Elasticity (physics)

Elasticity is a branch of physics which studies the properties of elastic materials. A material is said to be elastic if it 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^[1] by Robert Hooke in 1675 as a Latin anagram^[2] "ceiiinossssttuv", 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 only elastic 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 stress-strain curve is one tool for visualizing this transition.

Furthermore, not only solids exhibit elasticity. Some viscosity.

See also

• Stiffness
• Elastic modulus
• Linear elasticity
• 3-D elasticity
• Pseudoelasticity

References

1. ^ http://www.lindahall.org/events_exhib/exhibit/exhibits/civil/design.shtml
2. ^ cf. his description of the catenary, which appeared in the preceding paragraph.

• W.J. Ibbetson (1887), 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