Modified entropic elasticity of rubberlike materials

In the first part of the paper, consisting of Sections 2 and 3, physical grounds are adduced for weakening the concept of strictly entropic elasticity as applied to elastomeric materials. The resulting notion of modified entropic elasticity is shown to provide an alternative formulation of a model of rubberlike thermoelasticity proposed by Chadwick (1974). In the second part (Sections 4 and 5) Chadwick's model is generalized by allowing the deformation-dependent part of the internal energy to be a symmetric function of the principal stretches rather than depending only on their product, as in the original development. Consistently with the molecular theory of polymer networks, and with experimental findings, the extended model predicts that the deviatoric stress is not entirely entropic in origin, but arises in part from changes of internal energy. The energetic fraction of the retractive force in an extended cylinder is calculated and discussed in some detail and the paper concludes with a correlation of theoretical results with measurements on specimens of a lightly cross-linked natural rubber.