An alternative form of the Arruda–Boyce model, using the first five terms of the inverse Langevin function, is
where  is a material constant.  The quantity  can also be interpreted as a measure of the limiting network stretch.
If  is the stretch at which the polymer chain network becomes locked, we can express the Arruda–Boyce strain energy density as
We may alternatively express the Arruda–Boyce model in the form
where  and
If the rubber is compressible, a dependence on  can be introduced into the strain energy density;  being the deformation gradient.  Several possibilities exist, among which the Kaliske–Rothert extension has been found to be reasonably accurate.  With that extension, the Arruda-Boyce strain energy density function can be expressed as
where  is a material constant and  .  For consistency with linear elasticity, we must have  where  is the bulk modulus.