# Hooke's law

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## Hooke's law:

see elasticityelasticity,
the ability of a body to resist a distorting influence or stress and to return to its original size and shape when the stress is removed. All solids are elastic for small enough deformations or strains, but if the stress exceeds a certain amount known as the elastic
.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Hooke’s Law

a basic law expressing the relationship between the stress and strain of an elastic body. It was formulated by the English physicist R. Hooke in 1660 for the simplest case of the elongation or compression of a rod in the following form: the absolute elongation (compression) Δ/ of a cylindrical rod is directly proportional to the tensile stress N, that is, Δ/ = kN, where k = l/ES (l is the length of the rod, S is the area of its cross section, and E is the modulus of longitudinal elasticity, which is a mechanical characteristic [constant] of a material). Hooke’s law can also be conveniently represented in the form σ ‗ E∈, where σ‗ N/S is the normal stress acting in a cross section and ∈‗ Δl/l is the relative elongation (compression) of the rod.

With shearing stress, Hooke’s law is written as τ = G/γ, where τ is the tangential stress, γ is the shear, and G is the so-called shear modulus. In the presence of shear, the tangential stress is directly proportional to the shear.

The generalized Hooke’s law—for a body of any arbitrary shape—states that six quantities determining the stress at a point are expressed linearly by six quantities determining the strain in the neighborhood of the point under consideration. In these equations the coefficients of proportionality are called elastic moduli. In anisotropic bodies, for example, crystals, the elastic moduli are different in different directions, so that in the general case the elastic properties of a solid are characterized by means of 21 elastic moduli. For isotropic bodies, the number of independent elastic constants reduces to two.

Hooke’s law is not valid when certain stresses (or deformations) attain limiting values characteristic for each material and the body passes into an elastic-plastic state. Hooke’s law is a basic relationship applicable in calculating the strength and deformability of structures and buildings.

### REFERENCE

Il’iushin, A. A., and V. S. Lenskii. Soprotivlenie materialov. Moscow, 1959.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

## Hooke's law

[′hu̇ks ‚lȯ]
(mechanics)
The law that the stress of a solid is directly proportional to the strain applied to it.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## Hooke’s law

A law stating that the deformation of an elastic body is proportional to the force applied, provided the stress does not exceed the elastic limit of the material.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.
References in periodicals archive ?
In this case, the distance of two particles situated at the two ends of a joint is always constant, and Hooke's law is no longer useful.
Indeed, mathematically, the pigment matrix reasonably obeys Hooke's Law during the rapid phases of aggregation and dispersion (see Table 1), and thus can be considered as a spring that is alternately stretched and compressed.
Hooke's law, that "stress is proportional to strain," also was transformed into a homogeneous equation in the manner pioneered by Fourier.
The little AE in the Hooke's law area is rather to be explained by faults in the experimental process (like imprecise gripping, the floating working piston or some deformed specimen).
Hooke's Law states: "If the applied forces on a body are not too large, the deformations resulting are directly proportional to the forces producing them." Which means, in actual human being language, if we load a spring past its elastic limit, it permanently deforms.
The constitutive model proposed in this paper is formulated using the generalized curvilinear form of Hooke's Law. Extensive use of components of the Eucidean metric tensor enabled formulation in a material coordinate system.
Modulus of Elasticity: Young's modulus, the initial slope of the stress vs strain curve where Hooke's Law applies before the elastic limit is reached.
According to Hooke's Law, the force or stress is proportional to the strain, or:
In both cases the change in length is defined by Hooke's law, which was covered in Richard Albrecht's article on telescope structures (S&T: January 1989, page 97, and February 1989, page 210).
An instructive counter-example of how scientific progress can consist of successive reductions in the empirical content of the relevant propositions is provided by the history of Hooke's law (of elastic behaviour).
In the case of elastic conditions, the expression within the brackets <> vanishes, and the constitutive relation (7) reduces to the Duhamel-Neumann form of Hooke's law.

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