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Research Papers

Effects of Loading Conditions and Skull Fracture on Load Transfer to Head OPEN ACCESS

[+] Author and Article Information
Timothy G. Zhang, Kimberly A. Thompson, Sikhanda S. Satapathy

U.S. Army Research Laboratory,
Aberdeen Proving Ground,
Aberdeen, MD 21005

Manuscript received March 22, 2017; final manuscript received August 8, 2017; published online October 4, 2017. Assoc. Editor: Alba Sofi. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

ASME J. Risk Uncertainty Part B 4(2), 021007 (Oct 04, 2017) (10 pages) Paper No: RISK-17-1049; doi: 10.1115/1.4037647 History: Received March 22, 2017; Revised August 08, 2017

This study focuses on the effect of skull fracture on the load transfer to the head for low-velocity frontal impact of the head against a rigid wall or being impacted by a heavy projectile. The skull was modeled as a cortical–trabecular–cortical-layered structure in order to better capture the skull deformation and consequent failure. The skull components were modeled with an elastoplastic with failure material model. Different methods were explored to model the material response after failure, such as eroding element technique, conversion to fluid, and conversion to smoothed particle hydrodynamic (SPH) particles. The load transfer to the head was observed to decrease with skull fracture.

Impact-induced head injury has been hypothesized to involve one or more injury mechanisms, including skull fracture, bridging vein rupture, diffuse axonal injury, cavitation, etc. Even though a significant amount of research has been reported for many of these injury mechanisms in animal models, postmortem human subject (PMHS) and surrogate systems, a clear picture of loading conditions leading to head injury has yet to emerge. Impact experiments were conducted on cadavers to study the skull fracture [13]. In some of these experiments, the cadaveric heads were defleshed. The methodology to map the experimental observations on surrogates to the response expected from a live human is not yet available. One of the primary impediments in developing such map is a lack of tissue and injury models applicable to the relevant loading conditions. As a first step toward developing such a map, mathematical models are need to be developed to simulate these injury types so that the relationship between loading conditions and injury types can be assessed.

Head injury criterion (HIC) [4] was derived from the integration of the resultant linear acceleration at the center of gravity of the dummy head, not considering the rotational acceleration. The HIC is not based on the injury mechanism. A generalized linear skull fracture criterion, the skull fracture correlate was developed in Ref. [5] based on the PMHS data by averaging the acceleration over the HIC time interval.

Tensile fracture is a typical failure mode expected in the brittle bone material. Most reported material models for bone utilize an isotropic elastic or an elastic–plastic stress–strain relationship. A principal strain and principal stress-based failure criteria are commonly used for simplicity. Fracture occurs when the maximum principal strain exceeds a critical value. However, this critical value has been reported variously in the literature, for example, as 0.5% for skull [6], 1.6% for cortical bone, and 4.5% for cancellous bone [7]. Similarly, a maximum principal strain of 0.42% for skull cortical layer, a maximum principal stress of 20 MPa for skull diploe layer, and a plastic strain of 1.2% for facial bone were used to model fractures in Ref. [8]. Von Mises stress and maximum pressure criteria were used for lower leg fractures in Ref. [9]. Effective plastic strain was used for the failure criterion in Ref. [10]. Statistical analysis of experimental data shows that 448 mJ of skull internal strain energy has a 50% probability to cause skull fracture as reported in Ref. [11]. However, the internal strain energy is calculated for the whole skull, which is not practical for use in the finite element model. Orthotropic material models were also used for bone material in Ref. [12], where the material failure was based on Tsai–Wu criterion. Fracture criterion with peak force, peak acceleration, and HIC were presented for skull fracture in Ref. [13].

In this paper, we explore the role of potential skull fracture arising out of impact loading conditions on the load transfer to the head. Two impact conditions were studied: the head-impact against a rigid wall, and the head impacted by heavy, rigid projectiles. Cases with and without skin and flesh were used to understand their effect on load transfer. Cadaver skulls were sometimes fixed during the impact tests [1,14]; however, the boundary conditions at the neck area are not fixed when a live human head is impacted. Therefore, both fixed and free-boundary conditions were included in the study to understand the effect of two extreme cases. In the computational head model, different failure models were investigated using plastic strain as the failure parameter. The skull in the impact zone was modeled with a cortical–trabecular–cortical layered structure.

