Rubber modeling using uniaxial test data

Accurate modeling of large rubber deformations is now possible with finite-element codes. Many of these codes have certain strain-energy functions built-in, but it can be difficult to get the relevant material parameters and the behavior of the different built-in functions have not been seriously evaluated. In this article, we show the benefits of assuming a Valanis-Landel (VL) form for the strain-energy function and demonstrate how this function can be used to enlarge the data set available to fit a polynomial expansion of the strain-energy function. Specifically, we show that in the ABAQUS finite-element code the Ogden strain-energy density function, which is a special form of the VL function, can be used to provide a planar stress-strain data set even though the underlying data used to determine the constants in the strain-energy function include only uniaxial data. Importantly, the polynomial strain-energy density function, when fit to the uniaxial data set alone, does not give the same planar stress-strain behavior as that predicted from the VL or Ogden models. However, the polynomial form does give the same planar response when the VL-generated planar data are added to the uniaxial data set and fit with the polynomial strain-energy function. This shows how the VL function can provide a reasonable means of estimating the three-dimensional strain-energy density function when only uniaxial data are available.