## 2 Materials and Methods
### 3D Simulation of the Proposed Soft Pneumatic Actuator (SPA) System  
To ensure the optimal deformation of the proposed SPA, the pressure distribution of the proposed 3D model and the proposed elastomeric materials (A15 Shore, A10 Shore, and Sylgard 184) was analyzed using the finite element method (FEM). The 3D model of the SPA was designed in Solidworks (Dassault Systemes SOLIDWORKS Corp., Waltham, MA, USA) and then imported to ANSYS 2019 R3 for FEM analysis. It was assumed that the proposed compression system with a chamber should be able to provide homogeneous pressure regardless of the location of the cuff. For ensuring a balanced pressure, the air pressure was observed on the inner wall of the chamber. The SPA system for the analysis is shown in Figure 3 with fixed supports surrounding all edges highlighted in blue to imitate real-life behavior. Gravity was also considered for the solid domain, and it acted in the negative y direction.  
Since this study employed elastomeric material, a physics nonlinear mechanics mesh with linear element order was adopted. The mesh method used for the SPA system was a hex-dominated element shape. Curvature and proximity capturing were activated. The experimental element size was set at 1 mm for all simulations which resulted in a total number of 300,196 elements. The minimum element quality based on skewness was 0.90.  
In this study, a controlled condition of 23 s of inflates, 7 s of hold, and 7 s of deflate (23-7-7 s) in one cycle cumulating in 37 s was simulated. This method is a recommended treatment cycle by a commercially available intermittent pneumatic compression (IPC) device for daily home care of the lower limb [32]. The pressure was applied using the ramp function, with the gradual increment of the pressure from 0 to 120 mmHg from t = 0s to t = 23 s. Furthermore, in each simulation, the pressure was applied progressively throughout 44 sub-steps. This was a crucial variable because it prevents the load from being delivered entirely at once, which often leads to convergence problems, particularly when working with soft materials that have a low Young's modulus [33].  
The three silicone elastomers' deforming structures affect the time and force with which they were applied to the skin. Additionally, they are highly dependent on the pressure, velocity, and material properties of silicone. The relationship between the input  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sylgard 184** & **A15 Shore** & **A10 Shore** \\ \hline Manufacturer & Dow Corning & Clay art & Clay art \\ Color & Colourless & Translucent & Grey \\ Shore hardness & A50 & A15 & A10 \\ Tensile strength & 980 psi & 537 psi & 475 psi \\ Density & 1.04 g/cm\({}^{3}\) & 1.35 g/cm\({}^{3}\) & 1.35 g/cm\({}^{3}\) \\ Elongation at break & 150\% & 771\% & 1000\% \\ Durometer shore & 50 & 15 & 10 \\ Young’s modulus & 1.32–2.97 MPa & 0.74 MPa & 0.25 MPa \\  & \(C_{1}=0.42480\) MPa & \(C_{1}=0.69760\) MPa & \(C_{1}=0.00204\) MPa \\ Model parameter & \(C_{2}=-0.15880\) MPa & \(C_{2}=-0.24484\) MPa & \(C_{2}=-0.17070\) MPa \\  & \(C_{3}=0.24350\) MPa & \(C_{3}=0.12629\) MPa & \(C_{3}=2.05000\) MPa \\  & [29] & [30] & [31] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties and constitutive model parameters of silicone elastomer.  
pressure, the deformation, and the applicability of the developed 3D model was measured, based on the chamber's deformation profile.