# FE Analysis of Motorcycle Helmet Performance under Severe Accidents
## 3 Finite Element Model
### Motorcycle Helmet Structure  
The open-face helmet model was divided into three parts: shell, foam, and comfort padding, as shown in Figure 2. All components were assigned as a deformable structure with the tetrahedral type of solid element, with only three degrees of freedom per  
Figure 1: Impact positions on the helmet structure.  
node (only translational in three directions). The whole model of the helmet structure consisted of 33,113 nodes and 123,617 elements. AUTOMATIC_SINGLE_SURFACE was utilized to generate self-contact for each component of the helmet structure, in which the static and dynamic friction coefficients were 0.2 and 0.1, respectively. Furthermore, CONTACT_INTERIOR was also employed to prevent a negative volume of soft material (foam) under impact load, which always causes termination during analysis.  
A permanent deformation commonly occurs with any structure under assorted impact severities. Thus, the nonlinear material properties were essential to consider in the analysis procedure. The shell component was made from Acrylonitrile Butadiene Styrene (ABS), while the foam and comfort padding were made from EPS foam and Polystyrene (PU) foam, respectively. Tensile and compression tests were performed for determining the plastic properties of the shell and foam components, respectively. The mechanical properties for each component are displayed in Table 1[38; 39], while the nonlinear material behaviors of the shell and foam are illustrated in Figure 3. The material properties of the shell and foam component were directly determined by testing in this study, as displayed in Figure 3a,b, respectively. Since this work did not serve the test for comfort padding, the properties in Figure 3c were used and obtained from [PERSON] et al. [38]. The total weight of the helmet structure was 1.02 kg, comprised of 0.89 kg from the shell, 0.098 kg from the foam, and 0.032 kg from the comfort padding. In LS-DYNA, the material model of MAT_024_PIECEWISE_LINEAR_PLASTICITY was assigned for the shell component. Both the foam and comfort padding were utilized in the material model as MAT_063_CRUSHABLE_FOAM and MAT_057_LOWDENSTITY_FOAM [40], respectively. The stress-strain relationship is necessary to be applied for all material models and components to recognize the nonlinear material behaviors during impact analyses.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials Properties** & **Shell** & **Foam** & **Comfort Padding** \\ \hline Density (kg/m3) & 1435.0 & 51.6 & 27.6 \\ Young’s modulus (MPa) & 2221.8 & 8.24 & 0.18 \\ Poisson’s ratio & 0.3 & 0.01 & 0.25 \\ Yield stress (MPa) & 42.2 & - & - \\ Tensile stress cut-off (MPa) & - & 3.6 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical properties of each structural component.  
Figure 2: Helmet structural model and its components.  
To apply the material properties in the LS-DYNA, coordinates of stress and plastic strain are commonly required to define nonlinear behaviors in MAT_024, while the relationship of stress and volumetric strain is assigned for foam properties.