# Numerical Analysis of EOD Helmet under Blast Load Events Using Human Head Model
## 2 Numerical Model
### Helmet Assembly Model  
The EOD helmet used in this work is shown in Figure 1 and is divided into five parts: helmet shell, visor, insolating joint, and interior foams, as known as hard foam and soft foam. The parts are modeled using 3D solids through Autodesk Inventor CAD software from original dimensions of components and meshed with Altair Hypermesh software, which allows optimal mesh strategies for the helmet geometry. Some characteristics of the element type, size, and number used for the different parts are in Figure 1 and Table 1.  
Figure 1: Explosive ordinance disposal (EOD) helmet model description. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parts** & \begin{tabular}{c} **Material Model** \\ **LS-Dyna** \\ \end{tabular}  & **N\({}^{*}\) Elements** & **Element Type** & \multicolumn{1}{c}{**Size**} & **Material Properties** & **Source** \\ \hline \multirow{3}{*}{Hlmet Shell} & \multirow{3}{*}{*} & \multirow{3}{*}{MAT\_COMPOSITE\_DAMAGE} & \multirow{3}{*}{40,952} & \multirow{3}{*}{Hexaedric solid} & - & 4 mm longitudinal/thickness & \multicolumn{1}{c}{} & [PERSON] et al. \\  & & & & & & & & \\ \cl  
The helmet shell is the most external part and constitutes the principal structural element of the EOD helmet. It is made of composite based on aramid fiber, which is widely used in the field of personal protection [21; 22; 28; 29; 30; 31; 32] due to the excellent resistance to weight ratio. Helmet shell thickness is 4 mm. *MAT_COMPOSITE_DAMAGE (MAT_022) has been used to define the mechanical behavior model of aramid composite, where it is defined as orthotropic material (9 elastic constants) and assumes a linear elastic behavior until failure [31]. The damage criterion used in this part of the model is based on the Chang-Chang model [33; 34] and considers three failure modes on composite: fiber breakage, matrix cracking, and matrix compression Equations (2)-(5). 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 the lamina plane, and 3 is the through thickness direction. It is worth mentioning that element deletion used is based on fiber tensile break. The failure modes (MAT_022) used in this work can be described as follow:  
At first, it is necessary to define \(\overline{\tau}\) parameter, the ratio between shear stress and shear strength as  
\[\overline{\tau}=\frac{\frac{\sigma_{12}^{2}}{2G_{12}}+\frac{3\alpha_{1}\sigma_ {12}^{4}}{4}}{\frac{S_{c}^{2}}{2G_{12}}+\frac{3\alpha_{1}S_{c}^{4}}{4}} \tag{1}\]  
where \(G_{12}\) is shear modulus, \(S_{c}\) is the longitudinal shear strength, \(\sigma_{12}\) is the shear stress, and \(\alpha_{1}\) is a non-linear shear stress coefficient (\(0<\alpha<0.5\)) determined by stress measurements, for which, in this work, due to the lack of literature data about it, zero value is assumed. Fiber breakage criterion is defined as  
\[F_{fiber}^{2}=\left(\frac{\sigma_{11}}{X_{T}}\right)^{2}+\overline{\tau}\ \ ;\ \sigma_{11}>0 \tag{2}\]  
where \(X_{T}\) is the tensile strength in fiber direction (longitudinal) and \(\sigma_{11}\) is the normal stress in that direction. When the failure criterion of Equation (2) is satisfied, \(F_{fiber}\geq 1\), 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 fiber cannot support loads along the axial (or longitudinal) and shear (transverse) directions and load is redistributed to the rest of the lamina. Matrix cracking criterion is defined as