## 4 Results and Discussion
### IM Measurements and Preliminary Mechanical Characterization (Anisotropic Response)
In the IM experiments, a cross-grating of 0.5 mm pitch was printed onto each specimen following indications provided in [34; 63]. Grating was modulated as the specimen deformed under the applied load. Moire patterns were obtained by digitally subtracting images of modulated grating at the various load levels selected for each biaxial test (to increase stability, images were recorded 1-2 min after having removed toroidal holder) from the reference image recorded for the unloaded state. A Dalsa CCD camera (1600 \(\times\) 1360 pixels, 2/3\({}^{\prime\prime}\)) with a Fujinon HF9 HA-1B objective, lined up and focused on the sample center, was utilized in the IM experiments. All moire patterns recorded in this study were analyzed with the Holo Moire Strain Analyzer(tm) (HMSA) Version 2.0 software (General Stress Optics Inc., Chicago, IL, USA). HMSA includes FFT, filtering, carrier modulation, fringe extension, edge detection and masking operations, quadrature, phase unwrapping, phase differentiation, removal of discontinuities, etc. In-plane displacement maps were obtained from Equation (11), setting the sensitivity \(\Delta\text{s}_{\text{u,v}}=0.5\) mm, equal to the grating pitch. Spatial frequencies encoded in moire patterns of u- and v-displacements were extracted from Fourier space. Strains \(\varepsilon_{\text{x}}\) and \(\varepsilon_{\text{y}}\) were directly computed by HMSA by differentiating phase maps. For the values of MR constants \(\text{a}_{10}=201.021\) kPa and \(\text{a}_{01}=13.201\) kPa determined in [34], assuming that the rubber membrane was homogeneous, isotropic and incompressible (i.e., \(\
u=0.5\)), the equivalent Young's modulus was \(\text{E}_{\text{MR}}=4(1+0.5)(201.021+13.201)=1285.332\) kPa. However, as mentioned before, the thickness of the tested membrane was found to vary over the whole specimen. Local variation of thickness may be amplified by the inflation process, which tends to stretch the membrane and reduce thickness as t = t\({}_{\text{o}}\)/\(\lambda_{\theta\theta}\)[64], where t and t\({}_{\text{o}}\), respectively, are the current and initial membrane thicknesses, and \(\lambda_{\theta\theta}\) is the circumferential stretch ratio. For this reason, membrane thickness was measured along the six diameters corresponding to the 12 loading directions selected in the planar biaxial tests (see Figure 7c). The measurement points were located at 0, \(\pm 1/8\), \(\pm 1/4\), \(\pm 3/8\), \(\pm 1/2\), \(\pm 5/8\), \(\pm 3/4\), \(\pm 7/8\) and \(\pm 1\) of the nominal membrane radius; the \"\(\pm\)\" notation indicates pairs of symmetric locations about the center of the membrane. Thickness variations were randomly distributed over the surface, and no preferential direction of variation could be identified. Overall, thickness variations became more significant as the membrane diameter increased, ranging from 2.9% (for the smallest membrane of 25 mm diameter) to 14.8% (for the largest membrane of 125 mm diameter) of the 1 mm nominal thickness. The system (32) was solved for the five membranes with diameters from 25 to 125 mm considered in the preliminary biaxial tests. For each diameter, two different sets of MR constants were determined by fitting the stresses developed for the \(\varepsilon_{\text{x}}\) or the \(\varepsilon_{\text{y}}\) strains; the corresponding values of equivalent Young's modulus were, respectively, denoted as \(\text{E}_{\text{MR}}\)\({}^{\text{(a)}}\) and \(\text{E}_{\text{MR}}\)\({}^{\text{(y)}}\). The degree of mechanical anisotropy of each membrane was, hence, defined as \(\beta_{\text{anis}}=\text{E}_{\text{MR}}\)\({}^{\text{(a)}}\)/\(\text{E}_{\text{MR}}\)\({}^{\text{(y)}}\). Interestingly, for each membrane, \(\beta_{\text{anis}}\) practically coincided with the average ratio of thickness values measured along orthogonal diameters. In particular, for the 100 mm diameter membrane mechanically characterized via inflation test, \(\beta_{\text{anis}}\)resulted equal to 1.127.