Assessment of Thorax Finite Element Model Response for Behind Armor Blunt Trauma Impact Loading Using an Epidemiological Database

Behind-armor blunt trauma (BABT) describes injuries that may occur to the thorax when protective body armor is impacted in a nonperforating event, leading to rapid deformation of the armor, and ultimately interact with the torso [1]. The focal nature of the interaction between the armor and the thorax can result in superficial contusion, hard tissue fracture, pulmonary contusion, and cardiac injuries [2], where the nature and extent of injury depend upon many aspects including the projectile construction, impact velocity, and armor construction [3].

At the impact location, the velocity of the torso-side, or back face, of the deforming armor exhibits a rapid rise to a maximum velocity within a few hundred microseconds followed by an exponential decrease until the maximum back face deformation (BFD) is achieved within a few milliseconds [4]. The specific timing depends on the projectile type and velocity, and the construction of the armor [5]. A widely used test criterion for protective armor measures the post-test deformation in clay backing resulting from a BABT impact. Armor is assessed on a pass or fail basis based on the maximum deformation of the armor impression in the clay. Tests on live Angora goats wearing flexible (soft) body armor (seven layer Kevlar 29 with handgun impacts at 244 m/s) demonstrated nonserious injuries [6] and further research led to the 44 mm maximum BFD criterion on conditioned Roma Plastilina #1 modeling clay [1,7]. Live animal testing has considered porcine lateral thorax impacts to investigate response and the potential for pulmonary contusion [8–10], and have identified the importance of impact location and influence of standoff on the resulting trauma. Testing on clay [11] has reported the profile shape to be parabolic for soft armor, compared to a nearly spherical shape for hard armor [5,12]. Although costlier than clay, gelatin has continued to be used for experimental testing to investigate projectile penetration [13–15] and BABT BFD [16–19]. Initially, ballistic gelatin was used as a torso surrogate; however, the cost of the material and the need for high-speed imaging to track deformation led to the identification of clay as a lower cost material with similar measurable post-test maximum BFDs compared to gelatin [1].

Postmortem human subject (PMHS) studies of blunt pendulum impacts on the torso defined a maximum load of 3.29 kN applied to the sternum resulted in minor skeletal fractures [20]. However, this threshold was noted to depend on the area over which the load was applied, and anticipated to depend on the rate of load application since momentum effects can become significant at high rates of loading. Intermediate velocity and low-mass blunt impacts from less-lethal weapons [21] have demonstrated the dependence of blunt impactor size and energy on thorax response. In a ballistic impact scenario, Bass et al. [11] used PMHS to evaluate polyethylene-backed armor impacted by a 7.62 mm projectile (670–800 m/s impact velocity) with a corresponding BFD of 30–40 mm in clay. Typical injuries included rib and sternum (transverse) fractures. The impact force was found to be relatively constant with increasing projectile velocity and a 50% risk of sternal fracture was identified for a peak sternal force of 24,900±1400 N.

Established thorax injury criteria in the automotive community such as deformation [22], the viscous criterion [23], and blunt criterion [24] have demonstrated correlation with the observed response and injury for free-flight (pendulum-type) impacts. However, in the case of BABT, it has been observed that the maximum deflection, viscous criterion, thoracic wall velocity, and other parameters may occur at different times during the impact [25] indicating further research is required to link the armor response and measurable thorax response to injury risk.

Human body models (HBMs) have been applied to assess the potential for thoracic injury from blunt impact scenarios, such as motor vehicle collisions. Models have been applied to assess gross thoracic kinematic metrics [26–29], and to investigate injury risk to the ribs, sternum [28,30–34], and to the lungs [31,32,35,36]. Some studies have extended these HBMs to BABT impact scenarios but have identified challenges and limitations in the ability to predict injury to the human body [2,36–41]. Such limitations include the need for high-deformation rate material properties, finite element mesh refinement, model contact robustness, computational stability, and model verification and validation (V&V). In addition, a critical limitation for applying HBM to BABT simulations is the need for representative BABT loading or boundary conditions [42]. As a result, many well-established HBMs are not sufficient to directly evaluate BABT impacts without incorporating numerous enhancements.

