## 5 Conclusions and Future Work  
This paper described a novel hybrid framework for mechanical characterization of soft hyperelastic membranes. The contribution of this study in terms of novelty was at least three-fold: (i) the characterization framework accounted for structural inhomogeneity and induced anisotropic response to symmetric loading; (ii) a novel one-shot projection moire model able to recover the whole 3D displacement field of inflated membranes; and (iii) a fast, efficient, robust enhanced hybrid metaheuristic optimization algorithm for solving large-scale inverse problems. The proposed framework combined biaxial tests (planar and inflation), one-shot projection moire (with two symmetric projectors that project cross-gratings onto the inflated membrane), a mathematical model to extract 3D displacement information from moire measurements and metaheuristic optimization. The deformation of the membrane was accurately measured by the moire setup that exploited the connections between moire and differential geometry. Metaheuristic optimization was performed with the HS-JAYA algorithm combining harmony search and JAYA methods. The HS-JAYA algorithm was inherently able to minimize the computational cost of the identification process as it always perturbed design moving along descent directions. The characterization framework was successfully applied to a 100 mm diameter natural rubber membrane exhibiting non-isotropic mechanical response because thickness varied over the specimen. The two-parameter Mooney-Rivlin constitutive model was used for modeling the hyperelastic behavior of the tested membrane. Several variants of the identification problem including up to 324 unknown material properties (local values of MR constants) and local thickness values were solved by minimizing differences between measured total displacements and those computed by an FE model simulating the inflation test. The identified thickness distributions were highly correlated and fully consistent with the distribution measured experimentally. The values of hyperelastic constants determined by HS-JAYA combined very well into an equivalent Young's modulus matching the level of anisotropy found from planar biaxial tests. The optimization process was very robust, and very little dispersion of solutions was seen. Although the characterization framework was described in great detail in this article and provided satisfactory results, some aspects have to be further analyzed in future studies. First, the characterization of highly anisotropic hyperelastic materials should be considered. However, this issue should not be critical because the proposed projection moire model does not rely on any assumption of the material's constitutive behavior; complications derive for the most part from anisotropic hyperelasticity modeling that usually entails a huge number of material parameters. It should be noted that natural rubber follows an isotropic hyperelastic behavior as it is universally acknowledged in the technical literature. The present study obviously was not aimed at proving the contrary. The goal (fully accomplished) was instead to show how to account for any structural inhomogeneity (for example, thickness variations) that may lead to a globally non-isotropic mechanical response of the specimen/structure to be characterized. The second aspect worthy of investigation is that the metaheuristic search engine may be further enhanced, considering the implications of the No-Free-Lunch theorem. For example, if material anisotropy is coupled to structural inhomogeneity, the number of design variables of the identification problem may exponentially increase and the number of search directions may become too large to be efficiently handled by a metaheuristic algorithm. However, HS-JAYA inherently employs elitist strategies in all steps of the search process, which enable the proposed algorithm to quickly converge to the optimum solution. Such an ability appears to be independent of problem size.