Computational Determination of Effective Working Length in Experimental Torsion Testing of Long Bones

Abstract

Torsion is the preferred mode of loading for ex vivo whole-bone mechanical testing due to its robustness to alignment artifacts and ease of implementation. Results from a nondestructive torsion test are usually reported as torsional stiffness, S, or the slope of the torque-angle curve. However, torsional stiffness depends on specimen working length and cannot be compared between experiments with different bone lengths or test setups. Alternatively, the length-independent torsional rigidity can be calculated as GJ = S×L, using the working length L of the specimen. This paper presents evidence that the effective working length exceeds the length of the unpotted bone segment and depends on the amount of twisting allowed by the fixture through the potted ends. Multiple fixture design parameters were systematically varied to quantify how each individual change influenced the effective working length. Common variations in design parameters related to potting contributed up to 5.15% variation in effective working length, while changing the method of coupling the sample to the test frame contributed up to 17.1% variation. These results suggest that effective working length calibration is essential to enable data aggregation between experiments conducted with different setups. To assist other researchers who wish to calibrate their own setups, this investigation also provides practical guidance on how to determine the effective working length of a complex torsion test assembly using finite element analysis with nonlinear contact mechanics. Detailed procedures for setting up a contact solution are documented with recommendations on adjustments to achieve convergence.