Talk:Elastic energy

Merge article with Elastic potential energy
It seems self-evident that this article and the article on Elastic potential energy are on exactly the same subject and should be merged. I suggest this page be left as a redirect. Comments? --71.198.38.153 09:20, 21 August 2007 (UTC)
 * Agreed, go for it! ;) Random89 (talk) 21:14, 29 November 2007 (UTC)
 * Most definitely merge it. As both pages are quite short, each would benefit the other, and I gather that “elastic potential energy” is a more scientifically proper term, so using this article as a redirect seems wisest as well.  The redundancy here represents many ‘clone’ articles that are somewhat embarrassing for Wikipedia, and the sooner it is rectified the better.  Kudos for putting this on the radar.  Wii Owner 3.14 (talk) 05:46, 1 April 2008 (UTC)

Merged or not, the definition herein related to elastic potential energy (indeed proper terminology) was mis-characterized as a total energy rather than energy density. I cleaned that up along with imposing some internal consistency of notation. I will go fetch at least one standard reference which uses the same notation and terminology (Landau and Lifshitz comes to mind) and post it subsequently. scanyon 23:43, 5 June 2010 (UTC) —Preceding unsigned comment added by Patamia (talk • contribs)

Correcting basic physics of the article
I corrected the definitions and notational harmonization with respect to the elasticity of material in a continuum and noted same in comments above. However, as I look at the other parts of the article I see some fundamental errors. I will correct one more now and perhaps return to this later, but before doing more I'd like anyone who has a larger view of the present connection between this and other articles to please comment. Depending on the comments, it might make sense to collaborate to further improve the article. Incidentally, despite a lack of transition, the thermodynamic definition at the top might arguably be related to the elasticity definition -- if for no reason other than the fact that potential energy is widely and consistently defined in terms of it. However, it is also arguable that the thermo def is not about elasticity per se which is normally confined to non-fluid systems. The physics at a low enough level corresponds, but it might be wise to dispense with the thermo part and focus on making the rest of the article clearer and more robust. Comments invited. In the meantime I will fix the opening derivation -- to wit:

Beware that while E is a general notation for energy, in the context of elasticity E is very commonly used to denote Young's modulus -- which also has other commonly used symbols. Anyway, lambda and mu are the common symbols for the lame' constants, but these mostly occur in continuum elasticity. Young's modulus can be defined in terms of lame constants. In any case, the first and second equation are not related to each other by the text and there is an inexplicable change in notation for the elastic energy. It is certainly true that k is the elementary text book convention for Hooke's constant -- but that constant is defined for a spring of known initial length, whereas the moduli are independent of the scale of the system. Let me clean this up and and then someone can comment on the improvement. scanyon 00:38, 6 June 2010 (UTC) —Preceding unsigned comment added by Patamia (talk • contribs)

Okay, I'm back to begin the fixup discussed above. I will document as I go so that anyone questioning what I am about to do, or just plain interested in checking it for correctness, can follow along. First off, be careful with springs. Springs are typically coiled stiff material. A given spring with generally uniform cross section within the coil does display a linear constant -- Hooke's constant "k" -- that relates applied/restoring force linearly to elongation. Slowly developed strain is uniform (constant along the length) for springs and wires for uniform cross sectional geometries. For a stretching wire (of any uniform cross section) "k" and physical parameters of the wire can be used to derive the Youngs modulus of the material -- but this is not true for a spring. When a spring is stretched, a lot of the elastic strain is in the form of shear arising from a twisting of the coiled material. E and "k" are NOT simply related. More fundamentally, it needs to be emphasized that moduli like Young's modulus are properties of the material, and most often of isotropic material. Hooke's constant is a property of the elastic part of a system -- sometimes simple sometimes not. The generalized elastic modulus C discussed in the article is the complete generalization of the Modulus concept and, again a property of the material, not the system. All kinds of k-like values show up in mechanical systems if their elastic response is linear. It is also good, proper, and consistent with the literature to identify the lame constants as parameterizing elastic moduli of isotropic (and, I think cubic) crystals.

