  An expression is derived for the strain energy of a polymer chain under an
arbitrary three-dimensional deformation with finite strains. For a Gaussian
chain, this expression is reduced to the conventional Moony--Rivlin
constitutive law, while for non-Gaussian chains it implies novel constitutive
relations. Based on the three-chain approximation, explicit formulas are
developed for the strain energy of a chain modeled as a self-avoiding random
walk. In the case of self-avoiding chains with stretched-exponential
distribution function of end-to-end vectors, the strain energy density of a
network is described by the Ogden law with only two material constants. For the
des Cloizeaux distribution function, the constitutive equation involves three
adjustable parameters. The governing equations are verified by fitting
observations on uniaxial tension, uniaxial compression and biaxial tension of
elastomers. Good agreement is demonstrated between the experimental data and
the results of numerical analysis. An analytical formula is derived for the
ratio of the Young's modulus of a self-avoiding chain to that of a Gaussian
chain. It is found that the elastic modulus per chain in the Ogden network
exceeds that in a Gaussian network by a factor of three, whereas the elastic
modulus of a chain with the generalized stretched exponential distribution
function equals about half of the modulus of a Gaussian chain.

Materials Science