The main goal of this study is to investigate the effect of a skull fracture on the load transfer to the head for low-speed impact against a rigid wall and impact by low-speed projectiles. Various methods were explored to model the skull fractures in LS-DYNA.

Geometry and Finite Element Model.

The head geometry used in this paper was obtained from a magnetic resonance imaging of a human head [15]. The head geometry was simplified in our study, as shown in Fig. 1(a). Four major components of the head are modeled: skin/flesh, bone, cerebrospinal fluid (CSF), and the brain. The skull is anatomically connected to the body through seven cervical vertebrae and six cervical disks. In experiments [1,14], the cervical spines are removed, and the base of the skull is fixed or attached to load application device. Therefore, the neck rotational dynamics is not captured in those measured load pulse data. In our model, the complex cervical geometries are simplified into a cylinder, i.e., the cervical spines are fused with the skull, and hence, their rotational dynamics will not be captured, but it provides a convenient way to study the bounding cases of skull constraint for translational motion. The mandible was not present in the experiments reported in Ref. [1]. We included the mandible bone in the model to represent experimental condition in Ref. [14]. However, it was rigidly connected to the skull in the model, and hence, any late time-relative motion between the skull and the mandible will not be captured. The effect of brain folds on load transmission is not expected to be significant and hence was not included in the model for computational simplicity. This head geometry is the same as the one used in our earlier study [15]. The head impacted a rigid wall at 45 deg with an initial velocity of V0.

The skull is composed of three main layers: two cortical layers sandwiching a trabecular layer. For computational efficiency, the skull can be modeled as an isotropic material by averaging the material properties of the individual layers. Such homogenized models are sometimes useful for capturing deformation response, but are not suitable to capture fracture and failure that would manifest differently in the cortical and trabecular layers. Therefore, to better capture the fracture, we utilized a three-layered structure near the impact region, where the material failure is most likely to occur, as shown in Fig. 1(b). The sum of the thicknesses of the cortical layers is similar to that of the trabecular layer.

Because of the complexity of the geometry, the head components are discretized into tetrahedral meshes as shown in Fig. 2(a). The skull part with a three-layer structure is meshed with hexahedral elements, as shown in Fig. 2(b). The numbers of elements along the thickness direction for the top cortical, trabecular, and bottom cortical layers are 3, 6, and 3, respectively. Tied contact algorithm was used at the interfaces where the hexahedral and tetrahedral meshes meet.

Only one half of the geometry was modeled to take advantage of sagittal symmetry of the head. The typical element length is about 2.5 mm, but the mesh size near the three-layer skull zone is smaller, about 1 mm long. The total number of elements and nodes are about 1.1 × 106 and 0.2 × 106, respectively.

When the skin and flesh are not included, as shown in Fig. 3, the impact location is shifted from point A to B due to the geometry difference.

In addition to the rigid wall impact, projectile impact to the defleshed head was also considered. Two projectile cases with same mass and diameter but different nose shapes—hemispherical, and flat—, as shown in Fig. 4 were modeled and compared with impact against a rigid surface. The projectile diameter was 48 mm, as used in Ref. [1]. In Fig. 4, the projectiles impacted the front of the head at 45 deg.

Free- or fixed-boundary conditions were applied to the bottom surface of the cylindrical bone representing fused cervical spine with the skull, as shown in Fig. 5, to explore the effects of boundary condition. Surface-to-surface contact was defined between the skull and CSF to allow separation and sliding between the two materials.

The skull is modeled as a multilayered and anisotropic material. For simplicity, it is sometimes modeled as isotropic material as in Ref. [16]. In this paper, a three-layered structure was utilized to model the skull near the impact zone, as shown in Fig. 1(b). Each of the three layers was modeled as an isotropic material. The stress–strain curve from tensile tests [17] was used for the skull properties, as shown in Fig. 6; however, the material model was simplified into an elastic model with plastic hardening. The use of tensile test data for compression and the use of a fracture model based on a critical strain value may not represent material response accurately. However, in this initial study, we have attempted to explore the role of fractures on loads transmitted to the brain, using fracture indicators, which may be sufficient for trend study. Young's modulus, yield stress, plastic-hardening modulus, and failure strain were read from the experimental data in Ref. [17] for the cortical bones (outer table), trabecular bones (diploe), and whole bone (composite). The material properties, including the density and Poisson's ratio υ are listed in Table 1.

