Product: ABAQUS/Explicit
This test is a case of homogeneous deformation of a cube of unit dimension. Four types of hyperelastic strain energy potentials are used: the polynomial (including the reduced polynomial and Yeoh forms, which are the most common particular cases of the general polynomial model), Ogden, Arruda-Boyce, and Van der Waals forms with coefficients drawn from Treloar's experimental data (Treloar, 1940).
Stress and strain data are entered using the *UNIAXIAL TEST DATA, *BIAXIAL TEST DATA, *PLANAR TEST DATA, and *VOLUMETRIC TEST DATA suboptions of the *HYPERELASTIC option. A least squares method is used to fit the experimental data. For the polynomial and Ogden forms the order of the series is determined by the value of the parameter N on the *HYPERELASTIC option. The following cases are analyzed:
Polynomial form with N=2 (5 deviatoric terms).
Reduced polynomial form with N=4 (4 deviatoric terms).
Yeoh form, which is equivalent to the reduced polynomial form with N=3.
Ogden form with N=3 (3 deviatoric terms).
Arruda-Boyce form.
Van der Waals form.
Figure 3.1.6–1 shows the initial and deformed shapes. Figure 3.1.6–2 through Figure 3.1.6–4 show comparisons of the computed nominal stress and strain in the stretching direction with Treloar's experimental data. The ABAQUS results are seen to match the experimental results closely for the entire range of deformation, especially when the Ogden model or the Van der Waals potential is used. Analogous results were obtained for all the material models using C3D10M elements.
Polynomial hyperelasticity case; C3D8R elements.
Reduced polynomial hyperelasticity case; C3D8R elements.
Yeoh hyperelasticity case; C3D8R elements.
Ogden hyperelasticity case; C3D8R elements.
Arruda-Boyce hyperelasticity case; C3D8R elements.
Van der Waals hyperelasticity case; C3D8R elements.
Polynomial hyperelasticity case; C3D10M elements.
Reduced polynomial hyperelasticity case; C3D10M elements.
Yeoh hyperelasticity case; C3D10M elements.
Ogden hyperelasticity case; C3D10M elements.
Arruda-Boyce hyperelasticity case; C3D10M elements.
Van der Waals hyperelasticity case; C3D10M elements.
Two additional input files are also included with the ABAQUS release for the purpose of testing the implementation of the Arruda-Boyce and Van der Waals strain energy potentials (file names: hyper_ab_uni.inp and hyper_vw_uni.inp).
Treloar, L. R. G., “Stress-Strain Data for Vulcanised Rubber under Various Types of Deformation,” Transactions of the Faraday Society, vol. 40, pp. 59–70, 1940.
