Elasticity (physics) 268923 226124943 2008-07-16T22:43:09Z Headbomb 1461430 elasticity is a property, not a branch of physics {{Continuum mechanics}} A material is said to be ''elastic'' if it [[deformation|deforms]] under [[stress (physics)|stress]] (e.g., external [[force]]s), but then returns to its original shape when the stress is removed. The amount of deformation is called the [[Strain (materials science)|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<ref>[http://www.lindahall.org/events_exhib/exhibit/exhibits/civil/design.shtml Arch Design<!-- Bot generated title -->]</ref> by [[Robert Hooke]] in 1675 as a Latin anagram<ref>[[cf.]] his [[Catenary#History|description of the catenary]], which appeared in the preceding paragraph.</ref> "ceiiinosssttuv", 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 (device)|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 (engineering)|yield strength]] of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the [[solid]] may deform irreversibly, exhibiting [[Plasticity (physics)|plasticity]]. A [[stress-strain curve]] is one tool for visualizing this transition. Furthermore, not only solids exhibit elasticity. Some [[non-Newtonian fluid]]s, such as [[Viscoelasticity|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 == <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 {{Physics-footer}} [[Category:Elasticity (physics)]] [[ar:مرونة]] [[bg:Еластична деформация]] [[cs:Pružnost]] [[da:Elasticitet (fysik)]] [[de:Elastizität (Physik)]] [[fa:کشسانی]] [[fr:Déformation élastique]] [[gl:Elasticidade (mecánica)]] [[ko:탄력성 (물리)]] [[it:Elasticità (meccanica)]] [[he:אלסטיות]] [[nl:Elasticiteit (materiaalkunde)]] [[ja:弾性]] [[pt:Elasticidade]] [[ru:Упругость]] [[simple:Elastic]] [[sk:Teória pružnosti]] [[fi:Kimmoisuus]] [[sv:Elasticitet]] [[vi:Lực đàn hồi]] [[uk:Пружність]] [[zh:弹性 (物理学)]]