An elastomer material is a polymer that has a viscoelastic behavior and very weak intermolecular forces, which cause it to have a much lower Young’s modulus (E) than that of other materials. This reduced E causes this material to possess a great capacity for deformation when proportionally low loads are applied. There are many types of elastomers, but they are classified essentially as unsaturated rubbers that can be cured by sulfur vulcanization, and saturated rubbers that cannot be cured by this process [
1]. The strain-stress curves for elastomers have a notable non-linear behavior, which is why Hooke’s law is not applicable. Nevertheless, for small deformations, Young’s modulus (E) can be approximated as the tangent to the strain-stress curve. The values of E that are obtained are of the order of E = 1 N/mm
2, which is something that makes clear the difference between elastomers and metals, crystals or glasses. Their macroscopic behavior is complex and depends on the time of load application, the temperature, the kind of vulcanizing, the historic loads and the state of deformation. Nevertheless, it is possible in general to achieve large deformations of the order of 100-700%, without entering the plastic region [
2]. All those material characteristics make it very difficult to define a model that is able to define their complete behavior. Over the years, several theoretical models have been proposed, and more are being proposed currently. However, there are a few that are used most commonly. These include Mooney–Rivlin [
3,
4], Arruda–Boyce [
5], Gent [
6] and Ogden [
7]. All of these explain the material behavior macroscopically. The theoretical models are different expressions of the deformation energy functions that are used in the large deformation theory that are determined by a series of invariant λ
i values and constants of material C
i [
8]. That is, due to the complexity of the material, a simple explanation has not been found despite attempts by many authors. No matter what material is selected for a theoretical model, it is necessary to test the elastomer in as many tensional configurations as required. The experimental characterization of these C
i constants requires the use of several standardized tests for: Tensile stress [
9], compression [
10], plane stress, volumetric compression and shear [
11]. Currently, there are several methods for measuring the stress-strain field by these tests to obtain the constants of material C
i. For example, there are those that are known as direct methods [
12]: The Moiré method [
13,
14], electronic speckle pattern interferometry method [
15], grid methods [
16] and digital image correlation method (DIC) [
17,
18]. Normally, these methods require expensive and complex experimental equipment to correctly determine the relationship between stresses and strains. Obtaining these elastic constants C
i directly from the stress-strain curves is usually achieved by a direct process that is known as curve-fitting. Another classical method that is known as "model updating" is based on inverse problems that are applied to numerical simulations of the finite element method (FEM) [
19,
20,
21]. Model updating bases its operating principle on the hyper-elastic models and their corresponding constants C
i that are implemented in the theory of FEM. The implementation of theoretical models with hyper-elastic behavior in the FEM makes it possible to conduct a very precise finite element (FE) analysis in which the same standardized tests that are mentioned above can be modeled. Model updating uses the experimental results (e.g., load-displacement data) for comparison with those load-displacement data that are obtained from the FE simulations. The force-displacement experimental curves that are obtained from standardized tests do not require equipment that is as expensive and complex as that required to obtain the stress-strain experimental curves of these same standardized tests. [
16,
22,
23,
24]. If the data that are obtained experimentally and those that have been obtained from the FEM differ significantly, it means that hyper-elastic model that was considered and its corresponding constants C
i are inappropriate for simulation of the behavior of the elastomer that is being studied. The theoretical hyper-elastic model and its corresponding constants C
i will be varied iteratively. The adjustment will be completed when the difference between the experimentally obtained data and the data obtained from the FEM do not differ significantly. Although this method of adjustment is well-known and used, it usually involves a high computational cost. This problem is amplified when the model of behavior that is being considered is more complex or when the number of standardized tests that are used to adjust the behavior of the studied elastomer is high. For this reason, model updating has never been used individually to adjust the constants C
i on the basis of the standardized tests mentioned above. In recent years, researchers have used several techniques to adjust the constants or parameters that define the behavior of FE models on the basis of experimental data. For example, the bio-inspired soft computing techniques and multi-response surface method (MRS) are some of the most frequently used [
25,
26,
27,
28]. These techniques usually reduce considerably the number of simulations required for the constants of the FE models that must be adjusted. Other researchers have used the model updating method or a similar procedure to find the parameters that best define the mechanical behavior of a given elastomer. However, in their adjustment, they have used a relatively small number of standardized tests [
29,
30]. This paper proposes a method to determine automatically the theoretical hyper-elastic material behavior models (Mooney–Rivlin, Ogden, Arruda–Boyce and Gent) and the corresponding C
i constants that are most appropriate for modeling the behavior of a group of elastomers. The proposed adjustment method is based on the experimental force-displacement data from the standardized tests, parameterized FE models based on the standardized tests and the multi-response surface method (MRS) with desirability functions. This combination of methods has never been used previously to determine automatically the theoretical hyper-elastic material behavior models and the corresponding C
i constants that are most appropriate for modeling the behavior of a group of elastomers using all standardized tests mentioned above. The proposed method was developed as follows: Firstly, several standardized tests (tensile, plane stress, compression, volumetric compression, and shear) were developed in order to obtain the experimental force-displacement curves of each standardized test. Then, each standardized test was replicated with respective FE models so that the Mooney–Rivlin, Ogden, Arruda–Boyce and Gent hyper-elastic models and their corresponding C
i constants were parameterized. From these parameterized FE models, the force-displacement curves were obtained. A Box–Behnken design of experiments (DoE) was developed in order to generate, for each of the theoretical hyper-elastic models, a design matrix with which to vary each corresponding C
i of the parameterized FE models. Using the force-displacement curves that were obtained from the FE models, and the MRS, quadratic regression models were generated for each standardized test for modeling an error function (ER). The latter will be minimized by applying it to each of the standardized tests. The EF represented the distance between the force-displacement curves that were obtained experimentally and those that were obtained by means of the parameterized FE models. This enabled us to mathematically model the distance between both force-displacement curves according to the C
i proposed in the design matrix. The best hyper-elastic materials models and their corresponding C
i constants were found when the ER functions defined for each of the standardized tests were minimized. This adjustment process was undertaken using desirability functions. As a practical example, the proposed methodology is validated with nitrile butadiene rubber (NBR), ethylene-vinyl acetate (EVA), styrene butadiene rubber (SBR) and polyurethane (PUR) elastomers. Agreement between the force-displacement curves that were obtained by the most appropriate FE models and those that were obtained experimentally demonstrates that the proposed methodology may be valid for determining automatically the most appropriate hyper-elastic model and its corresponding constants C
i to use to correctly define the hyper-elastic behavior of several elastomers. Also, the method that is proposed can be applied quickly for the optimal search of the C
i constants for a variety of elastomers. That is, only the experimental phase to obtain the force-displacement curve and the quadratic regression that is used to obtain the ER and its minimization by means of desirability functions would be the new phases that are required to adjust the constants C
i of the new elastomer. This means that the method that this paper proposes could be a faster, simpler and more economical way to obtain the C
i constants of any type of elastomer than other more sophisticated methods.