The 3YO dummy head model used in this study was scaled from six year old crash dummy shown in Figure 1 [6].

Figure 1. 6YO child crash dummy model (a) and head finite element model (b).

Morphing technique was applied to scale 6YO dummy head to 3YO head anthropometry. Scaling factors were calculated for head height, head breadth, and head depth in x, y, and z directions: λ x , λ y , and λ z as the ratio of base line length to the destination length. Now the scaled model, x is given as:

where R is the transformation matrix. Table 1 shows the scaling factors used.

Table 1. Factors used for scaling 6YO HIII dummy head model to 3YO anthropometry.

Morphing was done in LS-PrePost by constraining the parts to be morphed (Morph nodes) within a solid hex mesh (Constraining Element). The nodal coordinates are transformed appropriately according to their relative position within their constraining solid element as shown in Figure 2. This scaling procedure was applied in previous studies [7][8].

The materials properties of the dummy head and impacting plate are shown in Table 2.

The head model was removed from the dummy model for the impact test in accordance with crash dummy head drop test procedure [6]. Head drop test was conducted in LS DYNA code. Surface to surface contact with a friction coefficient of 0.2 as suggested by Li et al. [10] is defined between head and rigid plate. Hourglass energy was set to be 10% of the total energy. For frontal impact, the head was tilted so that z-axis form an angle of 28.5˚ with horizontal while the mid sagittal plane is vertical and for lateral impact the mid sagittal plane was tilted to make 35^o with impact surface from the top of the head [11]. For vertex and occipital impacts, the head was oriented such that the mid sagittal plane is 90˚ to the impacting surface. Figure 3 shows the positioning angles, impact locations

Figure 2. Morphing of 6YO dummy head to 3YO anthropometry.

Table 2. Crash dummy head materials properties [5][9].

ρ: mass density, E: Elastic Modulus, K: Bulk Modulus, ϑ : Poison’s Ratio,: G o : Short Term Shear Modulus, G 1 : Long Term Shear Modulus, β: decay constant.

Figure3. Head drop test orientation for five impact locations.

and simulation set up. The 3YO crash dummy head model has an element size that is computationally stable and economical for which calculation takes only 9 minutes to complete.

Impact velocities were calculated based on the drop height between head and impact plate according to the relation:

where h is the height of fall and g is gravitational acceleration.

The height of 150 mm was selected based on the distance between child head and child restraint seat or side door beams while 300 mm considered the frontal impact of child head with vehicle interior and pedestrian impact distances. This study didn’t cover higher drop heights which may lead to fracture of skull and other human tissues and this is beyond the capability of the crash dummy head model.

Peak resultant acceleration describes the peak magnitude of translational acceleration felt by the center of mass of the dummy head during impact. The resultant acceleration of the dummy model was measured by accelerometer located at the head center of mass which provides the components of acceleration in x , y , and z directions and the resultant acceleration is evaluated as [1]:

HIC is the main criteria used in assessing the head injury risk on impact. It is the standardized maximum integral of head acceleration measured at the center of mass within a specified time windows. It is calculated based on the equation [12]:

Where t 1 and t 2 are the initial and final times of intervals within which HIC reaches a maximum value. Acceleration is measured in unit of acceleration of gravity (g) and time in seconds. The ISO time recommended limits of 15 ms (HIC15) was used in this study. HIC15 was calculated within 10 ms simulation time because the peak acceleration was captured within this timeframe.

Von Mises stress is a crucial criterion in finite element modeling of soft tissue, assessing structural integrity and failure risk. It provides a scalar value combining stress components, predicting deformation or failure under external forces. By comparing calculated stress to a yield point, potential failure points and injury mechanisms in soft tissues can be determined. Von Mises stress- time graphs were recorded from the simulation results for the two drop heights and five impact locations.

The head model was validated against the available 9YO cadaver head peak acceleration reported by Loyd [13]. Head depth, height and circumference of 9YO cadaver used for the validation are 16.9 cm, 13 cm and 49.3 cm and drop mass was 2.17 kg [3] which is close to 18 cm-head depth, 13.5 cm-head height and 48.4 cm-head circumference and 2.02 kg-drop mass for 3YO [14]. It can be seen in Table 3 that the peak acceleration differs especially for frontal impact and this can be due to biomechanical differences of the 9YO child compared to 3YO. Though nine years old skull is more rigid and its tissue material properties differ from 3YO, the difference is acceptable due to scarcity of age matched cadaver data. It is also better than using adult scaled data. In addition, crash dummies are simplified models that may not capture variability in cadaver age and embalming. Mesh size and differences in geometry may also cause the response differences.