The other material models used for various components are listed below; more details can be found in Ref. [15]. The skin is modeled as an elastic material with the following properties:

Skin:ρ=1130kg/m3,E=16.7MPa,ν=0.499

The skin can be modeled as viscoelastic material [18]. However, in our study, the response duration is of the order of ms, whereas the typical viscoelastic decay constant is 5 s [18]. That results in a small change in the modulus during the time of interest. However, long time response would require incorporation of a visco-elastic model, which is not the focus of the study. The brain is modeled as a viscoelastic material with the following properties:

ρ=1040kg/m3, K=2.19GPaG0=41kPa,G=7.8kPa, β=700/s

where K, G0,G, and β are bulk modulus, short-term shear, long-term shear modulus, and decay constant, respectively.

The Gruneisen equation of state is used to model the volumetric response of CSF. The constants are

ρ=1000kg/m3,C=1484m/sS1=1.979,γ0=0.11

where C is the bulk sound speed, S1 is the slope of particle-speed, and shock-speed curve, γ0 is the Gruneisen coefficient.

The cavitation pressure can vary from −0.1 MPa for distilled water saturated with air to −20 MPa for distilled water degassed at 0.02% saturation under acoustic wave [19]. For most experiments, the cavitation pressure for water is reported to be between −1 MPa and −0.1 MPa due to the existence of cavitation nuclei [20]. The cavitation pressure level for CSF was found to have a significant effect on the transmitted stress in the CSF and the brain. In this work, −0.1 MPa is chosen as the cavitation pressure for CSF.

Modeling Bone Fracture.

Material failure was modeled for the skull but not for the skin, CSF, or the brain in this study. Modeling bone fracture is a challenging task. Bone is a brittle material in which crack initiation and propagation as observed in experiments [2] need to be modeled in order to capture the bone fracture. Instead of modeling crack initiation and propagation explicitly, which is computationally expensive, we adopted a simpler approach to obtain the general trends.

Three different methods were explored to model the skull fracture. First, the element is removed from the calculation when the failure criterion is satisfied. Element removal causes a sudden loss of mass, momentum, and energy. Therefore, numerical convergence could be slow and more expensive computation necessary to maintain desired accuracy. However, this method is efficient and widely used in the literature, for example, to model failure of tibia in Ref. [21]. Linear fractures in the skull were reproduced with element erosion in Ref. [12]. In the second method, the element is not deleted when the failure criteria are met. Upon meeting the failure criteria, the material model is changed to that of a fluid [22,23], i.e., the element loses its ability to carry tensile and shear stresses. In this method, mass and momentum of failed material is retained. However, the loss of shear strength could cause large deformation and ensuing reduction in time-step size. In the third method, the elements are converted into smoothed particle hydrodynamics (SPH) particles when the failure criterion is satisfied. The SPH particles carry mass, velocity, strength, and can interact with neighbor elements. Conversion to particles alleviates the mesh distortion issues with lesser penalty on efficiency and accuracy compared to the previous two methods. This algorithm is commonly employed to model brittle material fracture with reasonable results [24,25]. As a bench mark, we have also included results for the case, where material failure was not modeled by setting the failure strain to a large number. The four cases above are denoted as “erosion,” “fluid,” “SPH,” and “no failure,” respectively, in this paper.

The impact velocity was systematically increased by 1 m/s, starting with an initial value of 1 m/s until failure occurred in the skull when the head with skin was impacting against a rigid wall. It was found that the skull fractured when the impact velocity was raised to 3 m/s.

Impact Against a Rigid Wall
“No Failure” Case.

The results for the “no failure” case are presented in Fig. 7, which shows the time histories of rigid-wall forces for various impact velocities. After impact, the head deforms and the rigid-wall force increases. After peak force, the head starts to recover. When the wall forces become zero, the head is separated from the rigid wall. As the impact velocity increases, the force peak amplitude increases, the peak is reached earlier, and the pulse duration becomes shorter.

Figure 8 shows the time history of the rigid-body velocity of the brain, normal and tangential to rigid wall for various impact velocities. The absolute value of the normal velocity decreases as the head is deformed after impact. As the normal velocity increases from 0, the head starts to rebound from the rigid wall. The tangential velocity is not zero, indicating that the head is sliding/moving along on the rigid wall.

