CLASSIC STRAIN ENERGY FUNCTIONS AND CONSTITUTIVE TESTS OF RUBBER-LIKE MATERIALS

Abstract

ABSTRACT Four classic strain energy density (SED) functions for incompressible rubber-like materials, neo-Hookean, Mooney-Rivlin, Yeoh, and Ogden forms, are briefly reviewed. The strain–stress relations of the above-mentioned SED functions for uniaxial, planar (pure shear), and equibiaxial deformation modes and formulas for transforming tensile data to compressive data of these three special deformation modes are given. Three approximate criteria are proposed for judging the validity of test data obtained from various methods. It is found that Treloar's data are the most reasonable among six groups of published data judged using the proposed criteria. Different combinations of Treloar's data were used to determine the parameters of these SED functions. The effects of three special tests on determining the parameters of various SED functions using the curve-fitting tools provided by ABAQUS were analyzed. Uniaxial tension data were found to be sufficient for determining the neo-Hookean, Yeoh, and first-order Ogden models, whereas both uniaxial and equibiaxial data were necessary for determining the Mooney-Rivlin and Ogden (N = 2, 3) models, and planar data were unnecessary to determine the parameters for all reviewed SED functions.