components suffer low-velocity impact.

Quantitative analysis of the protective performance of bicycle helmet with multi-direction impact protection system in oblique impact tests

PurposeThe current study aimed to assess the protective performance of helmets equipped with multi-directional impact protection system (MIPS) under various oblique impact loads. MethodsInitially, a finite element model of a bicycle helmet with MIPS was developed based on the scanned geometric parameters of an actual bicycle helmet. Subsequently, the validity of model was confirmed using the KASK WG11 oblique impact test method. Three different impact angles (30°, 45°, and 60°) and 2 varying impact speeds (5 m/s and 8 m/s) were employed in oblique tests to evaluate protective performance of MIPS in helmets, focusing on injury assessment parameters such as peak linear acceleration (PLA) and peak angular acceleration (PAA) of the head. ResultsThe results demonstrated that in all impact simulations, both assessment parameters were lower during impact for helmets equipped with MIPS compared to those without. The PAA was consistently lower in the MIPS helmet group, whereas the difference in PLA was not significant in the no-MIPS helmet group. For instance, at an impact velocity of 8 m/s and a 30° inclined anvil, the MIPS helmet group exhibited a PAA of 3225 rad/s2 and a PLA of 281 g. In contrast, the no-MIPS helmet group displayed a PAA of 8243 rad/s2 and a PLA of 292 g. Generally, both PAA and PLA parameters decreased with the increase of anvil angles. At a 60° anvil angles, PAA and PLA values were 664 rad/s2 and 20.7 g, respectively, reaching their minimum. ConclusionThe findings indicated that helmets incorporating MIPS offer enhanced protection against various oblique impact loads. When assessing helmets for oblique impacts, the utilization of larger angle anvils and rear impacts might not adequately evaluate protective performance during an impact event. These findings will guide advancements in helmet design and the refinement of oblique impact test protocols.

COMPARISON OF DIFFERENT MATERIAL CONSTITUTIVE MODELS FOR PREDICTING AORTIC BIOMECHANICAL RESPONSE AND INJURY IN BLUNT SIDE IMPACTS

Traumatic rupture of the aorta (TRA) is highly lethal in motor vehicle collisions (MVCs). Human body biomechanical models (HUBMs) show promise as useful tools for better comprehension of the mechanical response and injury mechanism of TRA. However, the prediction accuracy largely depends on its material modeling. This study investigated the performance of the isotropic elastic material constitutive model (Mat_001) and the orthotropic elastic material constitutive model (Mat_002) for predicting aortic dynamic response and injury in blunt side impacts, via simulations against vertical and oblique side impact cadaver tests with previously developed HUBM. The aortic strain response, peak intraluminal pressure, thoracic deflections and injury distributions were compared. It was found that both Mat_001 and Mat_002 could be used to model aortic tissue, but Mat_002 presented more sensitivity to blunt side impacts in terms of strain responses. The thoracic rib cage and internal organs sustained more severe injuries under the oblique left side impact (AIS 5+) than those under the vertical left side impact (AIS 4+), whereas the aortic peri-isthmus exhibited a higher TRA risk in the vertical side impact than that in the oblique side impact, with regard to the peak longitudinal strain. The TRA could result from the aorta’s sudden stretch, and the peak longitudinal strain could be regarded as a main contributing factor to it. This study enhances our understanding of the aortic material modeling and injury mechanisms.

Crater radius analysis after dual droplets successive oblique impact on liquid film

Droplet impact is a common occurrence in nature, agriculture, and industry. The research on the multi‐droplet impact is fundamental to understanding the tangled nature of reality. This paper numerically studies the successive oblique impact of dual droplets on the liquid film by building an effective three‐dimensional model. The leading and trailing droplets are set to pass a certain impact point with the same velocity. The main contribution of this paper is the investigation of the effects of Weber number, liquid film thickness, impact angle, and impact time interval on the interface morphology evolution after the droplet impact. Results show that splash pattern conversion of the primary or secondary crown occurs with the change of these factors. Besides, the variations of the maximum crater radius in upstream, lateral, and downstream directions with time are quantitatively analyzed. The crater radius analysis is carried out from three perspectives, the variation during the single droplet impact, the change during the dual droplets impact, and the comparison between them. It is found that the crater of dual droplets impact exhibits shape distortion in the deformation period and appears a marked dimensional increase in the secondary expansion period.