A contemporary HBM thorax model (Waterloo Thorax model or WALT) was developed for automotive applications [43,44] and further enhanced with high-deformation rate material properties [30]. The WALT model included a detailed thoracic cage, internal organs (heart, lungs) and muscle tissue, but did not include skin. The mesh quality was improved and a mesh convergence study was performed, along with the improvement of the heart and lung tissue constitutive models for predicting injury [35]. Further validation of the thorax was performed for more complex automotive loading scenarios using PMHS side-impact scenarios [26,45]. In a parallel development path, the thorax model was further enhanced to model BABT impact events (BABT-WALT, Fig. 1) [42,46] and applied to investigate less-lethal kinetic weapons (LLKE) impacts [4,47,48] with enhanced costal cartilage properties [49] and refinement of the finite element mesh at the impact locations to improve the numerical accuracy of the model. The mechanical properties of the ribs and sternum were updated, including a failure criterion [50] to predict the onset of fracture. The model was demonstrated to predict sternum fracture for hard-armor BABT events [2] in agreement with PMHS data. The material model of the lungs was improved by using constitutive equations proposed by Yuen [51] and Cronin [52] and applied to investigate pulmonary contusion injury [42]. Mesh convergence studies have been previously performed [52] to determine the element density for the muscle tissues, lungs, and hard tissues. The thoracic response of the BABT-WALT was previously validated [26,27,30,35,43] using the LLKE PMHS experimental impacts [21], and the PMHS pendulum experiments in the frontal [53], lateral [54], and oblique directions [55]. In general, the BABT-WALT thorax was within the reported corridors for the 20 and 40 m/s LLKE impact cases, while demonstrating a stiffer response compared to the 60 m/s impact data. The model was in good agreement with the thorax compression [27,30,35] for frontal, lateral, and oblique impacts [53–55]. The current BABT-WALT thorax finite element model comprises 402,068 solid hexahedral, 36,536 shell, and 930 beam elements.

In an earlier study, BABT loading was applied to the WALT-BABT thorax model using a rigid spherical impactor, with prescribed velocity-time boundary conditions based on experimental measurements of hard-armor deformation [42]. This simplified boundary condition integrated the response of the projectile and armor by applying the BFD of the armor to the thorax over the duration of the impact event. Although computationally efficient, one limitation of this method is that the boundary conditions are representative of one impact scenario (projectile and armor combination), and assumed that the shape of the BFD was spherical throughout the impact event. Although the assumed spherical shape was consistent with observations in clay, the method did not account for the evolution of the armor back face shape, which may occur over time. This study reported increases in lung injury with respect to increasing BFD, a dependence on the diameter of the impactor, and recommended improvements in the boundary condition methodology for future studies.

Based on cases identified through the International Association of Chiefs of Police/Dupont Survivors' Club and various manufacturers, a BABT injury database (BABT-ID) has been developed. This dataset includes real-world cases of law enforcement agents, who have had ballistic impacts on their armor and survived [56]. This dataset includes information regarding the type of armor, impact location, medical records related to the event, type of projectile, and the impact standoff distance. Thoracic injuries resulting from BABT can range from minor to severe on the abbreviated injury scale (AIS) scale [57]. An alternate injury scale developed specifically for the BABT-ID [56,58] includes three levels or injury ranks: Rank 1 minor injuries (bruising and abrasions on surface tissue); Rank 2 moderate injuries (bruising with penetration, pulmonary contusion, and an open wound); and Rank 3 clinically significant injuries (internal injuries that may require intervention). An initial analysis involved the analysis of 47 cases [56]. These cases were recreated in the laboratory with the same armor, projectile, and impact distance on the standard Roma Plastilina clay backing material to relate the measured BFD to the injury outcome. Bir has reported for soft armor that a BFD of 29.2±12.4 mm corresponded to modest soft tissue damage (bruising) while a BFD of 43.6 mm corresponded to a 50% risk of a clinically significant injury (Rank 3). In this context, a clinically significant injury was defined as an injury requiring medical intervention or hospitalization.

The first objective in this study was to develop a novel methodology for applying realistic BABT impact conditions in computational thoracic models, in particular in this study, to the BABT-WALT thorax model. The second objective was to assess, using ten real-world, case-specific BABT loading conditions [56], if a computational model, like the BABT-WALT thorax, has the capability to evaluate and predict thoracic cage and lung injury from BABT loading.

Sternum fracture was predicted using an element erosion technique with critical plastic strain using material properties from the literature [50], and predicted fracture at a load of 25 kN [2], in agreement with PMHS test data [11]. The same approach and material properties were applied to the ribs for the prediction of rib fracture. The onset of hard tissue fracture was predicted when the first element was eroded at an effective plastic strain value of 2%. It should be noted that element erosion criteria are mesh-size dependent, so the value used in this study is specific to the WALT model but is similar to values used in other human body models [59]. The WALT model included representations of the thoracic cage, lungs, heart, and muscle tissue (outer tissue) (Table 1).

