 An alternative form of the Arruda–Boyce model, using the first five terms of the inverse Langevin function, is
where formula_11 is a material constant.The quantity formula_5 can also be interpreted as a measure of the limiting network stretch.If formula_13 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 formula_16 and
formula_17

If the rubber is compressible, a dependence on formula_18 can be introduced into the strain energy density; formula_19 being the deformation gradient.