## 1 Introduction
[10] used finite element simulation to improve forward motion on cross-slopes compared with single- or double-cantilever spring designs. [PERSON] et al. [11] calculated the bending deflection of the cam profile numerically and verified it for bending deflection at the point of contact by the finite element analysis method. [PERSON] et al. [12] obtained the deformation and stress of the rubber components and the cord reinforcements by FE simulation to judge the rationality of tire construction design. [PERSON] et al. [13] obtained predictions of the temperature, cure level distribution in the rubber part, and press force during a curing process from a developed finite element analysis. These studies have mainly used the finite element method to analyze structural wear, strength, and stiffness, and few have applied it to constitutive coefficient simulation and automatic search of the material properties of rubber materials. In studies of rubber elements constitutive models, most scholars have focused on rubber's molecular mechanical properties and composite materials' properties. [PERSON] et al. [14] presented a new phenomenological inelastic constitutive model for rubberlike materials and demonstrated its good correspondence to cyclic measurements for both uniaxial tension and simple shear tests up to large deformations. [PERSON] et al. [15] researched a phenomenological model for the viscoelastic behavior of natural rubber and its mechanical behavior. [PERSON] et al. [16] developed a fitting algorithm that can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed. This algorithm could quantitatively assess the ability of each SEF to reproduce the experimental data of both unfilled and highly filled rubber nanocomposites. [PERSON] et al. [17] proposed a one-dimensional constitutive model for elastomeric materials and captured the changes in constitutive behavior and energy dissipation associated with the Mullins effect. [PERSON] et al. [18] proposed a novel phenomenological constitutive modeling framework that incorporates damage and residual stress capabilities for solids. [PERSON] et al. [19] first attempted the analysis of the constitutive relations of filled rubber by calculating amplification factors related to stress and strain distributions. [PERSON] et al. [20] established a constitutive model of rubber compound material with the shear strain energy of cord/rubber and compiled the subprograms involved in a constitutive model of anisotropic hyper-elastic materials. The subprograms were used to form an effective prediction method for the deformation behavior of cord/rubber composites. [PERSON] et al. [21] proposed an optimization algorithm for model parameters fitting and predicted the mechanical behaviors of rubber-cord composites using the developed model. [PERSON] et al. [22] studied the elastic hysteretic properties of various polymer-damping composite materials. [PERSON] et al. [23] studied the mechanical properties of complex fabric-rubber composite under different temperatures based on macroscopic and meso-structural characterization. [PERSON] et al. [24] investigated the impact performance of composite panels consisting of plain-woven Kevlar fabric and rubber matrix. And they investigated the deformation and damage mechanism of fabric and composite under impact loading. All in all, most scholars have studied the influence of different rubber fillers on the rubber constitutive structure and the prediction of rubber-forming mechanical properties. However, few scholars have studied a large deformation constitutive model of rubber under different theories and the mechanical properties of composite rubber structures. Given the aforementioned issues, in conjunction with the operational characteristics of the hammer-lifting device and the rubber test data, this paper establishes a large deformation constitutive model of rubber based on phenomenological theory and derives distinct coefficients for the rubber constitutive model.