Hooke's Law
As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity. This idea was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", a linear relationship commonly referred to as Hooke's law. This law can be stated as a relationship between force F and displacement x,
where k is a constant known as the rate or spring constant. It can also be stated as a relationship between stress σ and strain :
where E Is known as the elastic modulus or Young's modulus.
Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, systems that exhibit symmetry, such as a one-dimensional rod, can often be reduced to applications of Hooke's law.
Read more about this topic: Elasticity (physics)
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“The truth is, the Science of Nature has been already too long made only a work of the brain and the fancy: It is now high time that it should return to the plainness and soundness of observations on material and obvious things.”
—Robert Hooke (1635–1703)
“There is but one law for all, namely that law which governs all law, the law of our Creator, the law of humanity, justice, equity—the law of nature and of nations.”
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