Figure 9 shows the peak pressure as it propagates along the line of impact for impact velocity of 3 m/s. The locations where the pressure values are plotted are shown in Fig. 10. The pressure profiles are similar to the rigid-wall force. The pressure in the skin/flesh, especially in the bone is at least one order higher than in the CSF and brain. As the pressure propagates into the CSF and brain, its amplitude drops. In the brain, the pressure profiles are similar, but the magnitudes decrease as the pressure propagates.

Figure 11 shows the peak pressure along the impact line as a function of its distance from the rigid wall. For all velocities, the trends are similar. The pressure increases when it propagates into larger acoustic impedance material, i.e., from the skin to bone, and decreases again when it propagates into smaller acoustic impedance material, such as trabecular and brain. The pressure in the skull components are the highest.

Figure 12 shows the in-plane and normal strains at 1.3 ms along the top and bottom cortical bone surfaces. The x and y coordinates are in-plane, and the z coordinate is in the normal direction for the curved-coordinates system, as shown in Fig. 13. The x strain (along the bone direction in the symmetry plane) is negative (compression) for top cortical, but is positive (tension) for the bottom cortical layer, which indicates that the bone (cortical, trabecular, and cortical) is undergoing bending. Both x-strain and z-strain exceed the failure strain of cortical bone. Therefore, the fracture would start from the top cortical bone, as will be shown in Sec. 4.1.2 for the case where material failure is included.

Since the top cortical bone exceeds the prescribed fracture strain for the 3 m/s case, this velocity is used for all subsequent cases in which fracture models were used for the skull.

Failure Case.

In this section, material failure is included. As discussed earlier, three different methods were used to model bone failure: fluid, erosion, and SPH.

Figure 14 shows the time history of rigid-wall forces for no failure, fluid, erosion, and SPH cases. When the material fails, the material's capability to undergo loading is weakened or is totally lost. Material failure causes the fast drop in the rigid-wall forces. In the fluid and erosion cases, the force recovers after a sudden drop to a lower value than the peak before decreasing again. However, for the “SPH” case, the force-drop is monotonic after failure and after a plateau for about 1.5 ms, continues to drop again.

Figure 15 shows the deformations and material failures in the contact area. If bone failure is not included, the skin/flesh is compressed after it impacts the rigid wall. The skin/flesh rebounds and is separated from the rigid wall after 3 ms. When a failure model is included, the cortical and trabecular bones start to fail around 1.3 ms. For the fluid case, failed elements behave like fluid, which can support only compressive pressure. The elements are easier to distort. When the elements are eroded after the material failure, the neighboring elements can easily deform. At 1.5 ms, a gap is clearly formed between the bottom cortical bone and the CSF. When the failed elements are converted to SPH particles, the adjacent elements still have interaction with the particles. At 1.5 ms, the skin does not contact the bottom cortical bone with particles in between, but it does contact the bottom cortical bone when the failed elements were eroded. The contact between the particles and elements slows down the movement of the skin and flesh. A similar gap is also seen between the cortical bone and the CSF.

Figure 16 shows the pressure time history for the four cases. The pressure drops as it travels from s3 to s7 along the impact line. When material fails, the pressure in the brain oscillates a lot due to sudden material removal or material weakening, which causes the shear stress, tensile stress, or all stress reset to be zero.

For erosion method, the material is removed from the model when it fails. This method is very efficient compared to the SPH method. The meshes can distort when they behave like fluid. For the remainder of the paper, only the erosion method will be used to model the material failure.

Skin and Flesh Effects.

Figure 17 shows the time histories of rigid-wall forces for various impact velocities for full cadaveric head and defleshed head. For the defleshed case, the rigid-wall force, which is also equal to the force on the head, has a smaller amplitude and a shorter duration. When the impact velocity increases, the force increases irrespective of presence of flesh. The time duration of the force pulse, the time between impact and rebound from the rigid wall, does not change appreciably when the flesh is absent. This is not the case for the case when flesh is present. The total mass of the defleshed head is about 45% less than that of the full head in the model. Consequently, the peak force is larger for the full head compared to the defleshed head. The pressures in the brain along the impact line are slightly larger for the defleshed head, as shown in Fig. 18, compared to the full head case, shown in Fig. 9(b). A shock wave is generated when the bone impacts the rigid wall for the defleshed case, which propagates into the brain without much energy being attenuated due to absence of the skin/flesh layer. Therefore, the skin and flesh appear to mitigate the peak pressure by acting as a cushioning layer.

