## 2 Materials and Methods
### Finite Element Models  
Helmets were purchased from a commercial vendor in Taiwan and were scanned using a three-dimensional (3D) optical measurement system (COMET 5, Steinbichler Optotechnik, Munich, Germany). For each helmet, 3D modeling data were obtained through eight scans, performed at intervals of 45\({}^{\circ}\). The eight scans were combined into a single 3D model using Geomagic Studio software (Geomagic, Morrisville, NC, USA). The dimensions of the helmet and solid structures in the 3D model were determined using SolidWorks software (version 2013, Dassault Systemes Corp., Waltham, MA, USA). Finally, the 3D model was converted to a finite element (FE) format, using ABAQUS software (Version 6.12, Dassault Systemes Corp., Waltham, MA, USA). When constructing the models, the small holes in the inner and outer surfaces of the helmet (e.g., those used for visor or chin strap attachment purposes) were retained, since they act as stress raisers, therefore affecting the mechanical response of the helmet. However, features such as air vents and plate surfaces, which are only used for aerodynamics and styling purposes, were excluded, in order to simplify the modeling process. In addition to the three traditional helmet designs described above, the present study also considered a novel open-face helmet design in which three parallel ventilation slots were incorporated into the upper-head region. As shown in Figure 3, each ventilation slot had a length of 150 mm and was separated from its neighbor by a distance of 10 mm. To determine the helmet design with an optimal compromise between user safety and user comfort, the simulations considered three different slot widths, namely 8, 14, and 18 mm. \begin{table}
\begin{tabular}{c c c c} \hline
**Standard** & **ECE R22.05** & **Snell M2010** & **DOT FMVSS 218** \\ \hline Allowed Impact Duration & N/A & N/A & 150 G for no more than 4 ms & 200 G for no more than 2 ms \\ \hline Allowed Peak Acceleration & 275 G & 300 G & 400 G \\ \hline \end{tabular}
\end{table} 
Table 1: Basic requirements of motorcycle helmet safety standards. Figure 3: Prototype open-face helmet design with additional ventilation slots. ### Finite Element Models  
Each of the helmets considered in the present study consisted of two components, namely a hard outer shell and a foam inner liner. When performing the simulations, the shell and liner were assumed to be fabricated of Acrylonitrile Butadiene Styrene (ABS) and Expanded Poly-Polystyrene (EPS), respectively. The material data for the ABS shell were taken from previous studies [9; 15]. Similarly, the material properties of the foam liner were derived from the stress-strain curves presented in previous experimental studies by [PERSON] et al. [15]. As shown in Figure 4, the static stiffness of the foam material linearly increased with an increasing compression rate, in both the elastic regime and the plastic regime. It is worth noting that this finding is consistent with the results of [PERSON] et al. [16], based on an empirically-derived constitutive model. The headform was modeled using solid hexahedron elements with single integration points and was assumed to be fabricated of aluminum. The model stiffness was deliberately increased, in order to prevent elastic deformation of the headform during impact; thereby interfering with the foam energy absorption results. (Note that while the headform could have been modeled using a rigid material, contact with elastic materials is more stable). Table 2 summarizes the material properties used for the various helmet components in the simulations. Figure 5a-c shows the FEA models of the full-face, open-face, and half helmets, respectively.