Elasticity (physics)


Elasticity (physics)

A material is said to be "elastic" if it deforms under stress (e.g., external forces), but then returns to its original shape when the stress is removed. The amount of deformation is called the strain.

Modeling elasticity

The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity. Good examples are a rubber band and a bouncing ball. This idea was first stated [ [http://www.lindahall.org/events_exhib/exhibit/exhibits/civil/design.shtml Arch Design ] ] by Robert Hooke in 1675 as a Latin anagram [cf. his description of the catenary, which appeared in the preceding paragraph.] whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force"."

This linear relationship is called Hooke's law. The classic model of linear elasticity is the perfect spring. Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, when considering simple situations of higher symmetry such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke's law.

Because most materials are elastic only under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.

Transitions to inelasticity

Above a certain stress known as the elastic limit or the yield strength of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. A stress-strain curve is one tool for visualizing this transition.

Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow, exhibiting viscosity.

See also

* Stiffness
* Elastic modulus
* Linear elasticity
* Pseudoelasticity
* Viscoelasticity

References

* W.J. Ibbetson (1887), [http://books.google.com/books?id=3mQSAAAAIAAJ&pg=PA162 "An Elementary Treatise on the Mathematical Theory of Perfectly Elastic Solids"] , McMillan, London, p.162
* L.D. Landau, E.M. Lifshitz (1986), "Course of Theoretical Physics: Theory of Elasticity" Butterworth-Heinemann, ISBN 0-7506-2633-X
* J.E. Marsden, T.J. Hughes (1983), "Mathematical Foundations of Elasticity", Dover, ISBN 0-486-67865-2
* P.C. Chou, N. J. Pagano (1992), "Elasticity: Tensor, Dyadic, and Engineering Approaches", Dover, ISBN 0-486-66958-0
* R.W. Ogden (1997), "Non-linear Elastic Deformation", Dover, ISBN 0-486-69648-0


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Elasticity — may refer to:*Elasticity (physics), continuum mechanics of bodies which deform reversibly under stressVarious uses are derived from this physical sense of the term, especially in economics:*Elasticity (economics), a general term for a ratio of… …   Wikipedia

  • Elasticity of cell membranes — A cell membrane defines a boundary between the living cell and its environment. It consists of lipids, proteins,carbohydrates etc. Lipids and proteins are dominant components of membranes. One of the principal types of lipids in membranes is… …   Wikipedia

  • elasticity — /i la stis i tee, ee la stis /, n. 1. the state or quality of being elastic. 2. flexibility; resilience; adaptability: a statement with a great elasticity of meaning. 3. buoyancy; ability to resist or overcome depression. 4. Physics. the property …   Universalium

  • physics — /fiz iks/, n. (used with a sing. v.) the science that deals with matter, energy, motion, and force. [1580 90; see PHYSIC, ICS] * * * I Science that deals with the structure of matter and the interactions between the fundamental constituents of… …   Universalium

  • elasticity — UK [ˌiːlæˈstɪsətɪ] / US [ɪlæˈstɪsətɪ] noun [uncountable] 1) physics the ability of a substance to stretch easily and then return to its original shape quickly the strength and elasticity of silk 2) the ability to change when the situation changes …   English dictionary

  • Linear elasticity — Continuum mechanics …   Wikipedia

  • coefficient of elasticity — noun (physics) the ratio of the applied stress to the change in shape of an elastic body • Syn: ↑modulus of elasticity, ↑elastic modulus • Topics: ↑physics, ↑natural philosophy • Hypernyms: ↑ …   Useful english dictionary

  • Rubber Elasticity — Rubber elasticity, also known as hyperelasticity, describes the mechanical behavior of many polymers, especially those with crosslinking. Invoking the theory of rubber elasticity, one considers a polymer chain in a crosslinked network as an… …   Wikipedia

  • modulus of elasticity — Physics. any of several coefficients of elasticity of a body, expressing the ratio between a stress or force per unit area that acts to deform the body and the corresponding fractional deformation caused by the stress. Also called coefficient of… …   Universalium

  • coefficient of elasticity — Physics. See modulus of elasticity. [1875 80] * * * …   Universalium


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.