There is some interaction, however. ε Please read the, Elastic potential energy in mechanical systems, Learn how and when to remove these template messages, Learn how and when to remove this template message, https://en.wikipedia.org/w/index.php?title=Elastic_energy&oldid=979745264, Articles needing additional references from June 2015, All articles needing additional references, Wikipedia introduction cleanup from June 2015, Articles covered by WikiProject Wikify from June 2015, All articles covered by WikiProject Wikify, Articles needing expert attention from February 2018, Wikipedia articles needing factual verification from February 2018, Articles with multiple maintenance issues, Creative Commons Attribution-ShareAlike License, This page was last edited on 22 September 2020, at 15:06. u i It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched. The strain tensor itself can be defined to reflect distortion in any way that results in invariance under total rotation, but the most common definition which regard to which elastic tensors are usually expressed defines strain as the symmetric part of the gradient of displacement with all nonlinear terms suppressed: where σ Einstein’s Equation and the Photoelectric Effect, Deriving the Equation for Elastic Potential Energy. {\displaystyle C_{ijkl}} l Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. We can therefore write: For a certain distance that the spring would extend (that we will call ), we can say that there is a maximum force required to hold it there, or that an average force was required over the entire distance (because a much smaller force is required to begin with and a higher force later on). k δ This category provides structured courses for your GCSE's. direction. The spring constant, which defines the amount of force required to deform a spring by a certain length (the workdone on the spring). However, all materials have limits to the degree of distortion they can endure without breaking or irreversibly altering their internal structure. j {\displaystyle \delta _{ij}} Beyond the elastic limit, a Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape. It corresponds to energy stored principally by changing the interatomic distances between nuclei. Thus beware (as here) that in some contexts a repeated index does not imply a sum overvalues of that index ( j Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. l is a 4th rank tensor, called the elastic, or sometimes stiffness, tensor[3] which is a generalization of the elastic moduli of mechanical systems, and Some or all of the formulas presented in this article have, Please help by moving some material from it into the body of the article. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. This constant is usually denoted as k (see also Hooke's Law) and depends on the geometry, cross-sectional area, undeformed length and nature of the material from which the coil is fashioned. Distance the spring is deformed (stretched or compressed) 2. Thermal energy in solids is often carried by internal elastic waves, called phonons. +