ABSTRACT
Introduction
High-rate non-penetrating blunt impacts to the thorax, such as from impacts to protective equipment, can lead to a wide range of thoracic injuries. These injuries can include rib fractures, lung contusions, and abdominal organ contusions. Ovine animals have been used to study such impacts, in a variety of ways, including in silico. To properly model these impacts in silico, it is imperative that the tissues impacted are properly characterized. The objective of this study is to characterize and validate two tissues impacted that are adjacent to the point of impact—costal cartilage and hide. Heretofore, these materials have not been characterized for use in computational models despite their nearly immediate engagement in the high-rate, non-penetrating loading environment.
Materials and Methods
Ovine costal cartilage and hide samples were procured from a local abattoir following USDA regulations. Costal cartilage samples were then cut into ASTM D638 Type V tensile coupons and compressive disks for testing. The cartilage tensile coupons were tested at 150 ε/s, and the compressive samples were tested at −150 ε/s. Identical coupons and disks were then simulated in LS-Dyna using a hyperelastic material model based on test data and experimental boundary conditions. Hide samples were shaved and cut into ASTM D638 Type V tensile coupons and validated in silico using identical boundary conditions and an Ogden rubber model based on test data.
Results
The structural responses of costal cartilage and hide are presented and exhibit typical behavior for biological specimens. The respective model fits in LS-Dyna were a hyperelastic- based “simplified rubber” for the costal cartilage and an Ogden rubber for the hide. The costal cartilage had a mean failure strain of 0.094 ± 0.040 in tension and −0.1755 ± 0.0642 in compression. The costal cartilage was also noted to have an order-of-magnitude difference in the stresses observed experimentally between the tensile and compressive experiments. Hide had a mean failure strain of 0.2358 ± 0.1362. The energies for all three simulations showed material stability.
Conclusions
Overall, we successfully characterized the mechanical behavior of the hide and costal cartilage in an ovine model. The data are intended for use in computational analogs of the ovine model for testing non-penetrating blunt impact in silico. To improve upon these models, rate sensitivity should be included, which will require additional mechanical testing.
In patients under 25 years of age, trauma is the leading cause of death, where most trauma is blunt force trauma, some of which occurs during conflict.1 Fatalities from penetrating wounds do occur; however, there are protective measures to reduce mortality rates in the case of high-rate non-penetrating blunt trauma for use in military and police applications. These measures such as body-borne armor reduce gunshot fatalities from 80% to 32%.2 However, when such protective equipment is used, it deforms rapidly, impacting the body. The residual energy from the equipment deforming can lead to internal injuries, such as lung contusions and rib fractures. Other high-rate non-penetrating blunt impacts to the thorax, such as from sports or automotive collisions, can result in a similar range of injuries, including rib fractures, lung contusions, and abdominal organ contusions.
Experimental and computational models have been used to better understand injury mechanisms and develop enhanced injury criteria. Historically, clay blocks and animal models have been used to study high-rate non-penetrating blunt injuries.3 Various types of animal models have been used in this field, including porcine models for neurological studies,4,5 caprine models for the development of the 44-mm back face standard,6 and caprine models for cardiopulmonology injury studies.7 A recent study has favored ovine models because of their similarities to humans in torso size and shape and similar pulmonary anatomy for pulmonary injury studies.8 To study high-rate blunt trauma further and better predict injury, computational models are being developed. However, such models require detailed descriptions of the anatomy and material properties of species that are not well characterized.8,9
In scenarios where the thorax is loaded at a high rate, the tissues known to absorb the greatest amount of energy are adjacent to the impact and include adipose tissue, ribs, costal cartilage, and hide; therefore, it is imperative that these tissues are properly characterized. Ovine rib characterization has been reported in the recent literature, and adipose tissue has been studied in porcine models,10–12 although not in the ovine species. Previous studies that have studied cartilage have utilized spherical indentation,13–15 cantilever loading,14 and quasi-static tension16 and compression17 tests on human tissue. The shear modulus was reported to be 1–3 MPa,15 the tensile strength was reported to be 4.27–7.2 MPa,16 and the reported elastic modulus in compression was reported to be 11.43 MPa.17 As for skin or hide, previous studies have investigated human, rat, goat, anuran (frog), rabbit, and porcine.18,19 Strain rates ranging from 0.01 to 4000 strain/s have been tested, with the resulting ultimate tensile strength ranging from 1 to 126.5 MPa.19
However, this previous research leaves a clear gap in knowledge for two other tissue types that are indicated as key load paths in non-penetrating blunt impacts, the cartilage and hide. Therefore, the focus of this research is on these latter two tissue types. The work proceeds with two main objectives: One experimental and the other computational. The first objective is to characterize the structural response of ovine hide and costal cartilage. The second is to utilize these data to fit constitutive models for these tissue types for use within ovine thorax finite element models (FEMs) to study high-rate blunt impacts.
