## 2 Materials and Methods
### Material Properties and Characteristics  
The crucial part of developing biocompatible and non-hazardous SPAs was the selection of suitable materials. Silicone elastomeric rubber is the most common material used in the 3D molding process to manufacture soft actuators [25]. In this study, we studied the properties of three different silicone-based materials as exhibited in Table 2.  
The elastomeric materials model was used to describe the behavior of the selected silicone, with the characteristic of absorbing large deformation without permanent distortion. The silicone elastomeric rubber could withstand huge strains of 500% [26]. Silicone rubber has an elastic stress-strain curve with non-linear relation, and is isotropic, incompressible, and generally independent of strain rate. The most common non-linear constitutive model with incompressibility constraints such as Neo-Hookean, Ogden, Mooney-Rivlin, and Yeoh models have been considered for hyperelastic material [27]. These models can be represented by one or more material parameters that can be obtained from the stress-strain curve in experiments. Mooney-Rivlin model is mainly utilized in the study of rubber's small deformation range, whereas the Yeoh model is prioritized in the study of rubber's wide deformation range and is recommended for significant deformation [28].  
The Yeoh model has the advantages of simplicity and excellent precision, and the material characteristics can be obtained through uniaxial compression experiments. The strain energy density function for [PERSON]'s 3 rd model is given by:  
\[W = C_{1}(I_{1}-3)+C_{2}(I_{2}-3)^{2}+C_{3}(I_{3}-3)^{3} \tag{1}\]  
where \(C_{1}\), \(C_{2}\), and \(C_{3}\) are model parameters, while \(I_{1}\), \(I_{2}\), and \(I_{3}\) are strain invariants of Cauchy-Green deformation tensors, respectively. In this study, A15 Shore, A10 Shore, and Sylgard 184 were studied as the material of the proposed SPA system. The constitutive model parameters for three silicone elastomers and their properties are tabulated in Table 2. The Sylgard 184 model parameter was retrieved from [PERSON] et al. [29] where the researchers use uniaxial tensile tests to identify the parameters of Yeoh models. In the ANSYS software (ANSYS 2019 R3), the A15 Shore is an elastomer. The model parameter values for A15 Shore  
Figure 2: Dimension of 3D model construction of the proposed Model B in mm: (**a**) top layer (**b**) nonexpendable bottom layer; and (**c**) side view.  
were retrieved from the ANSYS database [30] for the elastomer sample. The A10 Shore has the same properties as Dragon Skin 10 medium. The model parameters for A10 Shore were retrieved from [PERSON] et al. [31], in which the researchers use Evolutionary Inverse Material Identification (EIMI) to identify the parameters of Yeoh models.  
The three materials are flexible, extensible, and inexpensive. These silicones are highly resilient to deterioration and damage from extreme temperatures, non-toxic, and degradable [17]. However, for the optimal inflation and deflation of the proposed SPA, lower tensile strength was preferred to prevent persistent discomfort during compression.