## 4 Results and Discussion
### IM Measurements and Preliminary Mechanical Characterization (Anisotropic Response)  
The same intrinsic moire setup of Ref. [63] was used in this study for the preliminary planar biaxial tests. An assembly view of optical set is presented in Figure 7 together with the schematic diagram of the load distribution. Each specimen was placed in the center of a dodecagonal aluminum plate and circumferentially hooked by 12 nylon wires (Figure 7a-c). Each wire was connected to dead weights, which were progressively added to the wire so as to cover loading history selected for a given specimen within 10 load steps. The load was applied to sample by the 12 pulleys placed in the dodecagon side centers (Figure 7b). The toroidal holder prevented any micro-movements and rigid body motions of the sample, that might have developed in the loading phase. The two-parameter Mooney-Rivlin hyperelastic law [59; 60; 61; 62] is a classical phenomenological model. The strain energy density function W is:  
\[\text{W}=\text{a}_{10}\big{(}\overline{\text{I}_{1}}-3\big{)}+\text{a}_{01} \big{(}\overline{\text{I}_{2}}-3\big{)} \tag{31}\]  
where strain invariants of the Cauchy-Green strain tensor [C] are defined as \(\overline{\text{I}_{1}}=\text{tr}[\text{C}]\) and \(\overline{\text{I}_{2}}=\{\text{tr}^{2}[\text{C}]-\text{tr}^{2}[\text{C}]^{2}\}\). The Young's modulus in the X or Y direction is \(\text{E}_{\text{MR}}=4(1+\
u)(\text{a}_{10}+\text{a}_{01})\), while the shear modulus is \(\mu=2(\text{a}_{10}+\text{a}_{01})\). MR constants \(\text{a}_{10}\) and \(\text{a}_{01}\) are computed by minimizing the difference between the experimentally measured principal Cauchy stresses and theoretical values. A linear system is obtained:  
\[\left\{ \begin{array}{l}\left[\sum\limits_{k=1}^{\text{NTG}}\left({{\lambda_{ 1k}}^{2}}-\frac{1}{{{\lambda_{1k}}^{2}}}\right)^{2}\right]{a}_{10}+\left[ \sum\limits_{k=1}^{\text{NTG}}\left({{\lambda_{1k}}^{2}}-\frac{1}{{{\lambda_{ 1k}}^{4}}}\right)^{2}{{\lambda_{1k}}^{2}}\right]{a}_{01}=\frac{1}{2}\sum \limits_{k=1}^{\text{NTG}}\left[{{\sigma_{\text{TG}}}^{k}}\Big{(}{{\lambda_{1k }}^{2}}-\frac{1}{{{\lambda_{1k}}^{4}}}\Big{)}\lambda_{1k}^{2}\right]\\ \left[\sum\limits_{k=1}^{\text{NTG}}{{\left({{\lambda_{1k}}^{2}}-\frac{1}{{{ \lambda_{1k}}^{4}}}\right)^{2}{{\lambda_{1k}}^{2}}}\right]{a}_{10}+\left[ \sum\limits_{k=1}^{\text{NTG}}{{\left({{\lambda_{1k}}^{2}}-\frac{1}{{{\lambda_ {1k}}^{4}}}\right)^{2}{{\lambda_{1k}}^{4}}}\right]{a}_{01}=\frac{1}{2}\sum \limits_{k=1}^{\text{NTG}}\left[{{\sigma_{\text{TG}}}^{k}}\Big{(}{{\lambda_{1k }}^{2}}-\frac{1}{{{\lambda_{1k}}^{4}}}\Big{)}{{\lambda_{1k}}^{2}}\right]}\end{array} \right. \tag{32}\]  
Figure 7: Intrinsic moiré setup used for preliminary in-plane biaxial tests (similar to the setup used in [63]): (**a**) 3D assembly view; (**b**) details of loading apparatus; and (**c**) schematic representation of the load distribution showing the 12 loading directions that correspond to six diameters (etched lines). where \(NTG\) is the number of experimental data and k refers to the generic experimental measure. The system (32) can be solved if the true stresses \(\sigma_{TG}\)\({}^{k}\) and stretch ratios \(\lambda_{1k}\) at each load step are known. The nominal stress generated by the circumferential loads is \(\sigma_{\text{eng}}=\text{F}/\pi\text{td}\), where F is the sum of radial forces applied to the specimen, \(t\) is the nominal specimen thickness (i.e., 1 mm) and d is the specimen diameter between two opposite punching points. For \(k\)th measure, \"true\" Chauchy stress and stretch ratio are, respectively, determined as:  
\[\sigma_{TG}\text{${}^{k}$}=\lambda_{1k}\text{${}^{\text{-}}$}\sigma_{\text{eng }}\text{${}^{k}$} \tag{33}\]  
\[\lambda_{1k}=e^{\varepsilon_{TG}^{k}} \tag{34}\]  
where the true strains \(\varepsilon_{TG}\)\({}^{k}\) are determined via intrinsic moire for each load applied to the tested specimen. Here, load history was divided into 10 steps, and, hence, the \(k\) counter varied from 1 to 11.