METHODS
Cartilage Sample Procurement and Preparation
Young, hair-breed ovine complete rib cages with costal cartilage samples were obtained from a local abattoir following USDA regulations. The ribs were separated and used for a separate set of experiments (Fig.1, left).10 The cartilage specimens were prepared for high-rate tensile and compressive testing (Veryst Engineering, Needham, MA). The cartilage was removed between the sternum and the end of the ribs, avoiding the bony fragments within the sternum. The samples were cut to the size of a half-length ASTM D638 Type V tensile coupon using a die cut (Fig.1, right). Disks with a 1/4-inch diameter for compression testing were also cut from the cartilage samples.
FIGURE 1.
Left: Rib cage with the costal cartilage; right: Half-length ASTM D638 Type V costal cartilage samples.
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Cartilage Sample Testing and Analysis
After preparation, the samples were loaded at target strain rates of 150 s−1 in tension (N = 7) and compression (N = 5). Testing utilized a customized drop tower setup. The outputs included engineering stress and strain, and a two-term Ogden rubber material model was fit to all the tensile 150 strains (ε)/s data traces using MCalibration (PolymerFEM LLC, Needham Heights, MA). This was repeated for the compressive −150 ε/s data traces. The Ogden fit formed the basis for subsequent constitutive modeling of the cartilage.
Cartilage Simulation Validations
A representative structural response in terms of engineering stress vs. strain formed the basis for subsequent simulation work. The median stress–strain curve from experiments was selected for use in LS-Dyna. The median curve was selected based on the linear region after the toe region, where the median slope was utilized. The linear region stiffness was calculated using a linear fit to the last 100 data points in the experiment, where the stiffness was the slope of the fit line. Simulations were designed to match the experimental boundary and loading conditions. The aforementioned stress–strain data curve from a median response among the experimental data traces was input into LS-Dyna’s simplified rubber material model. This material model takes in an engineering stress and strain curve and fits an Ogden rubber model to the response. The damping coefficient (0.2), Poisson’s ratio (0.495), and bulk modulus (0.432 GPa) were all input based on the software manual requirements and to best represent the experimental data.20 Poisson’s ratio was selected based on the manual and literature, where 0.495 was within the range of what has been seen in cartilage.21 The bulk modulus was calculated using the general elastic equation, where it was converted from the elastic modulus (eqn (1)). In this case, the elastic modulus was the maximum slope of the stress–strain data trace input into LS-Dyna.
$$K = {\ }\frac{E}{{3\left( {1 - 2\nu } \right)}}$$
(1)
Material failure was accounted for using the MAT_ADD_EROSION card, where the median failure strains for tension and compression were referenced for individual element deletion. Median failure strain for tension and compression were determined through analysis of the experimental data. The same fitted material model was used for both tension and compression simulations, as this was required for further use in large-scale simulations.
