The Strain-Energy Function of a Hyperelastic Material in Terms of the Extension Ratios

A simple form of the strain-energy function of natural rubber results if the latter is expressed an an analytic function of the extension ratios rather than the invariants. For incompressible isotropic materials it is postulated that this is a separable symmetric function of the extension ratios, i.e., W = w(λ1) + w(λ2) + w(λ3). This form has been substantiated by critical plots using uniaxial and biaxial data reported in the literature by several investigators. The above form appears to be valid over a wide range of deformations (0.2≤λ≤3.5). An explicit representation of W for this range is given in graphical form. In the more limited range (0.6≤λ≤2.5) w(λ) has the analytic form w=2 μλ (lnλ−1).