  Soft tissues are complex media, they display a wide range of mechanical
properties such as anisotropy and non-linear stress-strain behaviour. They
undergo large deformations and they exhibit a time-dependent mechanical
behaviour, i.e. they are viscoelastic. In this chapter we review the
foundations of the linear viscoelastic theory and the theory of Quasi-Linear
Viscoelasticity (QLV) in view of developing new methods to estimate the
viscoelastic properties of soft tissues through model fitting. To this aim, we
consider the simple torsion of a viscoelastic Mooney-Rivlin material in two
different testing scenarios: step-strain and ramp tests. These tests are
commonly performed to characterise the time-dependent properties of soft
tissues and allow to investigate their stress relaxation behaviour. Moreover,
commercial torsional rheometers measure both the torque and the normal force,
giving access to two sets of data. We show that for a step test, the linear and
the QLV models predict the same relaxation curves for the torque. However, when
the strain history is in the form of a ramp function, the non-linear terms
appearing in the QLV model affect the relaxation curve of the torque depending
on the final strain level and on the rising time of the ramp. Furthermore, our
results show that the relaxation curve of the normal force predicted by the QLV
theory depends on the level of strain both for a step and a ramp tests. To
quantify the effect of the non-linear terms, we evaluate the maximum and the
equilibrium values of the relaxation curves. Our results provide useful
guidelines to accurately fit QLV models in view of estimating the viscoelastic
properties of soft tissues.
