Some unexpected behaviour in shear for elasticity models of arterial tissue that only use the I1, I4, I6 invariants

The phenomenological approach to the modelling of the mechanical response of non-linearly elastic arteries usually uses a reduced form of the strain-energy function in order to reduce the mathematical complexity of the model. A common approach eschews the full basis of seven invariants for the strain-energy function in favour of a reduced set of only three invariants. It is shown that these anisotropic materials behave as if they were isotropic for two important modes of shearing for cylindrical vessels, indicating possible deficiencies in shear stress predictions.