On the Modeling of Extension-Torsion Experimental Data for Transversely Isotropic Biological Soft Tissues

Abstract

For the problem of torsion superimposed on extension of incompressible nonlinearly elastic transversely isotropic circular cylinders, a simple asymptotic analysis is carried out on using a small parameter that reflects the moderate twisting of slender cylinders, which corresponds to a typical testing regime for biological soft tissue. The analysis is carried out for a subclass of strain-energy densities that reflect transversely isotropic material response. On using a four-parameter polynomial expression for the strain-energy density in terms of certain classical invariants, this analysis is shown to be in excellent agreement with experimental data obtained by other authors for rabbit papillary muscles. An explicit condition on the strain-energy density is obtained that determines whether the stretched cylinder tends to elongate or shorten on twisting. For the special case of pure torsion where no extension is allowed, this condition determines whether the classical or reverse Poynting effect occurs. For the rabbit papillary muscles, the theoretical results predict and the experimental results confirm that a reverse Poynting-type effect occurs where the stretched rabbit muscle tends to shorten on twisting.

Appendix

Criscione et al. [3] reported graphically the results of twisting an intact cylindrical papillary muscle taken from a New Zealand white rabbit. The specimen was held at an extension ratio of 1.04. The first plot of their Fig. 3 shows twisting moment (mN mm) versus twist (rad mm⁻¹). The digitized data points are given below in Table 1. The second of the plots in Fig. 3 of [3] details the average axial stress (mN mm⁻²) versus twist (rad mm⁻¹) necessary to maintain the given extension ratio. The results of digitizing the graphical data are given in Table 2.

Table 2 Digitized data for the intact muscle from the lower Fig. 3 of [3]