The length of the tensile cartilage coupon was 55.5 mm with a gauge length of 17.5 mm. The nodes at each end of the coupon were pulled in tension at a rate of 8.325 mm/ms or 150 ε/s to match experimental loading. The model included 1,280 hexahedral solid elements with an average edge length of 1.4 mm. The compression disk had the same dimensions as the experimental setup, with a 1/4-inch diameter and included 1664 hexahedral solid elements. For both simulations, the resulting engineering stress–strain curves were plotted against experimental data and visually assessed to validate the model response. Model stability was evaluated quantitatively by reporting the ratio of hourglass energy to total energy and ensuring that total energy is the sum of the kinetic and internal energies.
Hide Sample Procurement and Preparation
Ovine hide samples were obtained in the same manner as the costal cartilage, following USDA regulations and refrigerated. The hide samples were prepared using 2 approximately 22.5-cm2 samples of hide that were cut bilaterally from one animal caudal to the shoulder, and regions of interest for testing were shaved.
Hide Sample Testing and Analysis
The shaved hide specimens were sent for high-rate tensile testing (Veryst Engineering, Needham, MA). They were then cut into ASTM D638 Type V dog bones for high-rate tensile testing, all in the same direction to avoid response differences from fiber directionality because of Langer’s lines.22 The hide samples were loaded at target strain rates of 40 and 100 s−1 (N = 6 and 4, respectively). Testing utilized a customized drop tower setup, similar to the costal cartilage tests. The sample stress–strain data were then fit using a three-parameter hyperelastic Ogden rubber using MCalibration software (PolymerFEM, Needham, MA), and the initial shear modulus was calculated using eqn (2),23
$$2\mu =\sum{_1^{i = 3}} {\mu _i}{\alpha _i}\\[5pt]$$
(2)
In equation2, |$\mu $| is the shear modulus and each |${\mu _i}$| and |${\alpha _i}$| are considered to be material constants.23 The samples were then analyzed for rate dependence based on the strain rates and the initial shear modulus using a standard least squares regression model.
Hide Simulation Validations
The material model was fit for all data curves in tension using MCalibration (PolymerFEM, Dover, MA), and a three-parameter Ogden rubber material was used. The median stress–strain curve was selected for simulation work following the same methods that were used for cartilage. Since there were an even number of samples, a more stable model is reported. Simulations were then set up to match the experimental testing, with matching boundary and loading conditions. For hide, only tension was simulated since there was no compression testing because of the use of shells in the computational model. A similar coupon setup was used for hide with dimensions matching the ASTM D638 Type V standard.22 The hide coupon was composed of 508 shell elements, with no solid elements. The resulting stress–strain curve from the simulation was then plotted against experimental data. Model validation and stability evaluation were performed in the same manner as previously described for the costal cartilage. Model stability was evaluated by reporting the ratio of hourglass energy to total energy and ensuring that total energy is the sum of the kinetic and internal energies, similar to the methods used for modeling costal cartilage.
RESULTS
Cartilage Experimental Results
The stress–strain data curves from the experimental tensile and compressive experiments are shown in Fig.2 as dashed lines. In tension, the mean failure strain was 0.094 ± 0.040. A toe region was seen in some of the tension traces, where the sample stiffened as it was strained. In other traces, there was a generally linear response with a negligible toe region. As seen in Fig.2 on the left, some of the sample data traces were particularly “wavy,” which may be attributed to the inertial pressure wave propagation through the sample. However, this may influence the failure values of the samples because of the nonuniform stress state each sample with “wavy” behavior is in. This behavior was not seen in the compression samples. In compression, the mean failure strain was—0.176 ± 0.064. These samples had a toe region and then became strain-stiffened as they were compressed. The compression test data traces were much more consistent than the tensile samples, apart from one outlier.
FIGURE 2.
Cartilage simulation data trace (solid lines) and the experimental data traces (dashed lines) for tensile tests (left) and compression tests (right).
