COMPLETE CONSTITUTIVE RELATION OF HYPERELASTIC MATERIALS FOR TRELOAR’S EXPERIMENTAL DATA

Hyperelastic material is a typical one widely used in many fields such as aerospace engineering and civil industrials. However, due to the property of nonlinear large deformation, the constitutive behavior of hyperelastic materials is extremely complex and the models are quite different in form. Starting from the strain energy function, a complete constitutive relation of hyperelastic materials is studied within the theoretical framework of continuum mechanics in this paper. Firstly, the feature is analyzed for the experimental curves under three essential deformation modes like uniaxial tension, equibiaxial tension and pure shear, which are conducted by Treloar for a vulcanized rubber hyperelastic material. Next, the same stress conditions of the three deformation modes are summarized in detail, based on which the constitutive relationship is derived in a same manner in terms of the stress and the principal stretch ratio in the loading direction for the three modes according to the hyperelastic constitutive theory. The constitutive behaviors of two typical power-law strain energy functions, namely I_1^m and I_2^m , are accordingly studied for the three essential modes. The experimental curves are divided into the initial regime and the remaining regime, and then the neo-Hookean model is adopted for the initial regime while the power-law functions with variable exponents are used for the remaining regime. The complete constitutive model is eventually established after the model parameters are identified by minimizing the overall error functional of the three modes. The responses are re-predicted for the three essential deformation modes, and the results agree better with the experimental than other models available in published literature. The present work indicates that a complete constitutive relation can be obtained for a hyperelastic material in light of the experimental curves with whole deformation range under multiple deformation modes, which is therefore instructive and meaningful to theoretical research and engineering application of complex practical problems such as fracture of hyperelastic materials.