Hooke law

A law describing the relation between stress and deformation in an elastic body, within a certain range. It states that a small deformation is proportional to the forces applied to the body, i.e. the deformation tensor $u_{ik}$ is a linear function of the stress tensor $\sigma_{jk}$:

$$u_{ik}=\frac{1}{9K}\delta_{ik}\sigma_{ll}+\frac{1}{2\mu}\left(\sigma_{ik}-\frac13\delta_{ik}\sigma_{ll}\right),$$

where $\delta$ is the Kronecker symbol, $K$ is the modulus of compression and $\mu$ is the shear modulus. See Elasticity, mathematical theory of.

In its simplest form the law was experimentally established by R. Hooke in 1660.

References

[1]	E.M. Lifshitz, "Theory of elasticity" , Pergamon (1959) (Translated from Russian)
[a1]	I.S. [I.S. Sokolnikov] Sokolnikoff, "Mathematical theory of elasticity" , McGraw-Hill (1956) (Translated from Russian)
[a2]	S.P. Timoshenko, J.N. Goodier, "Theory of elasticity" , McGraw-Hill (1970)