Rubber modeling using uniaxial test data

Abstract

Abstract 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. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 837–848, 2001