Figure 19 shows the time history of rigid wall forces for no failure and erosion cases. The rigid-wall force only increases to about 0.7 KN when the bone material starts to fail. However, the rigid-wall force continues to increase to about 2 KN when the head continues to get compressed while moving toward the wall. For full head case, the rigid-wall force increases to a peak of 8 KN and drops fast once the skull starts to fail.

Figure 20 compares the failure in the skull in the impact zone with and without skin and flesh at 2 ms and 5 ms. The failure in the bone is more localized for the full head case. The bottom cortical bones do not fail for both cases. For the defleshed case, the failure occurs mear the impact zone.

Projectile Impact.

Figure 21 shows the time histories of force on the head when it is impacted by hemispherical- and flat-nosed projectiles. After impact, the force on the head is not affected by the boundary conditions at the bottom surface of the cylindrical bone until 0.6 ms. When the head has free boundary condition, the force on the head starts to decrease after a peak before decreasing to zero when the head is separated from the projectile. When fixed-boundary condition is used for the head, the force increases again around 1.5 ms when the projectile continues to load the head. The force on head drops when the projectile starts to rebound from the head; for example, the flat-nose projectile loses contact with the head around 4.7 ms. The force to the head is larger when the head is impacted by a flat-nose projectile due to a larger contact area. When failure is allowed, the force on the head increases at a much lower rate due to continuous failure in the bone. Similarly, the force is usually larger when the fixed-boundary condition is applied to the bottom surface of the cylindrical bone (neck area).

The force on the head, for the case when the defleshed head is impacted against a rigid wall, is also included in Fig. 21 for comparison. It can be seen that the results are very similar when the head is impacted against a rigid wall (which has free-boundary condition too) and a flat-nose projectile impacts the head with free-boundary conditions. The force duration is slightly longer, and the peak force is also larger when the head is impacted against a rigid wall. The head impacting a rigid wall is equivalent to a flat-nose projectile with infinite mass impacting at the same velocity for free-boundary cases.

Figure 22 shows the pressure evolutions at S3, S5, and S7 along the shot line in the brain for no failure case. For free-boundary condition case, the pressure is only plotted up to 2 ms since the force to the head is already zero at around 1.5 ms. After impact, the pressure propagates from the bone to the CSF and brain. The pressure decreases from S3 to S7 along the impact line until the fixed-boundary conditions take effect. The boundary condition at the bottom surface of the cylindrical bone starts to affect S7 earlier since it is closer to the boundary.

Comparison With the Literature Data.

Drop tests were conducted on cadaver heads [2], where linear to stellate fractures were observed for impact at 13.5 ft/s (4.1 m/s) to 17.4 ft/s (5.3 m/s). Drop tests against a rigid flat target showed that 100% fracture occurred in PMHS skulls at a 10 in height drop for frontal impact case [5], for which the impact velocity was calculated to be 2.2 m/s. In our study, skull fracture was observed for impact velocity of 3 m/s, which is similar to that observed in the experiments.

The computed rigid wall force or force transferred to the head from the projectile impact is listed in Table 2 for various cases studied in this paper. The cases where the bone fracture is indicated by element erosion, exhibited lower force amplitude compared to no-failure case. The flat-nosed projectile delivered higher force amplitude compared to the hemispherical nosed projectile. The rigid wall had the highest force amplitude due to the rigid constraint effect, as expected. Similar force amplitudes are reported in the experiments that range from 5 to 13 KN at skull fracture, albeit for a different impact condition than considered in this paper. An accurate comparison with experiment can be produced only after incorporating an accurate model for the skin and bone fracture, which is not available currently.

Low-velocity impacts (3.6–6.9 m/s) to unembalmed PMHS [14] were conducted to study the frontal skull fractures. The full heads were rigidly attached to an aluminum pendulum. The skull fractures were observed to be primarily linear in nature in the impact zone. One linear fracture originated at the point of impact and extended toward one of the orbital rims. The numerical results for head with skin impacting against a rigid wall can be used for comparison with this experiment. Figure 23 shows the fracture at 1.3 ms when failed elements were eroded and converted to SPH particles. It can be seen that two (SPH case) or three (erosion case) cracks generated after impact in the cortical bone. One crack is observed to extend from impact location toward the orbital rim as observed in the experiment.

