Talk:Stress (mechanics)/Archive 3

Thermal Stress
There is no apparent mention/disussion about thermal stress specifically (the thermal stress page just redirects to the article for this talk page, hence why I'm here).

The reason I mention this is that it's an important factor for things like computers, or any precise mechanics/electronics. -- Lee Carré 03:09, 2 May 2007 (UTC)
 * I think thermal stress is just stress resulting from strain resulting from thermal expansion. It may deserve mention here, but I think there's nothing special about thermal stress other than that it is an important source of stress.—Ben FrantzDale 17:30, 12 July 2007 (UTC)

Thermal expansion causes strain with out stress. The stress arises in a structure when its supports or constraints resist the change in size. —Preceding unsigned comment added by 64.126.190.120 (talk) 23:17, 20 October 2008 (UTC)


 * Sorry to drag this up again, but I just got sucked into what the OP mentioned; thermal stress just redirects to this page, and the word "thermal" does not appear in the article. I understand that thermal stress is really just "thermally-induced" stress, but if "thermal stress" is just going to redirect here, there should at least be a mention of it. Maybe a section about the causes of stress? -SidewinderX (talk) 13:13, 8 January 2010 (UTC)


 * Be bold. —Ben FrantzDale (talk) 13:55, 8 January 2010 (UTC)

Hi folks. I came here after a search for "thermal stress", just like the OP. I was trying to figure out what the E is in this equation my prof gave me: Thermalstress = -E * Thermalexpansion. I just figured out that it's the modulus of elasticity, but such things are probably worth mentioning, considering the redirect. I'd be bold and add a new section if I weren't only just learning this stuff. -Keith (Hypergeek14)Talk 14:15, 17 June 2011 (UTC)

EDIT: E is actually Young's modulus -Keith (Hypergeek14)Talk 14:28, 17 June 2011 (UTC)

Swedish version
http://sv.wikipedia.org/wiki/Dragsp%C3%A4nning it should be linked to the swedish article. The swedish article links to this one. Nunez81.225.24.40 (talk) 20:33, 31 January 2009 (UTC)Universitetsholmen

Notation and Interpretation
Notation: The article says that the matrix representation of the stress tensor as a matrix is a column of row vectors: $$ \sigma = \begin{bmatrix} \mathbf{T}_1 \\ \mathbf{T}_2 \\ \mathbf{T}_3 \end{bmatrix} $$ where $$\mathbf{T}_i dS$$ is the force exchanged across the plane normal to $$\mathbf{e}_i$$. This means that $$ d\mathbf{F} = dS \mathbf{\hat{n}}\sigma $$ where $$d\mathbf{F}$$ and $$\mathbf{\hat{n}}$$ are a row vectors, in order for the matrix multiplication to work out. This is not the standard for writing linear transformations. One would expect something much more like $$ d\mathbf{F} = \sigma\hat{\mathbf{n}} dS $$ where $$ \sigma = \begin{bmatrix} \mathbf{T}_1 & \mathbf{T}_2 & \mathbf{T}_3 \end{bmatrix} $$. Is there a reason why the tensor is defined the former way instead of the latter way? If so, this should be mentioned in the article.

Interpretation: In the section entitled "Stress as a Tensor", the following interpretation of the tensor is given: [the Cauchy stress tensor] takes the vector normal to any area element and yields the force (or "traction") acting on that area element. It does not specify the side of the directed area element on which the force is acting. The force could be acting on the positive side or the negative side. I interpret F as the force acting on the negative side so that the force vector is in the same direction as the normal vector when the material is under tension. This results in the following expression for the acceleration: $$ \rho\mathbf{a} = \partial_c \mathbf{T}_c $$. The right-hand side would be negative if F is the force acting on the positive side.Etoombs (talk) 08:31, 4 February 2009 (UTC)

Sign
It is not at all clear, whether a positive value for stress is identified with a "compressive" or "tensile" force.Eregli bob (talk) 11:11, 8 March 2009 (UTC)


 * It's a sign convention. I believe solids people go for positive as being tension whereas fluids people do the inverse (so positive is pressure). —Ben FrantzDale (talk) 22:05, 10 March 2009 (UTC)
 * And rock mechanics and soil mechanics people go for compression as positive as well. There is an explanation on the sign convention for the Mohr's circle but not an explanation for stresses in general at the beginning of the article. That needs to be added. Thanks for bringing it up. sanpaz (talk) 01:12, 11 March 2009 (UTC)

New introduction to the article
I rewrote the introduction. The intent is to quickly cover all the topics covered in the article. This way anyone reading the introduction has a good overview without having to go through the whole article. I must admit the intro is long. I am not sure if this is acceptable for wikipedia articles. Some input from other editors is very much needed. I will change (hopefully improve) the first and second sections to try and avoid repetition of content. I will do this in the following two days. sanpaz (talk) 00:43, 12 March 2009 (UTC)