Except for left parietal and vertex locations, head acceleration is lower for 3YO than 9YO cadaver which explains the biomechanical differences between the two heads compared. The percentage difference in Table 3 is within 10% for all impact locations with the exception of front which might be due to age differences and characteristics of the dummy head. It should be noted that drop heights for all impact locations are approximated to 150 mm and 300mm in the comparison shown in Table 3.

Table 3. 3YO head model comparison with 9YO cadaver data.

Figure 4 shows a typical dummy model HIC15 for 150 mm drop height (1721 m/s impact velocity) for frontal test. The HIC15 is 239 as calculated by LS DYNA finite element code. Detail results for other impact locations and drop heights are presented in Table 4.

The Von-Mises stress which defines how head impact with vehicle structure affect the head tissue is an important parameter in determining bone fracture and deformation. The result for 150 mm drop height (1721 m/s impact velocity) is presented in Figure 5 with peak value of 1.29 MPa in 0.01 s simulation period.

Von Mises stress occurs at the impact point with rigid floor. Maximum Von Mises stress is obtained at 0.006 sec. Figure 6 shows the contour plot for Von Mises stress from 0 sec to 0.0075 sec.

Figure 4. HIC15 of crash dummy head at 150 mm drop height.

Table 4. 3YO head model HIC15 and maximum Von Mises stress for five impact locations.

Figure 5. Von Misses stress of crash dummy head at 150mm drop height.

Figure 6. Von Misses stress profile at some instances of the simulation.

Comparison of HIC15 for two drop heights with impact locations is shown in Figure 7. HIC15 values are generally higher for 300 mm drop height (2426 m/s impact speed) than 150 mm drop height (1721 m/s impact speed) for all impact locations; this is expected because the impact force which results in higher accelerations is high at high speed. HIC15 values are below the minimum acceptable value of 570 for 3YO. This means at these impact velocities the 3YO child would be safe even if the surface is rigid. High decelerations in vehicle crash results in high impact forces. HIC15 of 239 for 150 mm drop height in frontal impact is consistent to pediatric results reported by Loyd et al. [3]. Occiput experienced highest HIC15 than other locations with 530.5 for 300 drop height which is below the threshold of 570 for 3YO. This shows that the child seat head restraint should be able to absorb impact energy to reduce such high HIC15. 3YO Hybrid III dummy experienced high HIC15 at occiput in the results reported by Loyd [13]. Occiput was also reported to have highest peak acceleration in the work of Chen [2]. Occiput impact is as a result of rear impact due to whiplash. Vertex location experienced high HIC15 of about 480 which is in par with what was reported in the literature [13]. Impact on vertex is usually found in vehicle rollover or in child fall and it can be protected with helmet in bicycle or sports. Thus, the design of such helmets in the vertex should consider the high HIC15 in that direction. Right and left parietals experienced close HIC15 values at the two velocities and this is attributable to symmetrical nature of crash dummy head model and this is in line with cadaver and crash dummy head results reported by Loyd [13].

Figure 7. HIC15 of dummy head for the impact locations.

Maximum Von Mises stress is another parameter used to evaluate the injury severity at tissue level. Forehead experienced the highest stress than other locations as shown in Figure 8, though it has lowest HIC15 as shown in Figure 7 at the two drop heights. This is because HIC15 and von misses stress are different injury mechanisms. HIC15 measures injury risk based on linear acceleration and duration while von misses stress indicates localized material yielding. High stress can be attributed to dummy characteristics due to simplified skull construction which makes the front location to be stiffer than other impact locations. Left parietal shows close values of Von Mises stress at the two drop heights which might be due to symmetry and other dummy characteristics. The Von Mises stress ranges between 0.51 MPa to 1.88 Mpa. The lowest is found at vertex for the two heights. High heights experienced high Von-mises stress as expected because at higher drop height the impact energy is high which results in high stresses at the impact point. Von mises stress increase with height but is not consistent with HIC15 in particular head location because HIC15 measures kinematics of head excursion while Von-mises stress measures impact due to contact of material with rigid surface. Viscoelastic material properties of dummy head can predict Von Mises stress experienced by child head on impact hence could be used in safety assessment of vehicle.

Figure 8. Von Misses stress of dummy head for the impact locations.