## 3 Results
The slope of \(\hat{\sigma}_{fib}\) was (mean \(\pm\) standard deviation) \(13.011\pm 1.797\) for \(\lambda=1.08\), while it was zero by definition at \(\lambda=1\) (Figure 5b). Similarly, the slope (mean \(\pm\) standard deviation) of the total dimensionless stress \(\hat{\sigma}_{tot}\) was \(14.017\pm 1.797\), at \(\lambda=1.08\), while, by definition, the slope was one at \(\lambda=1\) (Figure 5c). The dimensionless curvature \(\hat{\kappa}_{mat}\) monotonically increased from zero (\(\lambda=1\)) up to 0.048 (\(\lambda=1.08\)) with a slope of about 0.59 (Figure 5d). On the contrary, the dimensionless curvature due to the fibrils' action \(\hat{\kappa}_{fib}\) had a bell-like shape (Figure 5e). In particular, this curve reached its maximum value (mean\(\pm\) standard deviation) \(28.771\pm 0.727\) at \(\lambda=1.035\pm 0.001\). The median, maximum, and minimum values of \(\max\{\hat{\kappa}_{fib}\}\) were, respectively \(29.085,29.141,27.471\), as shown in Figure 5f, together with the shape of their distribution. Finally, \(\hat{\kappa}_{tot}\) is studied in Figure 5g. In this case as well, the curve had a bell-like shape and reached the maximum value of \(6.840\pm 0.176\) at \(\lambda=1.035\pm 0.002\). The median, maximum, and minimum values of \(\max\{\hat{\kappa}_{tot}\}\) were respectively \(6.953,6.970,6.568\), as shown in Figure 5h, together with their distribution shape. Figure 5: Peroneal nerve (data for five axial elongations): (**a**) Dimensionless stress derived from the energetic contribution due to the matrix action. (**b**) Dimensionless stress derived from the energetic contribution due to the fibrils’ action. (**c**) Evolution of the total dimensionless stress. (**d**) Evolution of the dimensionless extrinsic curvature of the matrix stress. (**e**) Evolution of the dimensionless curvature of the fibrils’ stress. (**f**) Distribution of \(\max\{\hat{\kappa}_{fib}\}\). (**g**) Evolution of the dimensionless curvature related to the total stress. (**h**) Distribution of \(\max\{\hat{\kappa}_{tot}\}\). The proposed framework was also used to explore experimental data derived from the axial stretching of a canine left vagus nerve [25]. In this case, Equation (15) with \(K_{1}=9.731\) kPa, \(A=5.277\) kPa, \(D=10.171\), was able to closely reproduce the experiments (\(R^{2}=0.9998\), Figure 6a), while residuals (\(\Delta\sigma\)) spanned from \(-0.316\) to \(0.165\) (Figure 6b). The dimensionless stress due to the action of the matrix linearly increased from zero (\(\lambda=1\)) to \(0.088\) (\(\lambda=1.089\)), and the slope of this curve was \(58.39\) for \(\lambda\to 1\), as shown in Figure 6c. On the contrary, the dimensionless stress due to fibrils increased in a non-linear way from zero to \(0.089\), and the slope of this curve increased from zero (\(\lambda=1\)) to \(4.676\) (\(\lambda=1.089\)) (Figure 6d). Similarly, the total dimensionless stress increased in a non-linear way from zero to \(0.177\), and its slope spanned from \(1.000\) (\(\lambda=1\)) to \(12.384\) (\(\lambda=1.089\)), as shown in Figure 6e. Furthermore, the dimensionless curvature \(\hat{\kappa}_{mat}\) monotonically increased from zero (\(\lambda=1\)) up to \(0.052\) (\(\lambda=1.089\)) (Figure 6f), while the dimensionless curvature due to the fibrils' action \(\hat{\kappa}_{fib}\) had a bell-like shape (Figure 6g). In this case, the maximum value of the curve was \(\max\{\hat{\kappa}_{fib}\}=25.732\), which was reached at \(\lambda=1.0565\). Finally, \(\hat{\kappa}_{tot}\) was studied. This curve had a bell-like shape, and the maximum value was \(\max\{\hat{\kappa}_{tot}\}=6.183\) at \(\lambda=1.058\), as shown in Figure 6h. Figure 6: Vagus nerve: (**a**) Comparison between theoretical prediction and experimental values for the axial stretching of the nerve (\(R^{2}=0.9998\)). (**b**) Plot of the residuals. (**c**) Dimensionless stress due to the matrix action. (**d**) Dimensionless stress due to the fibrils’ action. (**e**) Evolution of the total dimensionless stress.