# Influence of Chinstrap Stiffness on Cerebrospinal Fluid Dynamics and Brain Stress in Helmet Impacts
## 3 Results
The semi-non-stretchable chinstrap's intermediate stiffness creates a unique mechanical conflict: it is stiff enough to partially decouple the chin guard from the mandible, allowing the guard to slide laterally across the jaw, yet not elastic enough to absorb significant energy through strap elongation. This partial decoupling reduces the effective contact area between the chin guard and the jaw, leading to localized stress concentrations at bony interfaces rather than distributing forces \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(x\) & \(\sigma_{\mathrm{actual}}\) & \(\sigma_{\mathrm{predicted}}\) & **Residual** & **Residual \%** & **Z-Score** & **Absolute** \\  & **(Normalized)** & **(Normalized)** & & **of \(\sigma_{\mathrm{actual}}\)** & **of \(\sigma_{\mathrm{actual}}\)** & **of Residual** & **Error \%** \\ \hline Highly Stretchable & \(0.0005357\) & \(0.000445\) & \(0.0000907\) & \(16.93\%\) & \(0.12\) & \(20.39\%\) \\ Moderately Stretchable & \(0.0018367\) & \(0.00226\) & \(-0.0004233\) & \(-23.05\%\) & \(-0.56\) & \(18.73\%\) \\ Semi-Stretchable & \(0.010714\) & \(0.0114\) & \(-0.000686\) & \(-6.40\%\) & \(-0.91\) & \(6.02\%\) \\ Semi-Non-Stretchable & \(0.10714\) & \(0.0579\) & \(0.04924\) & \(45.96\%\) & \(2.18\) & \(85.01\%\) \\ Minimally Stretchable & \(0.25612\) & \(0.293\) & \(-0.03688\) & \(-14.40\%\) & \(-1.63\) & \(12.59\%\) \\ Non-Stretchable & \(1.0\) & \(1.484\) & \(-0.484\) & \(-48.40\%\) & \(-2.20\) & \(32.61\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative analysis of stress transmission across six chinstrap stiffness configurations during helmet impact. The table compares observed (\(\sigma_{\mathrm{actual}}\)) and predicted (\(\sigma_{\mathrm{predicted}}\)) stress values normalized to the non-stretchable strap configuration (\(\sigma/\sigma_{\mathrm{Non-Stretchable}}^{peak}\)), along with residual differences, residual percentages, Z-scores, and absolute error percentages. Semi-non-stretchable chinstraps exhibit significant deviations from the exponential trendline (\(y=e^{1.622\times-7.715}\)), with a residual of \(45.96\%\) and an absolute error of \(85.01\%\), indicating an outlier behavior. This deviation is attributed to intermediate stiffness causing partial decoupling between the chin guard and mandible, leading to localized stress concentrations. Highly stretchable and moderately stretchable designs show lower stress transmission due to effective energy absorption through strap elongation, while minimally stretchable and non-stretchable designs transmit undampened forces directly to the skull base. evenly through soft tissues. As a result, the semi-non-stretchable configuration produces the highest residual stress (45.96%) and absolute error (85.01%) compared to the trendline, making it a clear outlier in the dataset. This phenomenon underscores the importance of balancing stiffness and elasticity in chinstrap design. While non-stretchable straps transmit undampened forces directly to the skull base and highly stretchable straps absorb energy through elongation, the semi-non-stretchable configuration occupies a hazardous middle ground where structural displacement introduces dynamic stress concentrations not accounted for in the logarithmic stiffness-stress relationship. This instability mechanism explains why the largest \(\theta\) and the \(\sigma\) outlier occur in the same configuration, emphasizing the need for careful material selection to avoid such detrimental intermediate behaviors. To reiterate the above concisely, Table 1 summarizes the quantitative analysis of stress transmission across chinstrap stiffness configurations, highlighting that the semi-non-stretchable strap is a clear outlier. This configuration exhibits a much higher residual (45.96%) and absolute error (85.01%) relative to the expected exponential trend, reflecting its unique instability: it is stiff enough to partially decouple the chin guard from the jaw, resulting in localized stress concentrations, but not elastic enough to absorb impact energy effectively.