Hooke's Law

Hooke's Law expresses the linear relation between stress and strain. It may be written either as

stress = stiffness * strain : $\sigma _{ij}=\sum _{k,l}^{3}C_{ijkl}\varepsilon _{kl}$

or as

strain = compliance * stress : $\varepsilon _{ij}=\sum _{k,l}^{3}S_{ijkl}\sigma _{kl}$

Both the stiffnesses $C_{ijkl}$ and the compliances $S_{ijkl}$ have 3x3x3x3=81 elements, but because of symmetries, they are not all independent. The number of independent elements depends upon the symmetry class of the medium:
Isotropic:2
Polar anisotropic: 5
Orthorhombic: 9
Monoclinic: 12