Exploitation of the linear theory in the non-linear modelling of soft tissue

It is shown here how the linear theory of incompressible, transversely isotropic elasticity can positively influence the choice of strain-energy function of the non-linear theory so that the corresponding models of the mechanical response of biological soft tissue have a motivation based on mechanics. Specifically, it is shown that the structures of the linear theory have non-linear counterparts that could prove useful in the modelling of the moderate strain regime of soft tissue and that the recovery of the linear theory when the non-linear theory is restricted to infinitesimal deformations has important consequences for the choice of the strain-energy function.