An Experimental Method to Obtain the Elastic Strain Energy Function from Torsion-Tension Tests

It has been observed by many authors that the rate of change of the strain energy function W with respect to two principal strain invariants, I1 and I2, is rapid near the origin; moreover, the mapping area of the strain invariants with I1-3 and I2-3 as coordinates is extremely small near the origin. It is found that by employing a torsion-tension test, one can have a complete and meaningful mapping near the origin. However, the mathematical representations of the twist moment M and normal force N vs. strain and strain energy function are complex. To circumvent this difficulty we propose the use of a set of solid cylindrical bars with different diameters, such that the difference in diameter of two successive bars is small. By considering differences in M or N as a function of difference in radius, at appropriate deformations (stretch and twist) selected such that I1 or I2 is held fixed, one can grossly simplify the stress-strain equations, to the point that one has a new way to investigate material response.