The risk of pulmonary contusion was calculated using a proposed metric of maximum transient hydrostatic stress (pressure) in the lung elements [52]. This proposed method assumes that the thoracic response from pendulum impacts to the thorax on PMHS associated with AIS 3+ injury can be related to the observation that having an AIS 3+ injury in the thorax is associated with acute respiratory distress syndrome (ARDS). Within the model, the maximum pressure in each element of the lungs was tracked during the impact event, and the magnitude of this pressure was associated with the risk of pulmonary contusion. The contusion threshold was determined using a set of oblique pendulum PMHS impact scenarios [30,55] associated with an AIS 3 injury level [57]. Specifically, a 6.7 m/s pendulum impact was shown to result in an AIS 3 level thoracic cage injury. In a separate study, Miller [67] concluded that there was a high risk of developing ARDS when the pulmonary contusion volume exceeded 20% of the total lung volume. Becher [68] similarly concluded that 24% of contused volume was significant in predicting ARDS. In this study, it was assumed that the onset of ARDS was associated with 20% contusion by volume of the lungs and corresponded to an AIS 3 lung injury. To estimate the transient pressure threshold for significant lung injury, the pendulum impact [55] was modeled using the BABT-WALT model, and the maximum transient pressures of the lung elements were ranked. The maximum transient pressure of the rank number that is equivalent to the number of elements that account for 20% of the lung volume was then set to the transient pressure threshold. The corresponding threshold was 45.5 kPa maximum transient pressure in the lung tissue. In this study, any element that exceeded the threshold value was deemed to be contused, and the volumes of contused elements were summed at the end of the calculation.

Ten cases from the BABT-ID were identified for investigation (Table 2). The cases were selected to include all three injury ranks or levels, a range of impact locations, and a range of BFDs. The number of cases was limited to ten since experimental testing ( Appendix A) was required to measure the transient armor deformation for the case-specific soft armor and projectile, and was only possible for the ten cases where the officer's actual soft armor, or a vest of the same size, make and model within five years of the date of the incident was available for testing. When possible, the same bullet from the incident was used; however, in some cases, not all of the details of the bullet were available (e.g., threat weight, type, or manufacturer). For those cases, the most commonly available bullet for the known caliber was used. Each of these ten cases, was tested on a 10% ballistic gelatin block to experimentally recreate the conditions described in the BABT-ID and characterize the backface signature of the incident. The deformation of the armor was recorded at 35,000 frames per second using a high-speed camera (Phantom V1212, Wayne, NJ). Medical records were available for six of the ten cases, while the impact locations were reported for all ten cases. All subjects were male, but the anthropometrics of each subject was not provided for all cases in the database.

The deformation of the armor was prescribed to the thorax model using a finite element mesh of shell elements, described as the BABT impact boundary condition (BIBC). The radial mesh of 1350 four-node shell elements, 1381 nodes, had a diameter of 120 mm, and a thickness of 2 mm (Fig. 2) corresponding to the maximum impact size measured in the 10 experimental cases. The element characteristic lengths ranged from 3 to 16 mm, owing to the radially diverging mesh. To reduce faceting during large deformations, the BIBC was meshed with concentric elements increasing in size from the point of maximum velocity and deformation (center) to the outer circumference, allowing for greater resolution in recreating the high-velocity deformations at the point of projectile impact, while the larger elements at the outer circumference were sufficient in recreating the relatively lower velocity deformations farther from the point of impact.

The dynamic armor deformation for each of the ten cases was measured experimentally using high-speed imaging recorded at 35,000 frames per second (Appendix  A). For each of the ten cases, the armor dynamic deformation profile was digitized at each increment in time from the high-speed imaging (Fig. 2(a)) using image tracking software (tracker v.5.0.6, Douglas Brown 2018). The measurements were not compensated for lens distortion; however, this should be a secondary effect for the setup used given that the target area was centered in the image. Evaluation of the pretest scale image confirmed that the square grid used as a reference marker was orthogonal and the grid size (pixel count per grid square) did not vary over the area of interest in the images. A surface-time history of the armor displacement was created from the digitized high-speed images. The following describes the process undertaken to create the armor back face surface from the measured 2D profile-time history.

First, the armor displacement data were extracted from the experimental test. For each high-speed image (i.e., at each time increment), the profile of the armor displacement was digitized, resulting in a set of 2D profiles describing the 2D profile-time history of the armor displacement (x,y,t) for each point on the edge of the BFD (Fig. 3(a)). The center of the y-axis of the impact event was identified at the start of the event as the point of projectile impact (dot in Figs. 3(a) and 3(b)).

