Entropy elasticity of isotropic rubber-like solids at finite strains

This paper presents a macroscopic continuum formulation and a numerical analysis of constitutive equations (for stress, entropy and heat flux) describing the thermoelastic behavior of amorphous cross-linked polymers above the glass transition temperature in which a specimen typically 'snap-back' with rubbery characteristics. The introduced coupled thermomechanical functional extends the classical strain energy function proposed by Ogden. Volume changes due to thermal expansion are regarded for a large temperature domain and play a remarkable role in thermoelastic materials. The non-linear thermoelastic problem is solved within a staggered (fractional-step) method which is based on a two-phase (isentropic) operator split. Each of the two symmetric sub-problems retains the characteristic dissipative structure of the implicit monolithic scheme which consequently results to an unconditionally stable product formula algorithm. The numerical analysis side shows in particular the capability of the theoretical framework reproducing the realistic physical stress-deformation-temperature relations of rubber. Distinctive attention is paid to the thermoelastic inversion phenomena, a remarkable property governing the class of rubber-like materials.