  The effects of thermal elastic fluctuations in rubber materials are examined.
It is shown that, due to an interplay with the incompressibility constraint,
these fluctuations qualitatively modify the large-deformation stress-strain
relation, compared to that of classical rubber elasticity. To leading order,
this mechanism provides a simple and generic explanation for the peak structure
of Mooney-Rivlin stress-strain relation, and shows a good agreement with
experiments. It also leads to the prediction of a phonon correlation function
that depends on the external deformation.
