  The modelling of off-axis simple tension experiments on transversely
isotropic nonlinearly elastic materials is considered. A testing protocol is
proposed where normal force is applied to one edge of a rectangular specimen
with the opposite edge allowed to move laterally but constrained so that no
vertical displacement is allowed. Numerical simulations suggest that this
deformation is likely to remain substantially homogeneous throughout the
specimen for moderate deformations. It is therefore further proposed that such
tests can be modelled adequately as a homogenous deformation consisting of a
triaxial stretch accompanied by a simple shear. Thus the proposed test should
be a viable alternative to the standard biaxial tests currently used as
material characterisation tests for transversely isotropic materials in general
and, in particular, for soft, biological tissue. A consequence of the analysis
is a kinematical universal relation for off-axis testing that results when the
strain-energy function is assumed to be a function of only one isotropic and
one anisotropic invariant, as is typically the case. The universal relation
provides a simple test of this assumption, which is usually made for
mathematical convenience. Numerical simulations also suggest that this
universal relation is unlikely to agree with experimental data and therefore
that at least three invariants are necessary to fully capture the mechanical
response of transversely isotropic materials.
