One-dimensional Hooke's Law | |

Robert Hooke, who in 1676 stated,
announced the birth of elasticity. Hooke's statement expressed mathematically is,
where | |

Generalized Hooke's Law (Anisotropic Form) | |

Cauchy generalized Hooke's law to three dimensional elastic bodies and stated that the 6 components of stress are linearly related to the 6 components of strain.
The stress-strain relationship written in matrix form, where the 6 components of stress and strain are organized into column vectors, is,
,
e = S·s
or,
,
s = C·e
where
In general, stress-strain relationships such as these are known as In general, there are 36 stiffness matrix components. However, it can be shown that conservative materials possess a strain energy density function and as a result, the stiffness and compliance matrices are symmetric. Therefore, only 21 stiffness components are actually independent in Hooke's law. The vast majority of engineering materials are conservative.
Please note that the |