The Influence of Headform Friction and Inertial Properties on Oblique Impact Helmet Testing

Helmet-testing headforms replicate the human head impact response, allowing the assessment of helmet protection and injury risk. However, the industry uses three different headforms with varying inertial and friction properties making study comparisons difficult because these headforms have different inertial and friction properties that may affect their impact response. This study aimed to quantify the influence of headform coefficient of friction (COF) and inertial properties on oblique impact response. The static COF of each headform condition (EN960, Hybrid III, NOCSAE, Hybrid III with a skull cap, NOCSAE with a skull cap) was measured against the helmet lining material used in a KASK prototype helmet. Each headform condition was tested with the same helmet model at two speeds (4.8 & 7.3 m/s) and two primary orientations (y-axis and x-axis rotation) with 5 repetitions, totaling 100 tests. The influence of impact location, inertial properties, and friction on linear and rotational impact kinematics was investigated using a MANOVA, and type II sums of squares were used to determine how much variance in dependent variables friction and inertia accounted for. Our results show significant differences in impact response between headforms, with rotational head kinematics being more sensitive to differences in inertial rather than frictional properties. However, at high-speed impacts, linear head kinematics are more affected by changes in frictional properties rather than inertial properties. Helmet testing protocols should consider differences between headforms’ inertial and frictional properties during interpretation. These results provide a framework for cross-comparative analysis between studies that use different headforms and headform modifiers.

Dynamic Responses of Single-Layer Reticulated Shells under Oblique Impact Loading

This paper focuses on the response of reticulated shell structures under oblique impact loads, with a departure from the traditional emphasis on vertical impact loads. These structures are typically utilised in large-span spaces such as iconic buildings and large venues. The study begins by establishing a numerical simulation method for reticulated shell structures subjected to oblique impact loads, which is then validated against existing experimental results. Building on this verified method, the research delves into the effects of varying impactor mass, velocity, and initial kinetic energy on the reticulated shell structure under oblique impacts, as well as the influence of different oblique impact angles. The study extensively examines the failure modes of the structure, node displacements in the structure, and variations in member stress under different impactor parameters. It further investigates how these parameters influence the maximum impact bearing capacity, impact duration, energy dissipation capability, and response forms of the structures, analyzing the reasons behind these effects. The findings offer valuable insights for further research and practical engineering design of reticulated shell structures.

Crashworthiness analysis of Dragonfly inspired tubes under multiple load cases

Nature's creatures have developed remarkable geometric structures for environmental adaptation. Dragonflies have evolved a rapidly flipping symmetrical four-wing system to enhance hunting efficiency. Inspired by the unique double-symmetric wing structure of the dragonfly, a group of multi-cell elliptic tubes (METs) are developed to enhance the energy absorption capacity of thin-walled tube for multiple load cases. The finite element models of MET with different cross-sectional configurations are established and validated by quasi-static axial crushing tests. The crashworthiness of MET under different load angles θ have been explored and extensively studied by simulation method through LS-DYNA. The results indicate that the crashworthiness of MET could be influenced by the number of basic corner elements. Moreover, MET demonstrates higher energy absorption efficiency in oblique compression as compared to axial compression. Theoretical models of axial and oblique compressions are developed to predict the mean crushing force, which are obtained by summarizing the deformation modes of MET and employing simplified super folded unit theory. Finally, multi-objective particle optimization (MOPSO) algorithm is adopted to explore the MET crashworthiness optimization under oblique impact, with peak crushing force (PCF) and specific energy absorption (SEA) as targets and geometric parameters L, α, F and thickness t regarded as design variables. A new knee-point selection method is used to select MET from the pareto set of solutions of different schemes. The results show that different weight coefficients have great influences on the optimization results and further study is needed.

High-velocity oblique impact experiments on ice and snow spheres: Implications for the collisional evolution of icy planetesimals at different thermal evolution stages