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Cartilage Simulation Results
The resulting data points from the median experimental tensile and compressive testing regimes were consolidated into one load curve for use in the simplified rubber material model in LS-Dyna following the methods described previously. The density of the cartilage was set at 1.04 × 106 kg/mm3, and the bulk modulus was calculated from eqn (1) as 0.432 GPa. The complete set of data used within the card is provided in the Supplementary data. Identical material cards were used for both the tensile and compression simulations, and the resulting stress–strain curves are seen in Fig.2 as solid lines.
Overall, the simulations match the experiments well. The simulations experienced material failure at strains that were expected based on the experimental data, at 0.1 and −0.13 strains, respectively. For both the tensile and compressive simulations, the hourglass energy to total energy ratio was 0. At failure in the tension simulation, the internal energy was 0.26 kJ, the kinetic energy was 0.21 kJ, and the total energy was 0.47 kJ These results showed the stability and accuracy of the model since the sum of the internal and kinetic energies was the same as the total energy. For the compression simulation, the internal energy was 0.107 kJ, the kinetic energy was 0.005 kJ, and the total energy was 0.112 kJ, which also showed model stability and accuracy.
Hide Experimental Results
The shear moduli that were calculated from the hide tensile experiments were considered different between the samples loaded at 40 and 100 ε/s (P = .011). At 40 ε/s, the calculated shear modulus was 5.85 ± 1.60 MPa, whereas it was 9.28 ± 1.66 MPa for the samples loaded at 100 ε/s. Therefore, the material response was considered rate-dependent in the tensile loading direction. This difference can also be seen in Fig.3 (left). The mean failure strain from all samples, regardless of the loading rate, was 0.236 ± 0.136.
FIGURE 3.
Left: Experimental data traces of high-rate tensile tests of hide at 40 ε/s (solid) and 100 ε/s (dashed); right: Hide simulation (solid) and experimental data (dashed).
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Hide Simulation Material Model
The hide FEM was run at both loading rates, 40 and 100 ε/s (Fig.3, right). While there is rate dependency, based on the final applications of the material model, it is not considered to be great enough to affect the FE ovine model. Because of not being able to include any strain rate dependency based on the material testing completed, they are identical. Visually, the simulation stress–strain curve falls within the experimental data, and fails at 50% strain, falling within the realm of the experimental data. The total energy at failure was 0.040 kJ. The internal and kinetic energies were 0.028 and 0.012 kJ, respectively, which sum to match the total energy at failure. Since the measured and calculated total energies are the same, the model is considered stable.
DISCUSSION
We present the experimentally observed structural response and in silico response of both ovine costal cartilage and hide in tension and compression. These are the first ovine-specific material characterizations and validated material models presented in the literature for use in a commercial dynamic finite element solver (LS-Dyna) for high-rate impacts. The costal cartilage utilized a simplified rubber material model, and the hide utilized an Ogden rubber material model.
For future applications, we require one material model that represents both the tensile and compressive behaviors of the costal cartilage well. There was asymmetry about zero strain between the two loading directions (Fig.4). This behavior created challenges for one material model to accurately simulate both loading directions.
FIGURE 4.
Consolidated compression and tension costal cartilage stress–strain curves.
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As seen in Fig.4, there is an order-of-magnitude difference between the magnitudes of the tensile and compressive stress–strain curves. Several different material models were investigated to determine which would best predict the behavior of the cartilage in both loading directions. The materials investigated within the LS-Dyna software included hyperelastic rubber, Ogden rubber, crushable foam, and Hill foam. Each of these were ultimately found to not represent the costal cartilage well in both directions, where often the compression direction was predicted to be up to an order of magnitude stiffer than the experimental data. The best material that predicted the costal cartilage in both orientations was the simplified rubber material model.