The failure of the skull depends on the head geometry, the presence or absence of skin and flesh, loading conditions, and the boundary conditions. Figure 24 shows the failure in the skull for various cases. The severity of failure is less when the head is impacted by hemispherical nose projectiles.

Various methods were used to model the skull fracture and to study the effects of skull fracture on the load transfer to the head in LS-DYNA. Impact of a human head with a rigid wall and projectile impact on the human head were modeled for low velocities at 45 deg (frontal impact) angle of impact. The neck or the rest of the body were not included in the model, but both free- and fixed-boundary conditions were used for the neck area as bounding cases.

The skull in the impact zone was modeled with a three-layered structure: top cortical, middle trabecular, and bottom cortical bone. Elastoplastic models were used for cortical and trabecular bones along with a failure criterion based on the effective strain. Three methods were used to model the failed material. Either the material was eroded, treated as fluid, or converted to SPH particles upon failure.

After the head impacts the rigid wall, the head deforms and the pressure propagates from the skin to the skull, the CSF, and the brain. The pressure amplitude attenuates as it travels to the CSF and the brain. After impact, the skull (cortical, trabecular, and cortical layers) experience bending load. The top cortical layer fails first as the effective strain exceeds the prescribed threshold value. A gap can form between the skull and CSF when the failed material is eroded or converted to particles.

The load transfer to the head drops when skull fracture occurs for all of the cases studied in this paper. When the defleshed head is impacted against a rigid wall, force on the skull is observed to be smaller compared the full head case, but a larger amplitude pressure pulse propagates to the brain for the former case. The two cases of the defleshed head being impacted against a rigid wall and the defleshed head being impacted by a heavy and rigid projectile with a flat nose produce very similar load transfer to the head. Impact from a hemispherical-nose projectile results in a smaller load transfer. The boundary condition at the neck area starts to affect the load transfer after about 0.6 ms.

The failure criterion used in this initial study on skull fracture effects, need to be refined and validated. Characterization experiments are necessary to obtain the accurate compression and tension response of the skull. Mesh distortion can cause inaccuracies to the adjacent elements when the failed elements are treated as fluid. Material erosion is the most efficient way to model failure, but it removes mass and momentum from the model and hence would suffer in accuracy. Therefore, the SPH method appears to be more suitable to model fracture as it conserves the mass and momentum, and the particles interact with the adjacent elements.

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Zhang, Y. Y. , He, F. , Li, C. L. , Gao, Y. , and Gao, P. , 2013, “ Simulation Analysis on Strength of Bucket Tooth With Various Soil,” Advanced Materials Research, 619, pp. 62–65. [CrossRef]
Dyna, L. S. , 2016, “ Keyword User's Manual,” Material Models, Vol. II, Livermore Software Technology Corporation (LSTC), Livermore, CA.
Johnson, G. R. , and Stryk, R. A. , 2003, “ Conversion of 3D Distorted Elements Into Meshless Particles During Dynamic Deformation,” Int. J. Impact Eng., 28(9), pp. 947–966. [CrossRef]
Johnson, G. R. , Beissel, S. R. , and Gerlach, C. A. , 2011, “ Another Approach to a Hybrid Particle-Finite Element Algorithm for High-Velocity Impact,” Int. J. Impact Eng., 38(5), pp. 397–405. [CrossRef]
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References

