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Hooke law

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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 is a linear function of the stress tensor :

where is the Kronecker symbol, is the modulus of compression and 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)


Comments

References

[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)
How to Cite This Entry:
Hooke law. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hooke_law&oldid=33415
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article