Talk:Linear elasticity

message: How's about having the standard 'physicists/engineers' notation for these equations included also. I doubt that many of these over 40 know the mathematicians 'differential forms' notation. Linuxlad 9 July 2005 12:12 (UTC)
:I added a page called 3-D Elasticity that does this, I believe.  I don't know what everyone wants to do with it, but I would have no problem combining the two pages.  I actually didn't see this one until after I'd made the 3-D elasticity one.  I think my version is at least as useful, since I don't see how a person could get any meaning from the Einsteinian notation forms, but then I'm not a mathmatician. - EndingPop 21:00, 23 December 2005 (UTC)
replies: text: The linear elasticity article should be a long article incorporating both the engineers point of view, and then at the end, possibly the mathematical condensed presentation. I think the contents of the 3-D Elasticity article should be merged into this one. Berland 07:56, 20 February 2007 (UTC)
thread_title: Physicists/engineers notation

message: The equation for  the acoustic algebraic operator was obviously wrong, since the unit tensor and the k-k dyad don't have the same dimensions. I think it is fixed, but I am not sure about the eigenvalue statements.
With regard to the Einstein notation, yes the meaning is a little more obscure, but it is a compact notation, and it carries an automatic error check as to whether an equation has physical meaning: Both sides of an equation must have matching indices, and any quantity which has all  indices in pairs is a quantity which is physically real, and does not depend on the coordinate system. Many theorems which are laborious to prove without the index notation can be quickly proved using the index notation and its rules. I wrote the indexed version of the acoustical operator, and you can see how neat it is. PAR 18:41, 6 May 2006 (UTC)
replies: text: That's wonderful when you're proving something, but that doesn't discount the fact that it hides the meaning. For an encyclopedia, being able to understand it is far more important than the mathematical elegance that may be inherent in the notation. - EndingPop 21:36, 26 June 2007 (UTC)
thread_title:  Fixed equation 

message: I made some changes (pretty major ones) to the introductory paragraph.  Let me know if I went overboard on my edit. Gpayette 06:49, 10 October 2007 (UTC)
thread_title:  Introductory Paragraph 

message: Trying to address the issue of including both the index notation and the engineering notation, I added in the article a table with both notations for the first equation (equation of motion). It is just a suggestion. If you guys think it is useful to present the rest of the article in this way, then we should do so. If you have a better solution or an improvement for this solution please comment. Sanpaz (talk) 21:15, 25 January 2008 (UTC)
replies: text: The table looks nice.  But I'm not sure we can do it through the whole article, and keep it readable. Perturbationist (talk) 02:53, 26 January 2008 (UTC)
replies: text:  I like the version shown on the page better than the one above, since it's clearer what is being shown. I agree that it'd be difficult to do on the whole page, but what about just on the major equations? - EndingPop (talk) 03:27, 31 January 2008 (UTC)
replies: text:  I think the major equations, yes. The more I work with this stuff, the more I realize that the index notation is the "language" of elasticity. Its most often (but not always) the best way to talk about the physics and mathematics of what is happening independent of any coordinate system effects. Its only when a particular solution in a particular coordinate system is sought that you go to the "full" equations. I think part of our job here is to communicate as much as possible to someone who has not learned the index notation, but also to motivate them to learn it, in order to more fully understand and speak about the physics of the situation without laboriously writing out every equation. So, yes, the major equations should be in all forms (full, abstract, and index), and perhaps a few demonstrations of the usefulness of the index notation for condensing the fully written equations without losing any meaning whatsoever, and in fact adding some insight. (e.g. the unmatched indices of a sum of terms must be the same and the matched indices must only occur in pairs, otherwise the equation is unphysical.) PAR (talk) 04:31, 31 January 2008 (UTC)

text: Ok, good. I'll convert a few more. PAR (talk) 16:46, 7 February 2008 (UTC)
thread_title:  Equations (notation) 

message: The link has changed from strain to this Saint Venant compatibility equations. I did not know of the existence of the second article. So my question is: Do you guys think this article should be merged into the strain article? I don't know if the compatibility equations have enough content to be its own article. I am going to suggest a merge. Sanpaz (talk) 15:47, 12 February 2008 (UTC)
replies: text: I don't understand the Saint-Venant's compatibility condition article, but it seems pretty technical and might be too much to transfer to the strain article. I do know that the compatibility conditions have a lot of content to them and probably will eventually deserve their own article, but right now I don't have a preference either way. PAR (talk) 17:40, 12 February 2008 (UTC)
thread_title:  About Stub article St. Venenat  equations 

