  We examine how the distribution of contour lengths and the high-stretch
stiffening of individual chain segments affect the macroscopic shear modulus of
flexible polymer gels, using a 2D numerical model, in which polymer segments
form a triangular network and disorder is introduced by varying their contour
lengths. We show that in the relevant parameter range: (i) the non-affine
contribution to the shear modulus is negligible, i.e. the Born approximation is
satisfactory; (ii) the shear modulus is dominated by the contribution
originating from equilibrium chain tensions. Moreover, mechanical equilibration
at the nodes induces specific correlations between the end-to-end distances and
contour lengths of chain segments, which must be properly accounted for to
construct reasonable estimates of chain pressure and shear modulus.
