## 1 Introduction
A novel mathematical model is developed to extract 3D displacement information from the moire measurements--the deformed shape of the membrane is approximated by a set of curved surface segments for which the model determines the average curvature. A fast, population-based metaheuristic optimization algorithm (HS-JAYA), combining the harmony search (HS) and the JAYA optimization methods, is implemented in order to solve the inverse problem entailed by mechanical characterization. The two methods combined into HS-JAYA have been selected for two reasons: (i) HS is one of the most common metaheuristic algorithms in engineering applications including also the solution of inverse problems; and (ii) JAYA has the most straightforward and inherently efficient formulation ever implemented in metaheuristic optimization. HS-JAYA always attempts to generate trial solutions that may improve the current best record included in the population of candidate solutions. For that purpose, gradient information and elitist strategies are utilized. Furthermore, exploration and exploitation are properly integrated into HS-JAYA and continuously alternated in the metaheuristic search process so as to minimize the computational cost of the inverse problem (1). Besides the novelty introduced by the proposed projection moire model and the hybrid HS-JAYA optimization formulation, the present identification framework also accounts for structural inhomogeneity of tested specimens, an aspect not very often considered in the literature on mechanical characterization of hyperelastic materials (see discussions in [37,38] and references cited therein). For this purpose, the inverse problem variants formulated in this study include up to 324 design variables, an unusually large number of unknown parameters in the mechanical characterization of soft matter. In summary, the contribution of this study to the field of mechanical characterization of soft materials is at least three-fold:  
* Development of a novel characterization framework for hyperelastic membranes, which may account for structural inhomogeneity and induced anisotropic response to symmetric loading;
* Development of a novel one-shot projection moire model able to recover the whole 3D displacement field of inflated membranes;
* Development of a fast, efficient and robust enhanced hybrid metaheuristic optimization algorithm for solving large-scale variants of the inverse problem (1). The feasibility of the proposed approach was successfully tested on a natural rubber membrane, which exhibited some degree of anisotropy in mechanical response because of its inhomogeneous thickness. The inflation test [39] was selected as the experimental loading protocol in the characterization process of the rubber membrane and the corresponding 3D displacement field was measured with the one-shot projection moire setup. The anisotropic response of the tested material was confirmed by planar equi-biaxial tests [40] carried out on five specimens of different sizes, and the corresponding 2D displacement fields were measured with intrinsic moire. The inflation test and the planar equi-biaxial test were selected for this study because they are the most commonly used experimental protocols for characterizing soft membranes made of hyperelastic material (e.g., [41; 42; 43; 44; 45; 46] and the studies cited therein). The rest of the article is organized as follows. Section 2 describes the proposed one-shot projection moire model and the experimental setup used in the study; the use of intrinsic moire for the additional in-plane tests also is documented. Section 3 describes the optimization algorithm used in the identification process. Section 4 presents and discusses the results of the identification process including also the results of preliminary intrinsic moire experiments. Section 5 summarizes the study and outlines future research.