The counterintuitive mechanical response in simple tension of arterial models that are separable functions of the I1, I4, I6 invariants

It is shown that some of the orthotropic models reported in the literature for the mechanical response of elastic arteries and which assume a separable dependence on the I1,I4,I6 invariants predict curious and unexpected behaviour in simple tension. Specifically it is shown that the out-of-plane stress response can be stiffer than the in-plane over a moderate range of strain and that when the in-plane response is much stiffer than the out-of-plane, as might be expected for a fibre-reinforced material, it is accompanied by a large auxetic response in the out-of-plane direction. This mechanical response for this class of orthotropic materials seems counterintuitive and it is hypothesised that it could be due to their well-known inability to fully recover the linear theory, on restriction to infinitesimal deformations. A generalisation of these models that is fully compatible with the linear theory is proposed. An alternative strategy of assuming that the fibres cannot support compression is shown not to be a universal remedy.