Traction vector
It's been brought to my attention that traction vector seems to have zero coverage in wikipedia, this seemed like a good place to bring this up. Surely it should be mentioned somewhere, possibly in this article?FengRail (talk) 17:10, 14 April 2009 (UTC)

Traction vector is another term for stress vector. I, or someone else, should include this term. I will work on it in the next days. sanpaz (talk) 17:21, 16 April 2009 (UTC)
 * Thanks - there's a disambig page you might want to wiki link through (see Traction), as well as Traction (engineering), which might need a "This article refers to the macroscopic force traction, for usage in finite element analysis see ..." at the top.
 * I'll leave it up to you. Thanks again.FengRail (talk) 17:29, 16 April 2009 (UTC)

Normal stress
Normal stress is redirected to this article, but there is no definition or explanation of what a normal stress is. Could it be added to the article? I cannot do it, because I don't know what it is really (compared to a shear stress). Mårten Berglund (talk) 12:19, 1 June 2009 (UTC)

Normal stress is explained in this article, in the section about Cauchy's stress principle. However, it is not shown in the introduction. Maybe it is necessary to do so. Thanks for the suggestion. I will try to make the explanation more clear. sanpaz (talk) 18:23, 10 June 2009 (UTC)

When I google it, it sounds as though normal stress simply means the component of stress normal to whatever reference surface you're looking at. In that case, it should be wikified as I have in the previous sentence. It's not perfect, because the normal component article only talks about components of vectors and stress is a tensor. But people will get the rough idea with that wikification more accurately and easily than with just the link to this article. In the article, though, it sounds as though the phrase refers specifically to the stress normal to a surface transecting an axially loaded body. I don't know which the phrase usually implies in what contexts, so I'm leaving it alone. --Dan Wylie-Sears 2 (talk) 07:43, 28 November 2010 (UTC)

Tensile testing
tensile test is redirected here - while this covers in detail the theory underlying this there is no discussion whatsoever about the practicalities of testing - just brief mentions that materials need testing. I think the testing probably needs its own article, however I am not in a position to write one (I just use the technique). —Preceding unsigned comment added by 213.83.104.235 (talk) 10:05, 10 June 2009 (UTC)


 * You are right that tensile test should not redirect to the stress article. Tensile test is more related to the article about strength of materials. In the this article, tensile strength and tests related to its measurement should be addressed. I will redirect tensile test to the article strength of materials for the time being. sanpaz (talk) 18:19, 10 June 2009 (UTC)

Trouble following lead
I am having difficulty understanding the lead. It states, in part:

stress ... is a measure of the average amount of force exerted per unit area of the surface on which internal forces act within a deformable body ... In other words, it is a measure of the intensity, or internal distribution of the total internal forces acting within a deformable body across imaginary surfaces. ... Does "on which" refer to the external "surface"? Or is the "surface" referred to not the external surface, but some "imaginary" internal surface? And what are the "imaginary surfaces"? Maybe it's just my lack of basic physical concepts. Ecphora (talk) 14:23, 10 July 2009 (UTC)


 * Hi Ecphora. Internal forces act on imaginary surfaces inside the body. We imagine these surfaces passing through a particular point inside the body. We want to know the stress at these points inside the body, when the body is loaded on its surface. To do this, our first reaction would be to think that we need to find what we called the stress vector on every single surface at any given point using this equation :$$T_j^{(n)}= \sigma_{ij}n_i\,\!$$ (I am showing the equation for reference, not to confuse). And, how many surfaces can we imagine passing through a point? The answer is infinite surfaces. You can always cut a body in half (a dinner bun for example) choosing infinite cuts passing through a particular point inside it. However, we don't actually need to find infinite stress vectors to find the stress at a point, because we only need to know the stress vector on three mutually perpendicular surfaces. Therefore, the stress at any given point can be found using the Cauchy stress tensor, which is formed by those three stress vectors just mentioned.


 * Please read also the first section in the article, called Definition of stress.


 * I hope this helps. If I am confusing in the explanation let me know. And let me know if the lead needs editing to make the concept more clear. sanpaz (talk) 14:47, 10 July 2009 (UTC)


 * We want to know the stresses at these points inside the body when the body is loaded on its surface - I wonder if you mean: we want to compute the stresses at internal points from knowledge of the external loads (forces acting) on the surface of the body.


 * How to compute something is a different question from what it is.


 * My understanding of the concept of stress is that one thinks of an infinitesimally small volume element inside (or anywhere in) a body, and asks what surface forces act on the volume element from the immediate surroundings. The forces in question are surface forces, not body forces. Body forces may of course be present, and participate in the total equilibrium &Sigma;F=ma.  The stresses are the surface forces divided by the area of the surfaces across which the forces act.


 * There is another distinguishing feature of the concept stress: Forces acting on differently oriented sides of the volume element are not added, they are listed separately. But only three mutually perpendicular orientations are counted. The oppositely oriented surfaces at the other side of the volume element are assumed to have forces that are the reaction forces of the corresponding sides of the neighbouring elements.


