  We identify three distinct shearing modes for simple shear deformations of
transversely isotropic soft tissue which allow for both positive and negative
Poynting effects (that is, they require compressive and tensile lateral normal
stresses, respectively, in order to maintain simple shear). The positive
Poynting effect is that usually found for isotropic rubber. Here,
specialisation of the general results to three strain-energy functions which
are quadratic in the anisotropic invariants, linear in the isotropic strain
invariants and consistent with the linear theory suggests that there are two
Poynting effects which can accompany the shearing of soft tissue: a dominant
negative effect in one mode of shear and a relatively small positive effect in
the other two modes. We propose that the relative inextensibility of the fibres
relative to the matrix is the primary mechanism behind this large negative
Poynting effect.
