Rotationally invariant viscoelastic medium with a non-symmetric stiffness matrix

The stiffness matrix of a viscoelastic medium is symmetric in the low-frequency and high-frequency limits, but not for finite frequencies. We thus consider a non-symmetric stiffness matrix in this paper. We determine the general form of a rotationally invariant non-symmetric stiffness matrix of a viscoelastic medium. It is described by three additional complex-valued parameters in comparison with a rotationally invariant symmetric stiffness matrix of a transversely isotropic (uniaxial) viscoelastic medium with a symmetric stiffness matrix. As a consequence, we find that the stiffness matrix of an isotropic viscoelastic medium is always symmetric.