Hooke's Law

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

stress = stiffness * strain :

or as

strain = compliance * stress :

Both the stiffnesses and the compliances 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