## 2 Materials and Methods
### Material Properties and Finite Elements Methods (FEA)  
RTV ZA 22A is a high-compliance hyperelastic material that possesses the ability to elastically deform several times more than its initial value at the moment of stress. Determining the mechanical characteristics of the material is important to establish and validate the real and simulated behavior employing the FEA of the actuators used. For this purpose, the tensile mechanical characteristics of the RTV ZA 22A material were determined using the ASTM D12 (method A) standard [30]. The dimensions of the specimens are 3 mm in thickness, a total length of 115 mm (where the length of the calibrated part is 33 mm), a width at the ends of 25 mm, and a width of the calibrated part of 6 mm. The tests were performed on a sample of 5 specimens on the Titan 2 Universal tensile testing machine (software version 7.0.4.14642) at a speed of 50 mm/min and with a cell force of 600 N, as shown in Figure 4b. From the experimental data obtained, for the accuracy of the results, outliers were removed. Based on the experimental results taken from the machine software, the characteristic curve in the form of engineering stress and engineering strain was plotted, with the curve representing the average of the values of the 5 specimens tested. The test results are shown in Figure 4a.  
The experimental data obtained from the tensile tests provide the possibility of determining a number of characteristics such as material elongation, Young's modulus of elasticity, and material constants needed to perform finite element simulation of the actuator. This is essential to determine the approximate behavior of the actuators tested. Also, another element to consider was to identify the actuating pressure required to achieve amplitude of motion values as close as possible to the phalanx amplitude of motion values. In the case of the PIP joint, the value is approximately 120\({}^{\circ}\). The conformity between the two values leads implicitly to greater efficiency and to a shorter recovery time.  
Obtaining this information was achieved using the finite element program Abaqus (Dassault Systems--6.13-1), and the simulation is identified in Figure 5a. Modeling of the PneuNets actuators was performed using the Yeoh hyperelastic model [31], for non-linear and incompressible materials based on the experimental data of the graph in Figure 4 engineering stress and engendering strain. The strain energy function for determining the 2 nd-order material constants is shown below in Equation (1):  
\[\mathrm{W}=\sum_{i=1}^{\mathrm{N}}\mathrm{C}_{i0}(\overline{\mathrm{I}_{1}}-3 )^{i}+\sum_{k=1}^{\mathrm{N}}\frac{1}{\mathrm{d}_{k}}(\mathrm{J}-1)^{2k} \tag{1}\]  
where W is a strain energy density, \(\mathrm{C}_{i0}\) are coefficients of the polynomial function, \(\overline{\mathrm{I}_{1}}\) is the first strain invariant, and J is the determinant of the elastic deformation gradient. The values of the Yeoh material constants of degree 2 obtained are \(\mathrm{C}_{10}=48.673\) (Pa) and  
Figure 4: Determination of mechanical characteristics: (**a**) The characteristic curve represents the average of the 5 specimens, (**b**) tensile testing machine Titan 2 Universal.  
C\({}_{20}\) = 962.03 (Pa). From the simulations, it can be seen compared to Figure 5b that the simulated bending amplitude is approximately equal to the actual bending one.