message: Would it be possible to define what the lowercase delta symbol in the Isotropic homogeneous media section represents?  I've been going through the article and linked pages, including the Einstein summation conventions but am not seeing it anywhere.  —Preceding unsigned comment added by 99.13.56.253 (talk) 10:44, 23 April 2010 (UTC)
replies: text: done sanpaz (talk) 15:19, 23 April 2010 (UTC)
thread_title:  Lowercase delta symbol in Isotropic homogeneous media section 

message: I think there may be an error in the Boussinesq-Cerruti solution.  Specifically, the G_11 (and G_22) terms.  What's there now is: 
:
b/r+ x^2/r^3+a*(z/r/(r+z)-x^2/r/(r+z)^2)
but I think it should be
:
1/r+ x^2/r^3+a*(1/(r+z)-x^2/r/(r+z)^2).
I've left off the 1/(4*pi*mu) factor.  My source is:
JUNSHAN LI and EDWARD J. BERGER "A Boussinesq-Cerruti Solution Set for Constant and Linear Distribution of Normal and Tangential Load over a Triangular Area" Journal of Elasticity 63: 137-151, 2001.  Also, I checked using Matlab's symbolic math toolbox, and the first formula does not satisfy the elastostatic equation.  The second formula does. Also, if the first formula is right, a 1/r factors out of the entire tensor.  This doesn't seem right.  Thanks for a well-written article.  —Preceding unsigned comment added by 134.174.9.30 (talk) 19:38, 29 September 2008 (UTC)
replies: text: The equations have been corrected.  There was a sign problem in the solution.  The solution given in Landau and Lifschitz p. 25 (eq. 8.18) has been checked by Maple and found to be correct.  That solution matches the new version of the equations with sign change. Bbanerje (talk) 03:02, 25 March 2009 (UTC)
thread_title:  Boussinesq-Cerruti solution Error? 

message: Elasticity tensor redirects here, but this article does not define what the elasticity tensor is. In fact, the article doesn't even mention "elasticity tensor", although this talk page certainly does. Is it the same thing as the stiffness tensor? This must be fixed. Mgnbar (talk) 18:48, 15 August 2010 (UTC)
replies: text: Yes, the stiffness tensor is called the elasticity tensor by some physicists.  The article redirects to Hooke's law now. Bbanerje (talk) 05:44, 17 August 2010 (UTC)
thread_title:  Elasticity tensor 

message: I believe there is a need to classify, differentiate and link the following pages;
Elastic wave, acoustic waves, acoustic emission, Rayleigh waves, Lamb waves, Love waves
I believe this section should be add in elastodynamics under waves.Dr eng x (talk) 05:44, 3 September 2010 (UTC)
thread_title:  New section needed 

message: In the first paragraph it is claimed that linear elasticity relies on the hypothesis that there is no set whose cardinality is strictly between that of the integers and that of the real numbers. This is surprising and should be elaborated.  —Preceding unsigned comment added by 83.255.40.174 (talk) 00:31, 15 September 2010 (UTC)
replies: text: It doesn't rely on the continuum hypothesis; the author must have meant that it models the material as a continuum. I've fixed it. Mgnbar (talk) 12:53, 16 September 2010 (UTC)
thread_title:  Linear elasticity and the continuum hyphothesis 

message: I believe the reasoning for the symmetry of the elasticity tensor was incorrect (under Anisotropic homogeneous media):
"As shown, the matrix  C_{\alpha \beta}\,\! is symmetric, because of the linear relation between stress and strain.  Hence, there are at most 21 different elements of  C_{\alpha \beta}\,\!."
A linear relation between stress and strain gives that  \sigma = C : \varepsilon\! but it doesn't mean that the tensor C is symmetric in \sigma and \varepsilon. The symmetry comes from the energy function which I've now changed. — Preceding unsigned comment added by AndrewDaleCramer (talk • contribs) 06:36, 4 April 2013 (UTC)
thread_title:  Symmetry of the elasticity tensor error? 

message: I ended up in this article while trying to find out if there is a standard, or at least most common, unit for measuring elasticity and what that might be. However, this article appears to only include equations for modelling elasticity, but doesn't go into what you might produce your answer in, or need to convert it into.
Sorry if I've completely missed a more relevant article, but I think this particular article could do with some examples (possibly in an examples section, to keep the rest clear for use as reference material). For my own specific case I really just want some means of quickly describing a material's elasticity with numbers (as opposed to just using terms like "very" =), but yeah, some examples would improve the article I think, if anyone is willing to add a couple of common ones? -- Haravikk (talk) 21:39, 10 June 2013 (UTC)
thread_title:  Common Measurement/Examples?