## 3 Results
Since it was found that \(s(\sigma_{mat},K_{1})=\frac{K_{1}-1}{K1}\), the larger the value of \(K_{1}=1+\Delta K_{1}\) (\(\Delta K_{1}\in Q\)) was, the more the value of its value converged towards one. Again, the effects of the changes in \(A\) or \(D\) were investigated on the stress functions due to the collagen fibrils. In this case as well, it was found that \(s(\sigma_{fib},A)=\frac{A-1}{A}\), (Figure 3b), for different values of \(A=1+\Delta A\), \(\Delta A\in Q\). Thus, the larger the value of \(A\) was, the more the value of \(s(\sigma_{fib},A)\) converged towards one. Similarly, the evolution of \(s(\sigma_{fib},D)\) is shown in Figure 3c for different values of \(D=1+\Delta D\), \(\Delta D\in Q\). The larger the value of \(D\) was, the quicker the value of \(s(\sigma_{fib},D)\) converged towards one. On the contrary, the larger the value of \(D\) was, the quicker the function \(ln[s(\tilde{\kappa}_{fib},D)]\) diverged, as shown in Figure 3d. Once having tested the suitability of the provided framework, Equation (15) was used to study the experimental response of a porcine peroneal nerve (five consecutive elongations up to \(\lambda=1.08\)) [19]. Figure 3: (**a**) Sensitivity of \(\sigma_{mat}\) with respect to increasing values of \(K_{1}\). The function converged towards one (black arrow). (**b**) Sensitivity of \(\sigma_{fib}\) with respect to increasing values of \(A\). The function converged towards one (black arrow). (**c**) Sensitivity of \(\sigma_{fib}\) with respect to increasing values of \(D\). The function converged towards one (black arrow). (**d**) Sensitivity of \(\tilde{\kappa}_{fib}\) with respect to increasing values of \(D\). The function diverged (black arrow). Stress data are reported as a function of stretch (Figure 4) and quantitatively compared to theoretical predictions through the \(R^{2}\) statistic and the computation of residuals (\(\Delta\sigma\)). This comparison resulted in \(R^{2}=0.9979\) for the first elongation (Figure 4a), \(R^{2}=0.9976\) for the second one (Figure 4b), \(R^{2}=0.9987,0.9989,0.9989\) (Figure 4c-e). Similarly, residuals ranged between \(-0.056\) kPa and \(0.091\) kPa for the first elongation (Figure 4f), while they ranged between \(-0.105\) kPa and \(0.086\) kPa for the second one (Figure 4g). Moreover, residuals spanned from \(-0.078\) kPa to \(0.078\) kPa (Figure 4h), from \(-0.077\) kPa to \(0.083\) kPa (Figure 4i), and from \(-0.074\) kPa to \(0.108\) kPa (Figure 4j), for the third, fourth, and fifth elongation, respectively. Finally, relevant quantities (mean \(\pm\) standard deviation) in Equation (15) were quantified and resulted in \(K_{1}=3.018\pm 0.130\) kPa, \(A=0.014\pm 0.001\) kPa, and \(D=66.893\pm 1.527\). Figure 4: Peroneal nerve: comparison between experimental data and predicted values. Experimental data (squares) are plotted in orange (see electronic version of the manuscript), while theoretical predictions are in black solid line. The \(R^{2}\) index is reported on the left column for each theory-data comparison, while the residual plots are on the right column. (**a**) Theoretical prediction of the first elongation (\(R^{2}=0.9979\)). (**b**) Theoretical prediction of the second elongation (\(R^{2}=0.9976\)). (**c**) Theoretical prediction of the third elongation (\(R^{2}=0.9987\)). (**d**) Theoretical prediction of the fourth elongation (\(R^{2}=0.9989\)). (**e**) Theoretical prediction of the fifth elongation (\(R^{2}=0.9989\)). (**f**) Plot of residuals related to the first elongation. (**g**) Plot of residuals related to the second elongation. (**h**) Plot of residuals related to the third elongation. (**i**) Plot of residuals related to the fourth elongation. (**j**) Plot of residuals related to the fifth elongation. Moreover, the dimensionless stress and curvature were investigated. In particular, the dimensionless stress due to the matrix contribution (\(\hat{\sigma}_{mat}\)) monotonically increased from zero (\(\lambda=1\)) to 0.080 (\(\lambda=1.08\), Figure 5a).