General Application To Elastic Materials
Objects that quickly regain their original shape after being deformed by a force, with the molecules or atoms of their material returning to the initial state of stable equilibrium, often obey Hooke's law.
We may view a rod of any elastic material as a linear spring. The rod has length L and cross-sectional area A. Its extension (strain) is linearly proportional to its tensile stress σ, by a constant factor, the inverse of its modulus of elasticity, E, hence,
where
this may also be expressed as:
Hooke's law only holds for some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke's law is valid for it throughout its elastic range (i.e., for stresses below the yield strength). For some other materials, such as aluminium, Hooke's law is only valid for a portion of the elastic range. For these materials a proportional limit stress is defined, below which the errors associated with the linear approximation are negligible.
Rubber is generally regarded as a "non-hookean" material because its elasticity is stress dependent and sensitive to temperature and loading rate.
Applications of the law include spring operated weighing machines, stress analysis and modelling of materials.
Read more about this topic: Hooke's Law
Famous quotes containing the words general, application, elastic and/or materials:
“They make a great ado nowadays about hard times; but I think that ... this general failure, both private and public, is rather occasion for rejoicing, as reminding us whom we have at the helm,—that justice is always done. If our merchants did not most of them fail, and the banks too, my faith in the old laws of the world would be staggered.”
—Henry David Thoreau (1817–1862)
“Great abilites are not requisite for an Historian; for in historical composition, all the greatest powers of the human mind are quiescent. He has facts ready to his hand; so there is no exercise of invention. Imagination is not required in any degree; only about as much as is used in the lowest kinds of poetry. Some penetration, accuracy, and colouring, will fit a man for the task, if he can give the application which is necessary.”
—Samuel Johnson (1709–1784)
“We want some coat woven of elastic steel, stout as the first, and limber as the second. We want a ship in these billows we inhabit. An angular, dogmatic house would be rent to chips and splinters, in this storm of many elements. No, it must be tight, and fit to the form of man, to live at all; as a shell is the architecture of a house founded on the sea.”
—Ralph Waldo Emerson (1803–1882)
“If only it were God’s will that printed and written materials have as much influence on the people as the princes and their censors fear! Considering the countless good books we have, the world would have changed for the better a long time ago.”
—Franz Grillparzer (1791–1872)