Second, the armor displacement data were applied to the nodes of the BIBC shell mesh by prescribing displacements to a single line of nodes across the diameter of the BIBC mesh. The nodal displacements were prescribed to each node, which corresponded to the position in the 2D profile, such that the center axis of the impact corresponded to the center node of the BIBC mesh (Fig. 3(c)). This process was applied to adjacent nodes in the clockwise direction around the center axis over an angle of 90 deg to generate two quadrants of surface contacting nodes with prescribed displacements.

Third, the remaining two quadrants of nodes were prescribed, linearly interpolated displacements such that a smooth transition occurred between the quadrants. Interpolation was performed between all pairs of nodes having the same radial distance from the center node of the mesh following a clockwise direction (Fig. 3(c)). This third step completed the approximation of the 3D surface of the armor back face displacement at a given time in the impact. The second and third steps were repeated for all image frames from the impact event, resulting in a surface-time history of the armor back face displacement, integrated with the BIBC shell mesh (Fig. 3(b)).

Early investigations using two orthogonal high-speed cameras identified that the armor deformation was relatively axisymmetric about the projectile impact path (center axis), so the process of approximation described above was considered reasonable. However, two cases (BABT ID–004 and BABT ID–017) demonstrated an asymmetric response, particularly later in the impact event. This asymmetry was attributed to projectile tumbling during interaction with the armor; and therefore, the approximation was less accurate. In one case (BABT ID–017), this asymmetry was associated with an impact close to the edge of the armor.

A typical deformation-time response (Fig. 4) of the maximum deformation point (red marker, Fig. 3) demonstrated a rapid increase in displacement over the first 1–2 milliseconds postimpact, followed by a roughly exponential decrease in velocity up to the maximum deformation (BFD).

For each recreated BABT scenario, the measured surface-time history of the armor displacement was integrated with the BIBC. Given that this was a prescribed displacement boundary condition; the material model of the shell elements did not affect the simulation outcome (Appendix  B) and the contact mechanics did not change for the variations in material properties considered. As a first check of the method and comparison to previous studies, the BIBC method was verified using an impact test of a rigid sphere impactor and was found to be in good agreement measured using the contact forces between the thorax, ribcage, sternum, and lungs; with minor differences mainly attributed to the differences in mesh between the sphere impactor and the BIBC (Appendix  B). This comparison was useful to ensure that both methods gave similar results and that previous findings using the rigid sphere impactor were relevant to this study.

For each of the ten cases, the case-specific BIBC was positioned relative to the thorax (Fig. 5) using locational descriptions available in the BABT-ID. The descriptions were subjective, and the BABT-WALT represents an average-stature male; therefore, there was some uncertainty in the positioning of the impactor in the model matching the real-world scenario. An example of a well-described impact location was case BABT ID–032 (Table 2, Fig. 4) that reported an abrasive injury 1 cm below the left nipple. Such descriptions were used to position the center of the BIBC relative to the thorax ensuring the shell mesh was oriented tangent to the outer tissue and positioned with a standoff distance of 0 mm from the impact location.

All recreations were simulated for a duration of 50 ms, which represented the loading and unloading of the thorax during the impact event. This relatively long duration was used to allow for the wave transmission, reflection, and superposition to be fully realized in the lung tissue which has a relatively low wave speed compared to muscle and bone. The finite element model was solved using a commercial finite element software (ls-dyna, version 7.1.2, LST, Livermore, CA). All models were stable, successfully ran to termination, and were postprocessed using commercial software (ls-pre-post, LST, Livermore, CA). The contact energy between the BABT-WALT and BIBC was extracted from the simulations along with the total energy absorbed by the BABT-WALT. The predicted hard tissue and pulmonary contusion injuries from the recreations were then ranked on a scale from 1 to 3 where a value of 1 indicated no ribs fractured or a percentage of total volume pulmonary contusion less than 10%, a value of 2 indicated 1 rib fracture or pulmonary contusion greater than 10% but less than 20%, and a value of 3 indicated 2 or more ribs fractured or pulmonary contusion greater than 20% [56,58].

