Hyperelastic Nonlinear Thermal Constitutive Equation of Vulcanized Natural Rubber

Abstract

Based on the tensor function, the nonlinear thermal constitutive equation and the corresponding strain energy function of hyperelastic isotropic materials are derived. The equation and the strain energy function are complete and irreducible, They contain 38 independent elastic constants and satisfy the tensor function representation theorem. The constitutive relation of rubber as a typical superelastic incompressible material is studied, The constitutive equation of thermal stress and the corresponding strain energy function of rubber are derived. 28 complete and irreducible elastic constants of rubber are determined. The stress-strain curves of vulcanized rubber at different temperatures (−50, −25, 0, 25, 75, 100 °C) were calculated under static uniaxial loading. The above conclusions and L.R.G. experimental data were fitted by multivariate nonlinear regression. The elastic constants of natural rubber vulcanized at 0 °C, and the specific values of thermoelastic constants. It provides important methods and data for further study of thermal sensitivity of rubber. By fitting the experimental data of vulcanized natural rubber, the constitutive equation can effectively describe the mechanical behavior of vulcanized natural rubber at different temperatures. The calculation process is simple and clear.