As for the hide material, the calculated modulus for ovine hide fell within the range of shear moduli seen in human skin. Human skin has been seen to have a shear modulus between 1.68 kPa and 46.98 MPa depending on region, loading orientation, and age of the individual.24 In contrast, our samples ranged from 3.22 to 11.11 MPa, falling into the range seen in human tissue. Since our samples were from young animals, there was minimal breakdown of collagen and other extracellular matrix components within the hide, keeping our range smaller than what might be seen in older human subject skin characterization tests. The resulting data traces were used to fit an Ogden rubber model because of the hyperelasticity of the hide from these tests.
The hyperelastic Ogden rubber model reliably represented material testing in simulation and was stable through the length of the simulation until element failure, which was based on experiments. The initial stiffness of the hide during the simulated tensile test was similar to what was seen experimentally; however, the magnitude of the simulated test was higher right before failure. It did fail at an appropriate strain within the scope of the data with a similar data shape to the experiment. To improve upon this model, additional experiments that include stress relaxation testing would need to be completed to fit a Prony series for viscoelastic characteristics. Currently, the model only utilizes data from one loading velocity, despite the strain rate sensitivities that were seen to exist in hide tissue.
Another limitation of this study is the assumption of uniform stresses and strains throughout the sample. For both the hide and costal cartilage materials, the hyperelasticity component leads to a nonuniform stress state, which influences the failure of the material. However, because of the high rate of loading, the sample does not have time to reach equilibrium before failure. To decrease nonuniformity, the sample size can be made smaller to reduce the time needed to reach equilibrium; however, it would be difficult to maintain the specimen integrity within the grips of the testing device throughout the duration of the test. This would be the case with other test devices, such as the split-Hopkinson bar, as the speed of loading will still cause nonuniform stress profiles and requires an area of the specimen to grip in order to load it. In future studies, additional methods can be used in this style of test to investigate the nonuniformity of the samples using digital image correlation.
Both the cartilage and hide validated material models will be useful in larger FE models that are ovine-specific and in high-rate loading environments, such as what occurs from high-rate impacts on protective equipment. These data will also be used to more accurately study the mechanisms of injury related to high-rate non-penetrating blunt impacts within ovine models.
ACKNOWLEDGMENTS
The authors would like to acknowledge the contributions of Veryst LLC. for assising with the experimental testing.
CLINICAL TRIAL REGISTRATION
Not applicable.
INSTITUTIONAL REVIEW BOARD (HUMAN SUBJECTS)
No human subjects were involved with this study.
INSTITUTIONAL ANIMAL CARE AND USE COMMITTEE (IACUC)
Not applicable.
INDIVIDUAL AUTHOR CONTRIBUTION STATEMENT
P.K.T. assisted with the conceptualization, data collection and analysis, and the manuscript writing. J.C. assisted with the data collection. B.K. and B.W.v.K. assisted with data analysis. C.M.W. and M.K. assisted with the conceptualization, funding, and manuscript writing. F.S.G. assisted with the conceptualization, project administration, corresponding author, and manuscript writing.
INSTITUTIONAL CLEARANCE
This paper was approved by DEVCOM ARL.
SUPPLEMENTARY MATERIAL
Supplementary material is available at Military Medicine online.
FUNDING
Funded by the U.S. Army Combat Capabilities Development Command Army Research Laboratory, #W911NF2120034.
SUPPLEMENT SPONSORSHIP
This article appears as part of the supplement “Proceedings of the 2023 Military Health System Research Symposium,” sponsored by Assistant Secretary of Defense for Health Affairs.
CONFLICT OF INTEREST STATEMENT
The authors have no competing interests to disclose.
DATA AVAILABILITY
The data will be available upon request to the corresponding author.
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Author notes
Presented as a poster at the 2023 Military Health System Research Symposium, Kissimmee, FL; MHSRS-23-09434. The views expressed in this material are those of the authors and do not reflect the official policy or position of the U.S. Government, the DoD, or the Department of the Army.
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