The BABT impact condition, comprising prescribed displacement-time histories to the nodes of the shell mesh, generated loading on the thorax at the defined location of impact. A typical BABT impact simulation was initiated by focal loading at the point of projectile impact, corresponding to the center of the shell element mesh (Fig. 6(a)). The prescribed displacement of the shell elements resulted in the deformation of the BIBC mesh into the thorax at the target location. One limitation of this study was that the same computational thorax model was used for all impact cases. Subject-specific HBMs were not considered due to limited anthropometric data for the individual subjects in the BABT-ID. In future studies, it is recommended that subject-specific thorax models be considered. The first contact was initiated between the BIBC and the muscle tissue on the outside of the thorax, causing localized deformation of the muscle tissue and subsequently engaging the thoracic cage (Fig. 6(b)), and finally causing loading on and stress wave transmission through the lungs (Fig. 6(c)). Owing to the focal nature of the BABT impact, represented by the BIBC, the deformation was primarily localized within the impact region. In other words, deformations of the thorax outside the impact zone were modest and no global motion of the thorax occurred during the 50 ms simulation time. The shell mesh, representing the armor, remained in contact with the thorax during the event up to maximum displacement. Although it is possible for the thorax to continue deforming and separate from the armor at later times, potentially during the unloading phase, that effect was not observed in the computational model or the gelatin experimental tests. The numerical contact algorithm and refined mesh of the thorax muscle tissue ensured robust contact with no unphysical interpenetration of the surfaces, as has occurred in coarser meshes [42]. Since the BFD histories were digitized from controlled, experimental tests, this method circumvented the need to model the armor and projectile. Therefore, the method could be implemented with any type of projectile and armor combination. One limitation of the BIBC method was that it required experimental measurements of the armor deformation resulting from a specific projectile impact. Unlike the spherical impactor method reported in the literature, the BIBC method could represent a loading surface that changed in shape over time, which did occur for the soft armor impact cases considered in this study. It was found that the rib fracture predictions were similar for both the BIBC and sphere impactor methods, while the predicted pulmonary contusion was lower for the spherical impactor method. In addition, the energy transferred to the thorax was lower for the spherical method, since the evolution of shape was not considered for the sphere impactor, and demonstrating the benefits of the BIBC methodology.

The initial kinetic energy, calculated from the projectile velocity and mass reported in the BABT-ID, was compared to the energy input to the thorax from the BIBC condition (Table 3) as a verification of the input boundary conditions. For a given impact, the total energy input to the thorax must be less than the projectile kinetic energy before the impact, owing to energy dissipation by the armor. The calculated ratios of energy input to the thorax, relative to the projectile energy ranged from 18% to 97% (Table 3). The large range in the ratios can be attributed to differences between the types of projectiles, armor, variability within the experimental setups, and the standoff distance. In general, higher ratios corresponded to higher initial projectile velocities. It should be noted that the recreation cases used the reported projectile–armor combinations from the BABT-ID database, so there may be cases where the projectile was stopped but was close to exceeding the armor perforation limit. Similarly, there could be cases where the projectile and armor were under-matched, potentially explaining the large range of energy values in Table 3.

The onset of rib fracture was identified by the erosion of the first finite element in a rib and in all cases, was followed by erosion of multiple adjacent elements through the entire cross section of the rib leading to a simulated rib fracture (Fig. 6(b)). The identification of rib fracture was straightforward to assess, given that the finite element code reported the location and time for any elements that were eroded, and in all cases, complete transection of the rib occurred. The first element erosion occurred early in the loading history, and complete fractures corresponded to the occurrence of maximum BFD. It has been reported in the literature that accurate prediction of rib fractures using HBM, particularly in automotive impact scenarios, is challenging and often differs from reported fractures in PMHS tests for pendulum or side sled impact scenarios [33]. In other words, the prediction of rib fracture location and number of rib fractures has been challenging in the automotive environment. This outcome has been attributed to anthropometric variations of the thoracic cage (rib shape and size), geometrical variations such as cortical bone thickness and trabecular bone density, and variations in hard tissue material properties between subjects [33]. The loading in automotive scenarios typically occurs over large regions of the thorax causing large-scale deformation and motion of the thorax, and therefore, may depend on the size and shape of the thoracic cage, and the connectivity of the thoracic cage at the sternum and spine [45]. In contrast, the focal nature of BABT loading causes localized bending of the rib at the point of impact, such that the curvature/shape of the rib and connectivity at the sternum and spine play a reduced role in the fracture. In the case of BABT, a fracture is dependent on the cross-sectional area and material properties of the ribs, arguably making the prediction of rib fracture in BABT events less complex compared to automotive crash scenarios. The deformation and fracture pattern of the ribs observed in the BABT cases supports this explanation. Following rib fracture, the thorax compliance generally increased, and the ribs could continue to locally load the underlying lung tissue. However, there was no laceration criterion included in the lung model, and therefore, this could not be assessed. The presence or absence of rib fractures predicted by the model agreed with the BABT-ID; 7 out of 10 cases agreed, while a higher number of rib fractures were predicted in 3 out of 10 cases (BABT ID–004, BABT ID–027, and BABT ID–046) and are discussed on a case-by-case basis below.