Yoganandan, N. , Pintar, F. A. , Sances, A., Jr. , Walsh, P. R. , Ewing, C. L. , Thomas, D. J. , and Snyder, R. G. , 1995, “ Biomechanics of Skull Fracture,” J. Neurotrauma, 12(4), pp. 659–668. [CrossRef] [PubMed]
Gurdjian, E. S. , Webster, J. E. , Lissner, and H. R. , 1949, “ Studies on Skull Fracture With Particular Reference to Engineering Factors,” Am. J. Surg., 78(5), pp. 736–742. [CrossRef] [PubMed]
Gurdjian, E. S. , and Webster, J. E. , 1958, Head Injuries: Mechanisms, Diagnosis, and Management, Little Brown, Boston, MA.
Versace, J. , 1971, “ A Review of the Severity Index,” SAE Paper No. 710881.
Philemon, C. , Lu, Z. , Rigby, P. , Takhounts, E. , Zhang, J. , Yoganandan, N. , and Pintar, N. , 2007, “ Development of a Generalized Linear Skull Fracture Criterion,” 20th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Detroit, MI, June 15–18. http://wbldb.lievers.net/09126.html
Bandak, F. A. , Vander Vorst, M. J. , Stuhmiller, L. M. , Mlakar, P. F. , Chilton, W. E. , and Stuhmiller, J. H. , 1995, “ An Imaging-Based Computational and Experimental Study of Skull Fracture: Finite Element Model Development,” J. Neurotrauma, 12(4), pp. 679–688.
Zhang, L. , Yang, K. H. , Dwarampudi, R. , Omori, K. , Li, T. , Chang, K. , Hardy, W. N. , Khalil, T. B. , and King, A. I. , 2001, “ Recent Advances in Brain Injury Research: A New Human Head Model Development and Validation,” Stapp Car Crash J., 45, pp. 369–394. http://www.academia.edu/13097600/Recent_advances_in_brain_injury_research_a_new_human_head_model_development_and_validation
Mao, H. , Zhang, L. , Jiang, B. , Genthikatti, V. V. , Jin, X. , Zhu, F. , Makwana, R. , Gill, A. , Jandir, G. , Singh, A. , and Yang, K. H. , 2013, “ Development of a Finite Element Human Head Model Partially Validated With Thirty Five Experimental Cases,” ASME J. Biomech. Eng., 135(11), p. 111002.
Lynch, M. L. , Wozniak, S. L. , and Sokolow, A. , 2015, “ Material Parameter Sensitivity of Predicted Injury in the Lower Leg,” U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, Report No. ARL-TR-7310. http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA617193
Wagner, C. D. , 2012, “ Computational Simulation of Skull Fracture Patterns in Pediatric Subjects Using a Porcine Model,” Ph.D. dissertations, Wayne State University, Detroit, MI. http://digitalcommons.wayne.edu/oa_dissertations/420/
Sahoo, D. , Deck, C. , Yoganandan, N. , and Willinger, R. , 2014, “ Composite FE Human Skull Model Validation and Development of Skull Fracture Criteria,” International Research Council on the Biomechanics of Injury Conference, Berlin, Germany, Sept. 10–12, Paper No. IRC-14-20 http://www.ircobi.org/wordpress/downloads/irc14/pdf_files/20.pdf.
Asgharpour, Z. , Baumgartner, D. , Willinger, R. , Graw, M. , and Peldschus, S. , 2014, “ The Validation and Application of a Finite Element Human Head Model for Frontal Skull Fracture Analysis,” J. Mech. Behav. Biomed. Mater., 33, pp. 16–23. [CrossRef] [PubMed]
Yoganandan, N. , and Pintar, F. A. , 2004, “ Biomechanics of Temporo-Parietal Skull Fracture,” Clin. Biomech., 19(3), pp. 225–239. [CrossRef]
Delye, H. , Verschueren, P. , Depreitere, B. , Verpoest, I. , Berckmans, D. , Sloten, J. V. , Van Der Perre, G. , and Goffin, J. , 2007, “ Biomechanics of Frontal Skull Fracture,” J. Neurotrauma, 24(10), pp. 1576–1586. [CrossRef] [PubMed]
Zhang, T. G. , Satapathy, S. S. , Dagro, A. M. , and McKee, P. J. , 2013, “ Numerical Study of Head/Helmet Interaction Due to Blast Loading,” ASME Paper No. IMECE2013-63015.
Zhou, Z. , Jiang, B. , Cao, L. , Zhu, F. , Mao, H. , and Yang, K. H. , 2016, “ Numerical Simulations of the 10-Year-Old Head Response in Drop Impacts and Compression Tests,” Comput. Methods Programs Biomed., 131, pp. 13–25. [CrossRef] [PubMed]
McElhaney, J. H. , Fogle, J. L. , Melvin, J. W. , Haynes, R. R. , Roberts, V. L. , and Alem, N. M. , 1970, “ Mechanical Properties of Cranial Bone,” J. Biomech., 3(5), pp. 495–511. [CrossRef] [PubMed]
Liu, Z. , and Yeung, K. , 2008, “ The Preconditioning and Stress Relaxation of Skin Tissue,” J. Biomed. Pharm. Eng., 2(1), pp. 22–28. http://www3.ntu.edu.sg/bmerc/contents/JBPE/J002/JBPE%202(1)%2022-28.pdf
Herbert, E. , Balibar, S. , and Caupin, F. , 2006, “ Cavitation Pressure in Water,” Phys. Rev. E, 74, p. 041603.
Caupin, F. , and Herbert, E. , 2006, “ Cavitation in Water: A Review,” C. R. Phys., 7(9), pp. 1000–1017. [CrossRef]
Dong, L. , Zhu, F. , Jin, X. , Suresh, M. , Jiang, B. , Sevagan, G. , Cai, Y. , Li, G. , and Yang, K. H. , 2013, “ Blast Effect on the Lower Extremities and Its Mitigation: A Computational Study,” J. Mech. Behav. Biomed. Mater., 28, pp. 111–124. [CrossRef] [PubMed]
Zhang, Y. Y. , He, F. , Li, C. L. , Gao, Y. , and Gao, P. , 2013, “ Simulation Analysis on Strength of Bucket Tooth With Various Soil,” Advanced Materials Research, 619, pp. 62–65. [CrossRef]
Dyna, L. S. , 2016, “ Keyword User's Manual,” Material Models, Vol. II, Livermore Software Technology Corporation (LSTC), Livermore, CA.
Johnson, G. R. , and Stryk, R. A. , 2003, “ Conversion of 3D Distorted Elements Into Meshless Particles During Dynamic Deformation,” Int. J. Impact Eng., 28(9), pp. 947–966. [CrossRef]
Johnson, G. R. , Beissel, S. R. , and Gerlach, C. A. , 2011, “ Another Approach to a Hybrid Particle-Finite Element Algorithm for High-Velocity Impact,” Int. J. Impact Eng., 38(5), pp. 397–405. [CrossRef]

