  We discuss the decomposition of the tensorial relaxation function for
isotropic and transversely isotropic Modified Quasi-Linear Viscoelastic models.
We show how to formulate the constitutive equation by using a convenient
decomposition of the relaxation tensor into scalar components and tensorial
bases. We show that the bases must be symmetrically additive, i.e they must sum
up to the symmetric fourth-order identity tensor. This is a fundamental
property both for isotropic and anisotropic bases that ensures the constitutive
equation is consistent with the elastic limit. We provide two robust methods to
obtain such bases. Furthermore, we show that, in the transversely isotropic
case, the bases are naturally deformation-dependent for deformation modes that
induce rotation or stretching of the fibres. Therefore, the Modified
Quasi-Linear Viscoelastic framework allows to capture the non-linear phenomenon
of strain-dependent relaxation, which has always been a criticised limitation
of the original Quasi-Linear Viscoelastic theory. We illustrate this intrinsic
non-linear feature, unique to the Modified Quasi-Linear Viscoelastic model,
with two examples (uni-axial extension and perpendicular shear).