Although the impact conditions were typically completed (loading, maximum deformation, and unloading) within 15–20 ms, a 50 ms simulation time was required to model wave propagation in the lungs, and to ensure the maximum transient pressure was achieved in all elements of the lungs for a given impact scenario. A script file was used with the thorax model to identify lung tissue elements that exceeded the transient pressure threshold and to calculate the corresponding lung volume. In general, the elements identified as exceeding the threshold and at risk of being contused were located within the impact zone on the thorax (Fig. 6(c)), as has been reported in the literature [3]. The predicted pulmonary contusion levels generally increased with increasing input energy to the thorax or BFD (Fig. 7(c)). However, pulmonary contusion injuries were not quantified in the available medical records, but instead were described qualitatively; therefore, could not be compared directly with the BABT-ID.

There were some differences between the computational model predictions and the reported injuries in the BABT-ID. For case BABT ID–004, it was reported that the survivor suffered a fracture of the ninth rib and internal organ injuries, but the model predicted two rib fractures sustained on the eighth and ninth ribs, a low level of pulmonary contusion (3.58%), and 311 J of work done on the thorax. The overprediction of the ribs fractured was attributed to the location of the BIBC, which was approximated based on the medical record description. A lower impact location would have isolated the ninth rib and possibly yielded a single rib fracture; however, for the purposes of this study, the impact locations were not readjusted or optimized from the reported data to match the reported injuries after the initial location was determined. For case BABT ID–027, which had the greatest experimental BFD measurement of the ten cases, the model predicted two rib fractures sustained at the sixth and seventh rib, pulmonary contusion of 9.59%, and 506 J of work done on the thorax. However, the BABT-ID reported liver contusion injuries with no ribs fractured. The discrepancy between the recreation results and the medical record may be attributed to the posture and environmental surroundings of the survivor while sustaining the injury. The medical record suggests the survivor was sitting within a vehicle during the BABT event, thus a sitting posture may have changed the thoracic compression, and penetration of a projectile within a vehicle could have reduced its energy compared to the experimental case. Lastly, for case BABT ID–046, the model predicted one rib fracture, 8.36% pulmonary contusion, and 198 J of work done on the thorax; however, there were no medical records available to confirm the presence of rib fractures. The absence of any significant injury sustained by the survivor of cases BABT ID–027 and BABT ID–046 suggests that other variables factored in the real-world scenarios that were not accounted for in the model boundary conditions. Live animal testing has considered porcine lateral thorax impacts to investigate the response and the potential for pulmonary contusion [8–10], and have identified the importance of impact location and influence of standoff on the resulting trauma.

Six of the ten recreated cases had reported injury ranks of 1, two had injury ranks of 2, and two had injury ranks of 3 (Table 3). Comparison of the injury ranks reported with those recreated resulted in eight of the ten cases yielding accurate predictions, and an underprediction for case BABT ID–017 and an over-prediction for case BABT ID–046. Unfortunately, complete medical records were not available for cases BABT ID–017 and BABT ID–046 and could not be assessed further. The discrepancies may be attributed to unknown factors of the real-life scenario that differed from the experimental recreation on gelatin, such as standoff that could be affected by the posture of the subject.

Computational modeling has been applied to understand armor impact scenarios [42], and to reproduce behind-armor reactions in gelatin [17], but has been limited in assessing BABT on humans. Specifically, detailed human models incorporating the necessary level of detail in the thorax have not been available, and have proven challenging with regards to applying BABT-type loading and relating the predicted trauma to that observed in experimental studies [40,69–71]. In developing an HBM for BABT simulations, Bracq [28,29] modeled rubber spherical impactors and PVC impactors and assessed the response of the HBM to high-velocity impacts, including lung and rib response. A study by Shen et al. [41] integrated projectile and soft armor finite element models to assess BFD predictions. However, a limitation acknowledged by Shen was that the study only investigated a single projectile–armor combination, while BABT scenarios encompass a large variation in boundary conditions at both the projectile–armor interface and the armor–thorax interface. This challenge was addressed in this study through the development of a methodology to apply representative BABT boundary conditions using measurements from specific projectile–armor combinations. In the future, it may be possible to generalize the developed BIBC methodology to undertake parametric studies of impact scenarios and injury risk. One of the challenges with current armor optimization is that it relies on single measurement of the maximum deformation in clay to correlate with a wide range of potential injuries including superficial contusion, laceration, rib fracture and pulmonary contusion. This study focused on rib fracture and pulmonary contusion as being those possible to investigate with a computational model. The proposed computational approach can shed light on the association of injury risk with different armor responses and ultimately contribute to enhance and optimize armor protection.

