The rubber mechanics at low temperature with large contribution of the internal energy change is important for engineering application of rubbery materials. The constitutive equation based on the change in internal energy and entropy was derived from the statistical thermodynamics with Hamiltonian equations. The continuous change in elasticity from transition state at lower temperature to rubbery state at higher temperature can be represented by this equation. This equation was used to describe the rubber fracture behaviors at a wide range of temperature and it showed a good agreement with the experimental results. It was also found that this equation could be applied to the finite element analysis to simulate the meso-scale stress-strain behaviors of the rubbery material with carbon black particles.
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