Extension and Torsion

Abstract

The deformations experienced by some biological tissues and biomaterials can be very complex. For example, we have seen that all six components of the Green strain [cf. Eq. (2.42), but relative to cylindrical coordinates] are nonzero in the wall of the heart, and each varies with position and time throughout the cardiac cycle (cf. Fig. 2.20). In such cases, we must often resort to sophisticated numerical methods to measure or compute the strain fields. Nevertheless, there are many cases in which the deformations are much simpler, as, for example, in chordae tendineae within the heart, which experience primarily an axial extension with associated lateral thinning (cf. Fig. 3.2). Indeed, as an introduction to biomechanics, it is often best to study simple motions such as extension, compression, distension, twisting, or bending, which allow us to increase our understanding of the basic approaches and which also apply to many problems of basic science or clinical and industrial importance. Whereas we considered small strains that occur during a simple inflation of a thick-walled tube in the last section of Chap. 3, here we consider in some detail small strains associated with axial extension and torsion, with an associated complete stress analysis for the latter for a linear, elastic, homogenous, and isotropic (LEHI) behavior of a circular member. Such analyses will be particularly relevant in bone mechanics.