There were a number of limitations associated with this study. The axisymmetric assumption of the BIBC loading was a good representation for eight of the 10 impact cases; however, two cases were not symmetric and one of these was associated with an impact close to the edge of the armor. Future studies should employ two orthogonal cameras to confirm if the response is symmetric for a given impact scenario.

The recreations were limited to 10 impact cases, primarily due to the availability of the same physical armor make and model for experimental recreation of the impact scenarios. The projectile velocity was based on the velocities reported by the ammunition used in the incident. Shot distance was based on what was reported by the survivor and confirmed with police reports when available.

There is a general lack of consensus regarding pulmonary contusion injury thresholds in the literature. Strain based injury criteria have been proposed in the literature for lung injury, but these are mesh dependent, and their relevance to lung tissue are unclear because the strains induced in impacts are often smaller in magnitude than the strains induced in physiological respiration. The injury metric proposed in this study was developed by combining data from several sources. The loading condition used to develop the criterion was from experimental pendulum impacts to the thorax on PMHS, that associated pendulum impacts with an AIS 3+ injury to the thorax. Other studies have associated a contusion volume of approximately 20% with the onset of ARDS [67,68], an AIS 3 injury. The proposed criterion assumed that the AIS 3+ injuries from the pendulum impact could be associated with a 50% probability of ARDS, corresponding to 20% lung contusion [67,68] by volume. The transient pressure criterion proposed in this study has been previously applied to blast [42] and automotive impact [35] scenarios, and has provided reasonable predictions relative to experimental data. Although this determined threshold worked well in the context of this study, this is only a proposed approach to lung contusion that requires further assessment.

The ribs were characterized with an isotropic elastic-plastic material model including deformation rate effects [30], using a strain-based, deterministic failure criterion. The prediction of rib fracture in automotive scenarios has been challenging; however, the focal nature of BABT loading and localized bending loading of the ribs resulted in the ability to predict fracture using the elastic-plastic material model without the need to incorporate detailed and complex rib geometries and costal cartilage. A further limitation was the use of literature material properties for the ribs, which are often from aged subjects. Although it has been reported that, on average, material strength may vary with age (e.g., reduction in cortical bone strength in the ribs [72], it has also been shown that the variability in material properties with age increases by a similar magnitude. The efficacy of the model for injury prediction was demonstrated by good agreement between the model and the number of fractures reported in the BABT-ID database (Fig. 7). Future studies should investigate the effect of rib mechanical properties on fracture prediction.

Challenges in capturing other aspects of the BABT events, such as posture, body type, and environmental surroundings, became evident when comparing to real-world data. The model used in this study represented an average stature male. Anthropometric differences between the subjects in the database and the model, along with differences in position of the body at the time of impact should be considered in future studies.

The position of the BIBC impact in the model was determined from the subjective description in the incident report and the medical records. The BABT-ID database was assembled using postincident medical reports, and did not include CT or MRI scans. It is possible that minor fractures may not have been reported or detected. The descriptions were limited to the available police and medical reports corresponding to each incident. The uncertainty with regards to the projectile impact location was a limitation of this study, and we are planning on conducting position sensitivity analysis in the future to quantify the effect of small changes in impactor positioning. There was neither quantifiable data reported in the BABT-ID regarding pulmonary contusion nor ARDS, thus introducing a limitation of the study in verifying the predicted lung injuries. Additionally, the descriptive locations of the BABT events presented variability in the recreation outcomes, since the description of “around the ninth rib' “and ‘between the ninth and tenth rib” could lead to a difference of one rib fractured or no ribs fractured, respectively.

Overall, the integration of an HBM developed and validated for investigating BABT and a new method of applying BABT loading that simplified projectile–armor interaction proved effective in recreating real-world BABT events and predicting rib fractures and injury ranks that were in good agreement with available medical records.