In order to determine the effect of impact angle on the impact strength of icy planetesimals, we conducted a range of oblique impact experiments for spherical ice and snow targets simulating icy planetesimals at different thermal evolution stages. The ice targets had no porosity and the snow targets had a porosity of 0.5. A polycarbonate or glass sphere impacted the ice targets at 744–1747 m s−1 and the snow targets at 938–5085 m s−1 over a range of impact angles from grazing to head-on collisions. All experiments were conducted using a two-stage light gas gun and a target chamber set in a cold room of −15 °C at Kobe University, Japan. The impact strength, which is a specific energy, Q, when the largest fragment mass is a half of the original target mass, for the ice and snow targets in a head-on collision was determined to be 12 and 520 J kg−1, respectively, whereas it was found that the impact strength depended on the impact velocity. Thus, the normalized largest fragment mass, ml/Mt, could well scale with the velocity dependent Q, that is, Qviγ (where ml and Mt are the masses of largest fragment and target, respectively, and vi is the impact velocity). At high Q, ml/Mt increased drastically with the decrease of impact angle when the impact angle was smaller than a critical angle, θc, and θc~30° for the ice targets and θc~45° for the snow targets. At small Q, ml/Mt continued to increase as the impact angle became smaller for both types of targets. The ml/Mt for oblique impacts had a good correlation with the effective specific energy, Qeff=Qsin2θ, where θ is the impact angle, and the effective impact strength was determined to be 16 J kg−1 and 499 J kg−1 for the ice and snow targets, irrespective of the impact angle. Furthermore, the scaling parameter, Πs_eff, which was proposed by Housen and Holsapple (1990) but includes Qeff instead of Q, multiplied by 1−ϕλ, where ϕ is the porosity, showed even better correlation with ml/Mt, and all ml/Mt data of ice and snow targets could be merged, irrespective of impact velocity and ϕ. Based on our experimental results and a theory on the oblique impact of solar system bodies proposed by Shoemaker (1962), we could estimate the degree of disruption (ml/Mt) at any impact energy and any impact angle for icy planetesimals. Our findings demonstrate that the degree of disruption for icy planetesimals that have experienced sufficient thermal evolution was larger than that for those that did not experience significant thermal evolution.

Could the Rebound Characteristics of Oblique Impact for SiO2 Particles Represent the Ash Particles?

Collisions between particles or with a surface have been widely applied, in which the restitution coefficients are the important parameter to describe the particle rebound behavior. SiO2 particles are often used instead of ash particles in theoretical analyses; however, whether this is justifiable has not been confirmed. This paper compares the rebound characteristics of oblique impact for SiO2 particles and ash particles by experimental and theoretical analyses. Based on the rigid-body theory, the tangential restitution coefficients, rebound angle-particle center, and reflection angle-contact path predicted by SiO2 particles are basically in agreement with the experimental results for ash particles, especially at large impact angles. However, there is a slight error at 2.2 m/s as the velocity approaches the critical capture velocity.

Aouelloul impact crater, Mauritania: New structural, lithological, and petrographic data

The Aouelloul circular structure (Mauritania), 0.4 km in diameter, is a simple impact crater, which formed approximately 3 Myr ago. The Aouelloul crater was confirmed to be an impact crater based on the presence of an extraterrestrial component in glass fragments found around the crater, but so far, no convincing evidence of shock metamorphism in minerals, such as shocked quartz grains, is reported. The crater has been visited by a small number of geologists and limited information is available on deformations and impact-related effects at the macroscopic and microscopic scales. Detailed petrographic investigations of eight sandstone samples, all collected at the rim of Aouelloul during a 2019's field campaign, show that tectonic deformation lamellae occur in a number of quartz grains, but did not reveal any evidence of shock metamorphism. New observations on the distribution of the impact glass at the Aouelloul crater, exclusively located in the southern and eastern outer parts of the crater, suggest an oblique impact, from possible directions ranging from south-west to north (clockwise). Geological and lithostructural data are also presented and show that the rim of the crater is characterized by more or less disturbed metric to pluri-metric blocks of rocks showing fracturing and dipping toward either the interior or the exterior of the crater. This study confirms previous works conducted at the Aouelloul crater and illustrates the difficulty in demonstrating the impact origin of relatively small craters.

Dynamic crushing behavior of a novel bi-directional gradient lattice structure under axial and oblique impact loadings

To meet the crashworthiness requirement of lightweight structures under different impact directions, a series of novel bi-directional gradient lattice structures (BD-GLSs) are proposed to improve their oblique impact resistance performance. In this paper, four types of BD-GLSs with both symmetric and asymmetric gradient topology configurations are constructed by varying the side lengths of lattice unit cells in xy-plane, and their crushing behavior under axial and oblique impact loadings are numerically investigated. The dynamic crushing behaviors are highlighted by comparing with the traditional uniform and uni-directional gradient lattice structures, which is validated via experiment studies. It is demonstrated that the specific energy absorption of the BD-GLSs with symmetric gradient topology configuration can achieve an increment of 42.26 % as compared to the uniform lattice structure. Moreover, the specific energy absorption of BD-GLSs with symmetric gradient topology configuration is 47.63 % higher than that of the uni-directional gradient lattice structure under oblique impact, which suggests that the bi-directional gradient topology can provide better crashworthiness performance under the oblique impact conditions. The symmetrical gradient topology configuration has greater bearing capacity and better crashworthiness under both axial and oblique impact loadings by comparing with other gradient topology configurations. The proposed bi-directional gradient topology configuration provides an optimal design strategy for the crashworthiness design of lightweight structures, especially in the case of unknown impact load directions, which has a great competitive advantage in crashworthiness applications.