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In this Rapid Communication we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the nonaffine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as F∝λ5/2 where λ is the deformation ratio. Thus a highly non-Hookian stress-strain relation is predicted.
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Vilgis et al. (1997) studied this question.
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