On the inadmissibility of separation of variables solutions in linear anisotropic viscoelasticity

The field and constitutive equations as well as the boundary conditions of linear anisotropic viscoelasticity are examined for possible solutions which are separable into products of time and spatial functions. It is shown that under no circumstances other than for constant Poisson’s ratios are such separation of variables solutions admissible, even though under these or some additional restrictive conditions they can exist in isotropic viscoelasticity.