## 4 Results and Discussion
### Detailed Mechanical Characterization of the 100 mm Diameter Membrane  
#### 4.3.1 Measured Displacement Fields  
As mentioned in Section 2.3, the 100 mm diameter natural rubber membrane was inflated at 1.07, 1.33, 1.60, 1.87 and 2.13 kPa. The one-shot moire model described in Section 2.2 was implemented in MATLAB. Equations (6) and (8)-(10) were used for determining the deformed shape of the inflated rubber membrane at each pressure level. The v-displacements (u-displacements) of the membrane horizontal (vertical) diameter were initially assumed to be equal to 0; initial values of displacements were initially corrected by including information on thickness distribution gathered experimentally. However, the deformed shape of the membrane was precisely reconstructed by the proposed moire model regardless of any assumption made on the values of displacement components. The maximum u-displacements recorded by the present moire setup for the different pressure levels were 0.542, 0.641, 0.769, 0.915 and 1.140 mm while the maximum v-displacements were 0.567, 0.674, 0.803, 0.961 and 1.167 mm; the corresponding out-of-plane displacements ranged between 6.047 and 13.932 mm. Figure 8 shows the map of the u-, v- and w-displacements for the maximum inflation pressure of 2.13 kPa. Figure 8: Displacement maps obtained by the proposed one-shot projection moiré setup for the 100 mm diameter natural rubber membrane inflated at the maximum pressure of 2.13 kPa: (**a**) u-displacement; (**b**) v-displacement; and (**c**) w-displacement (with indication of nominal symmetry axes and position of maximum deformation point). It can be seen that in-plane displacement patterns were symmetric enough with respect X- and Y-axes (see Figure 8a,b) although the actual thickness of the natural rubber membrane varied by about 14% along these directions. Figure 8c shows that contour maps of w-displacements are shaped as ellipses inclined with respect to horizontal (i.e., the X-axis) and vertical (i.e., the Y-axis) diameters of the membrane. The asymmetry of the out-of-plane displacement field of the inflated membrane is confirmed by the fact that the maximum w-deformation point (indicated by the star in Figure 8c) does not coincide with the center of the membrane (i.e., the intersection of x = 0 and y = 0 diameters). As mentioned above, displacement components of the inflated membrane were also measured with the two-projectors, one-camera IMPM setup described in Section 2.3, a variant of the setup used in [34]. The in-plane displacements were determined referring to the 2 mm pitch dot grating printed on the specimen and then corrected including information on the slope of the deformed surface given by the modulation of projected vertical lines. Since the light source, layout, illumination angles and pitch of the gratings selected for the two-projectors, one-camera IMPM setup were the same as those used in the one-shot projection moire measurements, the two optical setups obviously shared the same value of out-of-plane sensitivity. Figure 9 compares the u- and v-displacement fields measured with the present one-shot projection moire setup and the two-projectors, one-camera IMPM setup along two control paths corresponding to horizontal and vertical diameters of the inflated membrane (see insets of Figure 9). These diameters are parallel to the two sets of lines of the cross-gratings used by the one-shot proposed moire setup. Furthermore, they are, respectively, orthogonal and parallel to the vertical lines projected by the IMPM setup. Although these specifications might seem obvious, it should be noted that the inflated membrane actually does not deform in an axially symmetric way because the thickness is not constant throughout the specimen. Thickness was measured along the 12 loading directions (corresponding to six diameters) selected in the preliminary in-plane testing (see Section 4.2). However, each pair of orthogonal diameters may present a different mechanical response from the expected nominal behavior based on the amount of thickness variation.