In this study, we developed a finite element model consisting of an evaluation of a combat helmet subjected to low impact velocity and assessing for traumatic brain injury. The protective performance of the helmet was evaluated using an acceleration analysis of parameters such as HIC (head injury criterion).
2.1.1. Helmet Model
The combat helmet model used in this work is shown in
Figure 1. The helmet model assembly consisted of different parts, i.e., composite structure helmet, foams, and straps. Each part was modeled using CAD software Autodesk Inventor from original dimensions and meshed with Altair Hypermesh 13.0 software which enabled better mesh strategies and techniques.
The shell is the most external part of the helmet assembly and constitutes the principal protective structure of the combat helmet. It is made of composite aramid fibers with a phenolic matrix, which is widely used in lightweight personal protection manufacturing [
10,
28,
29,
30,
31,
32,
33] due to its high ballistic performance and good resistance and low weight ratio. The shell areal density is 8.86 kg/cm
2.
Due to the heterogeneity and anisotropy of the composite materials, *MAT_COMPOSITE_DAMAGE (MAT_022) was used to define mechanical behavior model of the aramid composite, through an orthotropic material model (9 elastic constants) and it was modeled as linear elastic until failure.
The damage criterion for aramid composite used in this work was modeled using the Chang-Chang model [
34,
35], which considered the following three principal intralaminar failure modes: fiber breakage, matrix cracking, and matrix compression, i.e., Equations (1)–(3). The direction assignment for the composite material is done in the local coordinate system (1,2,3), where 1 and 2 are the directions on lamina plane and 3 is orthogonal to the other directions, out of the lamina plane, through the thickness direction.
The intralaminar failure modes (MAT_022) can be described as follow:
Fiber breakage criterion is defined as:
where
is the tensile strength in the fiber direction (longitudinal) and
is the normal stress in the same direction.
When the failure criterion of Equation (1) is satisfied, , all elastic constants involved on the failed lamina plane are set to zero, ( = 0). Failed fibers cannot support loads along the axial (or longitudinal) and shear (transverse) directions, and the load is redirected to the rest of the lamina.
The matrix cracking Equation (2) and matrix compression failure Equation (3) are defined as:
where
is the tensile strength in the 22-dir,
is the transverse compressive strength, and
is the normal stress in that direction. When matrix cracking or matrix compression failure criterion is satisfied,
or
, and all of the elastic constants except elastic modulus in 11 direction (
), are set to zero. This resembles that the lamina cannot provide support in the shear directions of the fibers; hence, the corresponding shear modulus is also set to zero.
In addition, the
parameter is the ratio between shear stress and shear strength as follows:
where
is shear modulus,
is the longitudinal shear strength,
is the shear stress, and α is a nonlinear shear stress coefficient (0 < α < 0.5) for which, in this study, a zero value is assumed.
Finally, since it is a multilayer composite material, a failure criterion has to be defined for the delamination of the layers, which is formulated as follows:
where
,
, and
, are the tensile and shear strength in through thickness direction and
,
, and
are normal and shear stress in the out-of-lamina-plane direction.
The mechanical properties of aramid composite used for this model are listed in
Table 1.
The mechanical behavior model previously described, and the mechanical properties mentioned (in the case of aramid composite components) are widely used in works that analyze the dynamic behavior, generally ballistic, of the type of composite materials used in personal protection.
Another part of the helmet assembly is the straps which are modeled using Hypermesh 13.0 software, through CAD module. This part was designed from previous dimensions of a real model. The helmet was positioned on each head/dummy in the correct position. About these, straps are modeled using surfaces over the external surface of the head/dummy and helmet internal surface.
The mechanical behavior of the straps was modeled as linear elastic behavior (MAT_ELASTIC) with the following mechanical properties: 1400 kg/m3 for the density, 1000 MPa for the elastic modulus, and 0.44 for the Poisson coefficient.
The pad suspensions were made up of two components, i.e., a hard foam to absorb impact energy and a softer foam whose function was to provide comfort to the wearer. These parts were modeled in CAD and exported to Hypermesh software to mesh, see
Figure 2. The total thickness of each foam pad was 21 mm. Three different foam pads were modeled, due to frontal and rear foams and the four lateral foam pads were the same. The top foam pad differed from the two others.
It is important to mention that these types of foams are manufactured in such a way a single part is formed where each trough thickness half corresponds to hard foam and soft foam. For this model, the foams were modeled like a single solid, and each half was assigned equivalent foam properties.
The mechanical behavior of each component polyurethane foam was modeled using the MAT_LOW_DENSITY_FOAM option for low-density elastomeric foams with high compressibility.
Table 2 shows the mechanical properties of both foams [
14,
36,
37].
Moreover, polyurethane foam has a high sensitivity to strain ratio, and yield stress also varies with this parameter. Experimental compression tests on both types of foams, up to a strain rate of 50 s
−1, are found in the literature [
34]. However, polyurethane foams are subjected to higher strain rates on impact events. For this reason, the stress–strain curves from low strain rate up to higher strain rates levels were extrapolated. Li et al. [
37] extrapolated the curves from 2 to 2500 s
−1, as is shown in
Figure 3.
The geometrical model of the shell was meshed using 110,440 hexahedral of 8-node elements with reduced integration and, 8 elements through thickness. The foams pads were also meshed with hexahedral 8-node elements. The rear and front foam pads were created using 12,688 elements, each lateral foam pad had 5832 elements, and the top foam pad was meshed with 21,456 elements. Six elements through thickness were used for the mesh of the foam pads. The straps were modeled using 1912 hexahedral elements of 8-node with reduced integration.
2.1.2. Human Head Model
The human head numerical model used in this study was developed by a co-author, Dr. J. Antona-Makoshi [
27], and was validated through different impact events with high probability to occur in a traffic accident, inducing cerebral injuries. The numerical model of the human head was obtained by computerized tomography (CT) and magnetic resonance imaging (MRI).
The complete head is a compound of multiple parts to reproduce, with high realism, a real human head, i.e., scalp, white and grey matter brain, corpus callosum, falx cerebri, are some of the elements that are distinguished in the numerical model. In addition, one part of the human neck is defined with C1 to C7 vertebrae and their respective intervertebral disks and ligaments.
The total mass of the human head model is 6.47 kg.
Figure 4 shows the numerical model of the complete head with details of internal parts. It is important to mention that the head assembly is modeled symmetrically with respect to the sagittal plane.
The mechanical proprieties of the human head model are summarized in
Table 3 [
27].
The human head mesh is created using 291,948 solid elements and 53,609 shell elements. For further details of the human model see the doctoral thesis of Dr. Antona-Makoshi [
27].