Introduction

In the previous chapter on fibres, the material behaviour was constantly considered to be elastic, meaning that a unique relation exists between the extensional force and the deformation of the fibre. This implies that the force versus stretch curves for the loading and unloading path are identical. There is no history dependency, and all energy that is stored into the fibre during deformation is regained during the unloading phase. This also implies that the rate of loading or unloading does not affect the force–stretch curves. However, most biological materials do not behave elastically.

An example of a loading history and a typical response of a biological material is shown in Figs. 5.1(a) and (b). In Fig. 5.1(a), a deformation history is given that might be used in an experiment to mechanically characterize some material specimen. The specimen is rapidly stretched to a certain value, then the deformation is fixed and after a certain time restored to zero. After a short resting period, the stretch is applied again but to a higher value of the stretch. This deformation cycle is repeated several times. In this case the length change is prescribed and the associated force is measured. Figure 5.1(b) shows the result of such a measurement. When the length of the fibre is kept constant, the force decreases with time. This phenomenon is called relaxation. Conversely, if a constant load is applied, the length of the fibre will increase. This is called creep.

When the material is subjected to cyclic loading, the force versus stretch relation in the loading process is usually somewhat different from that in the unloading process. This is called hysteresis and is demonstrated in Fig. 5.2. The difference in the response paths during loading and unloading implies that energy is dissipated, usually in the form of heat, during the process. Most biological materials show more or less the behaviour given above, which is called visco-elastic behaviour. The present chapter discusses how to describe this behaviour mathematically. Pure viscous behaviour, as can be attributed to an ideal fluid, is considered first.