Prediction of the twisting moment and the axial force in a circular rubber cylinder for combined extension and torsion based on the logarithmic strain approach

摘要

It has been previously shown by Kakavas (2000) that a strain energy function based on a logarithmic measure of strain for hyperelastic solids can characterize the material very well. Due to the incompress-ibility constraint the first logarithmic invariant vanishes, and the function is expressed in terms of the second and third invariants. The available domain of the strain energy function can be determined by plotting the third invariant of the logarithmic strain as a function of the second one. The involved four material parameters can be determined by fitting with the experimental data. The proposed function was applied for the prediction of the twisting moment and the axial force for a cylinder under simple torsion. The derived equations were applied for the prediction of published experimental data by Rivlin and Saunders (1951) and a comparison with the approach proposed by Anand (1986) was made. All moderate strain non-linearities are incorporated in the logarithmic strain measure.