Figures

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Fig. 1

Simplified geometry of (a) head (skin and flesh, bone, CSF, and brain) and (b) three-layer geometry for skull in the impact zone

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Fig. 2

(a) The mesh for the head components and (b) the mesh for the three-layer geometry for the skull in the impact zone

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Fig. 3

(a) The defleshed head impacts a rigid wall at 45 deg, and (b) the impact location changes from A to B when the skin and flesh are absent

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Fig. 4

Frontal impact of (a) hemispherical-nose and (b) flat-nose projectile

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Fig. 5

Free- or fixed-boundary conditions applied to the bottom surface of the cylindrical bone

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Fig. 6

The stress–strain curves for the skull components

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Fig. 7

The rigid-wall force for various impact velocities

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Fig. 8

Time history of brain rigid-body velocity

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Fig. 9

Time history of pressure along the impact line in: (a) skin/flesh, bone, and CSF and (b) brain

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Fig. 10

The locations for the pressure

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Fig. 11

The peak pressure along the impact line

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Fig. 12

In-plane strain and normal strain for (a) top cortical bone surface and (b) bottom cortical bone surface

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Fig. 13

Curved coordinates for top cortical and bottom cortical

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Fig. 14

Time history of rigid-wall force for various failure models

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Fig. 15

Bone failures for (a) “no failure,” (b) “fluid,” (c) “erosion,” and (d) “SPH” case

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Fig. 16

The time history of pressure in the brain modeling skull failure with (a) no failure, (b) fluid, (c) erosion, and (d) SPH

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Fig. 17

Time histories of rigid wall force for various impact velocities with and without skin and flesh

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Fig. 18

Time histories of pressure along the impact line in the brain for defleshed head case

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Fig. 19

Time histories of rigid-wall force in defleshed head

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Fig. 20

The failures in the impact zone for (a) full head and (b) defleshed head

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Fig. 21

The time history of force to the head impacted by a (a) hemispherical-nose and (b) flat-nose projectile for fixed and free-boundary conditions

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Fig. 22

The time history of pressure in the brain when the head is impacted by a (a) hemispherical-nose and (b) flat-nose projectile for fixed-and free-boundary conditions

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Fig. 23

The fractures at 1.3 ms in the skull for (a) “erosion” and (b) “SPH” case

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Fig. 24

The fractures at 1.3 ms in the defleshed head (a) impacted against a rigid wall, impacted by a (b) flat-nose projectile, free boundary conditions, (c) flat-nose projectile, fixed boundary conditions, (d) hemispherical-nose projectile, free boundary conditions, and (e) hemispherical-nose projectile, fixed boundary conditions

Tables

Table Grahic Jump Location
Table 1 The material properties for skull components
Table Grahic Jump Location
Table 2 Computed force transfer to the head (in KN)

Errata

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