That said, I will begin a slow and careful rewrite starting from some fundamental concepts. In the interest of being more encyclopedic than pedantic I will keep some things short, but I am not personally one who thinks that encyclopedia which leaves out essential ideas is of much use to anyone. Clean me up if you want to, but its always best to start off with a bit more that everyone understands than to be so glib that no one but the experts really understand what is going on. And by the way, my personal viewpoint is as a physicist, but this topic can also be expressed from an engineering perspective. Fortunately, unlike, say, thermodynamics, the engineering viewpoint fo this topic is not alien to the physics minded. -- scanyon 20:17, 6 June 2010 (UTC)

Last night I rewrote the 'thermodynamics'-based initial section to tie it in better with the topic. I did this to see how it would look, but I continue to have reservations about having that section there in the first place. At the level of microscopic physics, compressing a fluid does store the internal energy in substantially the same way as compression of a solid. However, it is rare to see fluids discussed in the context of "elasticity" -- and some professionals will balk at it. I am leaving the section in for now to see how it can be cleverly, but appropriately, tied into the rest of the article, but I would love some other opinions about this. A fluid (gas or liquid) has no self-maintained boundary shape and internal pressure is uniformly whatever applied pressure is. Both these statements are the opposite of what applies to solids. The energy principles are, nevertheless, essentially the same -- the fluids being a much simpler case. We should think about this... ---scanyon 16:53, 7 June 2010 (UTC) —Preceding unsigned comment added by Patamia (talk • contribs)

After verifying the historical use (see reference cited) of the term "elastic energy of a fluid" in the early development of classical thermodynamics, I comfortable leaving in a revised version of the corresponding section as a transition to the balance of material focused on elastic energy within solids. The current plan is to finish polish of the intro and fluid compression sections, build more erudite transition to tensor-based elasticity energetics, and then finsh off the piece. There are clearly a number of notational inconsistencies that remain, but already the article is becoming more useable. Sorry, but I must work slowly using snatches of available time. I think in the end the article will meet appropriate standards and all the caveats will be removed. scanyon 17:00, 9 June 2010 (UTC) —Preceding unsigned comment added by Patamia (talk • contribs)

Possible mistake in formular
I think there is a mistake in the formular for elastic energy / Helmholtz potential of an isotrophic linear elastic continuum in this article. But I'm not an expert and don't have appropriate literature at hand at the moment. That's why I don't dare to change the actual article.

I think instead of:
 * $$ f(\epsilon_{ij}) = \lambda \left ( \sum_{i=1}^{3} \epsilon_{ii}\right)^2+2\mu \sum_{i=1}^{3} \sum_{j=1}^{3} \epsilon_{ij}^2$$

it should be only half of that:
 * $$ f(\epsilon_{ij}) = \tfrac{1}{2} \lambda \left ( \sum_{i=1}^{3} \epsilon_{ii}\right)^2 + \mu \sum_{i=1}^{3} \sum_{j=1}^{3} \epsilon_{ij}^2$$

I checked by substituting into
 * $$ \sigma_{ij} = \left ( \frac{\partial f}{\partial \epsilon_{ij}} \right)_S. $$

and compared to the formular given in Hooke's_Law:

\sigma_{ij} = \lambda~\varepsilon_{kk}~\delta_{ij} + 2\mu~\varepsilon_{ij} $$ —Preceding unsigned comment added by 202.72.132.182 (talk) 05:45, 1 April 2011 (UTC)

j

 * ? Tugzy76 (talk) 07:40, 12 August 2015 (UTC)

Rubber motor is NOT an example of elastic POTENTIAL energy
The work that can be done by a stretched rubber is due the entropic force, not potential energy. See the wikipedia entry for https://en.wikipedia.org/wiki/Rubber_elasticity : "The result is that an elastomer behaves somewhat like an ideal monatomic gas, inasmuch as (to good approximation) elastic polymers do not store any potential energy in stretched chemical bonds or elastic work done in stretching molecules, when work is done upon them." So I am removing the link to rubber motor and adding a single sentence noting the difference.

It would be great if someone could provide a more comprehensive discussion of entropic elasticity in this entry. Nick (talk) 18:48, 19 December 2015 (UTC)

Modulus of Resilience
Add the modulus of resilience as it is the elastic energy stored in a material when stretched. 83.247.101.111 (talk) 09:12, 11 February 2023 (UTC)