A detailed thorax model with injury prediction capabilities for hard tissue fracture and a proposed pulmonary contusion criterion was assessed for ten cases from the BABT-ID, where the measured back face deformation for the actual projectile and armor combinations were implemented in a novel methodology to apply a BABT impact boundary condition (BIBC). The BIBC method comprised of a radial finite element shell mesh representing the back-face armor deformation at the impact location, without the need to model the complex response of the projectile and armor. The ratio of energy input into the thorax to pre-impact projectile kinetic energy was always below 1.0, as expected, since the armor absorbed some of the energy. However, the ratio varied from 0.18 to 0.97 demonstrating the wide variation in output for different projectile and armor configurations.

The computational thorax model demonstrated numerical stability when subjected to the ten BABT impact conditions. In general, the number of ribs fractured, percent pulmonary contusion, and therefore injury rank, all increased with increasing BFD, BFV, and energy input into the thorax. The thorax model predicted rib fractures that were generally in agreement with the medical reports from the BABT-ID.

Several limitations were identified in this study including: only ten cases were recreated owing to the available BFD data, which required testing with the specific armor and projectile from the case reported in the BABT-ID; and the locations of the BABT impacts were determined from the BABT-ID, but in some cases were approximated based on the medical records. The latter point is important since small variations in impact location could lead to outcome differences with respect to rib fracture.

The methods developed in this study can be used to prescribe and assess BABT loading conditions and the associated injury risk, and ultimately to support future armor system assessment.

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  Army Research Laboratory (ARL) (Contract Award No. W911NF-17-2-0229; Funder ID: 10.13039/100006754).

Cases from the BABT-ID were recreated by impacting each specific armor with the specific projectile at the velocity reported in the BABT-ID (Fig. 8). The armor was backed by ballistic gelatin, which was transparent and enabled high-speed imaging of the armor deformation during the impact event. Impact tests were undertaken following The 2004 Joint Service Wound Ballistics IPT Gelatin Testing Standard. The gelatin block (10% ballistic gelatin) was 406 × 152 × 152 mm (16 × 6 × 6 in) and was calibrated on one side using ball bearing (BB) impacts at 175–184 m/s (575–605 ft/s). The depth of penetration was confirmed to be within the acceptable range (74.6–95.25 mm) as required in the test standard, and upon completion of the calibration, the opposite side of the gelatin block was used for soft armor testing. Before the test, the gelatin temperature was confirmed to be within specification.

Three projectile test shots were undertaken prior to impacting the armor and gelatin to confirm the precise projectile impact location, absence of projectile yaw using witness cards, and the projectile velocity measured with a chronograph (Caldwell Ballistic Precision Chronograph, #721122) and confirmed with high-speed video (Phantom V1212, 512 × 384 pixel resolution).

The gelatin block was located on a specially constructed polycarbonate enclosure with the case-specific soft armor located on the strike face of the gelatin and held in place by Velcro straps, which did not affect the dynamic deformation of the armor during the impact. The high-speed camera was oriented perpendicular to the side of the gelatin block to view the armor and gelatin deformation during the impact (Fig. 8). Before impact testing, static images with reference scales at the impact location were taken using the high-speed camera to provide calibration data for the subsequent impact image analysis. The impact event was recorded at 35,000 frames per second and the high-speed camera was triggered by the projectile firing signal, with sufficient recording duration to capture the entire impact event.

The BIBC sensitivity to the density and Young's modulus used in its material model was investigated and its loading results validated against a rigid sphere impactor. The BABT-WALT thorax was loaded horizontally at a 45-deg angle between the frontal and sagittal plane using the BIBC with varying density and Young's modulus. Investigation of the sensitivity to density demonstrated a negligible change in contact force response between a density of 8.9 × 10⁻⁸ ton/mm³ and 8.9 × 10⁻¹⁰ ton/mm³ (Fig. 9). Similarly, investigation of the sensitivity to Young's modulus demonstrated a negligible change in the force response between a modulus of 1000 MPa and 200,000 MPa. Therefore, it was concluded that the material properties used for the BIBC did not produce unassociated effects during impact.

The BIBC loading method was validated against a spherical projectile impact at the same 45-deg angle on the BABT-WALT thorax. The contact force responses between the outer muscle tissue and ribcage, outer muscle tissue and sternum, and ribcage and lungs were compared for both methods of loading (Fig. 10). The force responses were measured for a duration that fully encompassed the loading phase and the majority of the unloading phase. This investigation yielded reasonable agreement of the contact force with minor differences attributed to the mesh differences between the rigid sphere and the BIBC. The rigid sphere mesh pattern was automatically generated and enhanced for its hexahedral elements, whereas, the BIBC concentric circle mesh was enhanced for recreating an evolving asymmetric surface over time.