9.3.1 Generalized Hooke's law form

By assuming the form $\tau^{mn} = \rho \, C^{mnij} \, e_{ij}$, one immediately assumes that the only relevant forms of the viscosity tensor are those satisfying

C^mnij = C^mnji (9.23)

since the strain or deformation tensor e_ij is symmetric. This constraint reduces the degrees of freedom to $3 \times 3 \times 6 = 54$. The 6 arises from the 3 + 2 + 1 = 6 degrees of freedom in a symmetric $3 \times 3$ matrix.