## 3 Experiments and Simulations
### Simulation Details for the Material Test  
One of the well-established commercial finite element analysis programs, ABAQUS, was used for simulation of the uniaxial tensile test. The material parameters in the HGO model were estimated based on the stress-stretch curve of the porcine abdominal aortic tissue as a function of the tissue orientation to validate the computational simulation technique. The geometries of the uniaxial tensile test specimens used were constructed by considering the dimensions in the experiment and reference [17], as shown in Figure 3a. The orientations for the collagen fiber in the intimal, medial, and adventitial strips were set as 18.8\({}^{\circ}\), 37.8\({}^{\circ}\), and 58.9\({}^{\circ}\), respectively, as shown in Figure 3b [26] and Figure 4.  
As indicated in Section 3.1, fixed and straight-line motion conditions were applied as the experimental boundary and loading conditions, as shown in Figure 3. In particular, under the loading condition, the tensile loading directions, which were divided into circumferential and longitudinal directions relative \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{3}{c}{**Sample Dimension (in mm)**} & \multicolumn{3}{c}{**Tensile Load Direction**} \\ \cline{2-5}  & **Width (Top)** & **Width (Middle)** & **Length** & **Thickness** & **Relative to Oriented Strip** \\ \hline AC1 & 14.96 & 9.98 & 24.97 & 1.98 & Circumferentially \\ AC2 & 15.10 & 10.04 & 25.05 & 2.01 & Circumferentially \\ AC3 & 14.98 & 10.01 & 25.03 & 2.01 & Circumferentially \\ AC4 & 15.05 & 10.01 & 25.01 & 1.99 & Circumferentially \\ AC5 & 15.01 & 9.99 & 25.00 & 2.03 & Circumferentially \\ AL1 & 15.02 & 10.02 & 24.98 & 2.01 & Longitudinally \\ AL2 & 15.04 & 10.02 & 24.99 & 2.02 & Longitudinally \\ AL3 & 14.97 & 10.03 & 25.01 & 1.97 & Longitudinally \\ AL4 & 14.99 & 9.98 & 24.98 & 2.01 & Longitudinally \\ AL5 & 15.04 & 9.97 & 25.03 & 2.01 & Longitudinally \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tissue specimens of the porcine abdominal aorta in the tensile test (AC: Aorta and Circumferentially (Load direction), AL: Aorta and Longitudinally (Load direction)). Figure 2: Schematic of the uniaxial tensile test specimens and experimental apparatus. (**a**) Dimensions of the test specimens; dimensions in millimeters. (**b**) Closer view of the specimen fixation. (**c**) Universal testing machine. to the axis of the aorta, were considered. In addition, the HGO model for an anisotropic hyper-elastic material was applied for determining the material properties in the simulation. The hexahedral (C3D8 RH-type) element, which is the eight-node linear brick, reduced integration with hourglass control, hybrid with constant pressure, was adopted during simulation. When the material response is incompressible such as soft tissue, the solution to a problem cannot be obtained in terms of the displacement history only, since a purely hydrostatic pressure can be added without changing the displacement. The nearly incompressible case showed behavior approaching this limit, in that a very small change in displacement produced extremely large changes in pressure, so that a purely displacement-based solution was too sensitive to be useful numerically. Accordingly, ABAQUS removed this singular behavior in the system by treating the pressure stress as an independently interpolated basic solution variable, coupled to the displacement solution through the constitutive theory and the compatibility condition, with this coupling implemented by a Lagrange multiplier. This independent interpolation of pressure stress was the basis of these \"hybrid\" elements. More  
Figure 4: Circumferential orientation of the collagen fiber in the layer [26]. Figure 3: (**a**) Boundary and loading conditions and (**b**) orientations of the fiber and mesh in the tensile test specimen.