Macromolecules, Vol.32, No.15, 5004-5016, 1999
A new analytical and experimental approach to rubber thermodynamics
The statistical theory of rubber elasticity is thermodynamically reanalyzed using a proper temperature reference state, which proves that the energetic contribution to the stress, resulting from temperature changes, is equal to zero. This is in contrast to the traditional analysis that yields a nonzero energetic term even though the theory is derived by assuming purely entropic contributions. Using a proper temperature reference state, a nonlinear thermoelastic constitutive equation is obtained from a strain energy function and empirical observations about the stress-temperature behavior of elastomeric materials. This relationship is used to model the thermoelastic behavior of cross-linked natural rubber that had the thermoelastic response measured using vibrational holographic interferometry. Holographic interferometry allows resolution of the true principal stresses of a thin film in uniaxial or biaxial extension. Thermoelastic data for natural rubber in uniaxial and biaxial extension have been successfully modeled using the constitutive approach presented.