## 3 Results and Discussion
### FEM Simulation  
The experimental data presented in Figures 6 and 7, corresponding to the tensile behaviour of the longitudinal and circumferential samples from the porcine urethra, were obtained using the protocol outlined in Section 3.1. The mean value (the point-wise arithmetic mean over the samples considered) of the last cycle (the load-unload cycle corresponding to higher stretch values), together with the FEM model outlined in Figure 5 were the input data for the FEM simulation process. To obtain the material parameters associated to the nonlinear constitutive models corresponding to Equations (1)-(3), the experimental data (in the stress-strain format) were fitted directly by the ABAQUS software package. For the hyperelastic material models available, the software conducts a stability analysis during the fitting process. Those models deemed unsuitable to be used for simulations with the proposed FEM model (due to material instabilities in the experimental strain range) were discarded. Table 1 presents a relation of the viable (stable) models and their material parameters. Figures 10 and 11 compare the experimental data in the form of point-wise mean curves of longitudinal and circumferential samples, with the corresponding FEM simulations. In general, the same model was stable for both datasets; however, for higher polynomial orders (\(n=5\) and \(n=6\) order), there was a difference--with the fifth-order Reduced Polynomial (RP) model being stable only for the circumferential sample while the sixth-order RP model was stable only for the longitudinal sample. Considering the longitudinal data (Figure 10), all the models tested could provide an adequate estimation of the experimental data up to a 30% deformation (\(\lambda\approx 1.3\)). For stretches up to \(\lambda\approx 1.5\), there are two clusters of model results. The first cluster includes the third-order Ogden model (\(n=3\)) and the \(n=2,3,6\) RP models. Despite the significant deviations observed for deformations over 50% (\(\lambda>1.5\)), these models seem to follow  
Figure 9: Comparison of the experimental results of circumferential samples of the urethra from male pig and male human subjects (grey ribbon—STD of the results of the current study). the experimental stress evolution. Of the remaining models, the first-order Ogden model (\(n=1\)) and specially the Neo-Hookean model, the \(n=1\) RP model displayed the worst performance in modelling the experimental mechanical behaviour of the porcine urethra in the longitudinal direction. In general, the FEM models reached a maximum stress of \(\approx\)70 kPa while the experimental data reached \(\approx\) 110 kPa, which can be interpreted as the experimental data being 36% stiffer than the simulations for \(\lambda=2.0\) (100% deformation). It is noticeable that the models with a higher number of parameters (Table 1) have a better performance--the third-order Ogden (\(k=6\)), sixth-order RP (\(k=6\)) and third-order RP (\(k=3\)). Conversely, the models with the poorest outcome were those with a lower number of parameters--the first-order Ogden (\(k=2\)) and Neo-Hookean model (\(k=1\)). Regarding the circumferential data (Figure 11), the only reliable model in the \(1.0\leq\lambda\leq 1.2\) range was the third-order Ogden model (\(n=3\)). This model could be used to approximate the mechanical behaviour of the circumferential porcine urethra to deformations as high as 35% (\(\lambda=1.35\)), despite the evident divergence (between the third-order Ogden and experimental data) for deformations over 30% (\(\lambda>1.3\)). None of the remaining constitutive models (Ogden (\(n=1\)), Neo-Hookean, RP (\(n=2\)), Yeoh and RP (\(n=5\))) were able to approximate the experimental curve across the stretch range considered. On average, the FEM models reached \(\approx\)25 kPa for 100% deformation (\(\lambda=2.0\)), while the experimental data had a maximum stress 3 times higher \(\approx\) 75 kPa.