View source for Hooke law

{{TEX|done}}
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====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top"> E.M. Lifshitz, "Theory of elasticity" , Pergamon  (1959)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a1]</TD> <TD valign="top"> I.S. [I.S. Sokolnikov] Sokolnikoff, "Mathematical theory of elasticity" , McGraw-Hill  (1956)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top"> S.P. Timoshenko, J.N. Goodier, "Theory of elasticity" , McGraw-Hill  (1970)</TD></TR>
</table>