# Evaluation of Combat Helmet Behavior under Blunt Impact
## 2 Materials and Methods
### Introduction to the Development of the Numerical Model
#### 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  
Figure 1: Combat helmet shell, foams, and straps. 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:  
\[F_{fiber}^{2}\ =\ \left(\frac{\sigma_{11}}{X_{T}}\right)^{2}+\overline{\tau}\ ;\ \sigma_{11}>0 \tag{1}\]  
where \(X_{t}\) is the tensile strength in the fiber direction (longitudinal) and \(\sigma_{11}\) is the normal stress in the same direction. When the failure criterion of Equation (1) is satisfied, \(F_{fibre}\geq 1\), all elastic constants involved on the failed lamina plane are set to zero, \((E_{11}=E_{22}\ =\ G_{12}\ =\ v_{12}\ =\ v_{21}\ =0)\). 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:  
\[F_{matrix}^{2}\ =\ \left(\frac{\sigma_{22}}{Y_{T}}\right)^{2}+\overline{\tau}\ ;\ \sigma_{22}>0 \tag{2}\]  
\[F_{matrix}^{2}\ =\ \left(\frac{\sigma_{22}}{2s_{c}}\right)^{2}+\left[\left( \frac{Y_{c}}{2s_{c}}\right)^{2}-1\right]\frac{\sigma_{22}}{Y_{c}}+\overline{ \tau}\ ;\ \sigma_{22}<0 \tag{3}\]  
where \(Y_{t}\) is the tensile strength in the 22-dir, \(Y_{c}\) is the transverse compressive strength, and \(\sigma_{22}\) is the normal stress in that direction. When matrix cracking or matrix compression failure criterion is satisfied, \(F_{matrix\ crack}\geq 1\) or \(F_{matrix\ comp}\geq 1\), and all of the elastic constants except elastic modulus in 11 direction (\(E_{11}\)), 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 \(\overline{\tau}\) parameter is the ratio between shear stress and shear strength as follows:  
\[\overline{\tau}\ =\ \frac{\frac{\sigma_{12}^{2}}{2C_{12}}+\frac{3\alpha_{1 }\sigma_{12}^{4}}{4}}{\frac{S_{c}^{2}}{2C_{12}}+\frac{3\alpha_{1}S_{c}^{4}}{4}} \tag{4}\]  
where \(G_{12}\) is shear modulus, \(S_{c}\) is the longitudinal shear strength, \(\sigma_{12}\) is the shear stress, and \(\alpha\) is a nonlinear shear stress coefficient (\(0<\alpha<0.5\)) for which, in this study, a zero value is assumed.