 * I find the definition in the first sentences of the lead hard to read and lacking in clarity. The trouble is of course that one would like to find a formulation that would satisfy everyone, from the novice to the expert. This is not possible. I think the best solution is to decide on a single version of the concept, and stick to it for the whole first paragraph. It does not need to be the most general concept, I think that would be another mistake that affects many Wikipedia articles. Just settle on an understandable version of the concept, but describe it with reasonable precision. Illuminating the concept from other points of view should be placed in an "introduction" section after the lead. Now, this whole subject is very big, and while the text has many raw spots, I feel the whole is quite admirable. My thanks to everybody.


 * Looking at the statements in the first paragraph one by one, I think they can be criticised as follows:


 * In continuum mechanics, the concept of stress, introduced by Cauchy around 1822, is a measure of the average amount of force exerted per unit area of a surface within a deformable body on which internal forces act (Figure 1.1).
 * "Introduced by Cauchy" is of course interesting, but hardly essential for the definition. Avoid loading an already heavy initial phrase. The same goes for the time of introduction.
 * "average" does not apply to the stress tensor that applies at a point. The average amount of force per unit area, that would be a description of the concept of "average stress", not "stress".
 * "force exerted within a (...) body": This lacks precision. Forces always act on something, and stating what that something is helps clarify what forces are meant. You may be misled by the idea that the entire body is relevant, but that is not really the case. We often want to compute the stress at every point in order to understand the distribution of forces, but that does not mean that there is a single stress applying to the whole body. One must decide if one wants to describe the concept of stress at a point, or a concept of a stress field, and stick to that decision throughout. Assuming stress, not stress field, in any particular instance you measure or compute the forces acting on an infinitesimally small volume element around or next to a point. In the case of a stress field one must still compute the stress at each point and then (conceptually) repeat for every point.
 * "within a deformable body": While it may be a good thing for the sake of context, to remind the reader that deformations exist, and suggest that the stresses can have some relation to deformations, I think this should not be packed into the very first statement. Since all real bodies are deformable the statement does not loose much if the word is omitted. On the other hand, it would be nice to have, as early as possible, a statement that clarifies what stress is not, including strain. It may be noted that stress is not actually possible in real objects without some deformation.
 * "on which internal forces act": How do you define "internal forces"? Could it be forces whose reaction force act on the same object? This part of the definition says that stress is only present if parts of the object act on each other. I feel this part of the statement could be omitted. Instead, the notion of surface force acting on infinitesimal volume elements should be described with sufficient clarity.


 * In other words, it is a measure of the intensity or internal distribution of the total internal forces acting within a deformable body across imaginary surfaces.
 * This statement adds the concepts of intensity and distribution, but "distribution" follows no more from "stress" than from "force". It refers to "total forces" but it is not clear to me in what way the relevant forces are "total". In this statement forces again act "within" a body, but not on anything in particular. "Across imaginary surfaces" is more like a hint than like a complete disclosure (but see my final paragraph below). All in all the statement is rather wordy for the amount of clarity it provides. I suggest the ideas contained in this statement be moved to a separate paragraph, whose purpose would be to rub in that stress has the dimension of pressure; it is like an intensity in that it is an intensive quantity: considering a smaller section of the object does not reduce the numbers. That paragraph could perhaps expand on the difference between stress and pressure: stress captures directions of force as well as shear.


 * These internal forces are produced between the particles in the body as a reaction to external forces applied on the body.
 * What about the forces inside a slab of pre-stressed concrete? I feel the author has been thinking too much about particular problems where the stresses arising from a given external loading are to be computed. Now, this very comment of mine is perhaps an excessive negativity. Providing a particular context or mind frame is a good thing even if some generality is lost. Yet I feel that the needs of the really helpless novice are better catered for in an "introduction" section. If the lead can be made really Spartan, maybe it would become so short that the novice is not put off before (s)he finds the intro section.


 * External forces are either surface forces or body forces.
 * The distinction between surface and body forces is important. External/internal is somewhat a distraction. I am not sure, that depends perhaps on the perspective induced by a particular problem to be solved using the concept of stress. The exact place of the distinction external/internal may require some more thinking. Perhaps "external forces" is what is often easily known, while "internal forces" is what we need to compute in the form of stress.


 * Because the loaded deformable body is assumed as a continuum, these internal forces are distributed continuously within the volume of the material body, i.e., the stress distribution in the body is expressed as a piecewise continuous function of space coordinates and time.
 * There is a heavy repetition of the words "loaded" and "deformable". Otherwise, I think it is a good thing to clarify that the concept is part of a macroscopic analysis, not usually incorporating atoms and quantum effects. I would like a slight rewording: The body is usually considered a continuum, and the stress is assumed to be a (piecewise) continuous functions of the space and time coordinates. (That is, move the word "assumed" so it affects the stress also, not just the object.)


 * One could perhaps say something somewhere in the article, about how, if one imagine a body divided in two by an imaginary surface, all volume elements on one side of the surface (but adjacent to the surface) act on the volume elements on the other side of the surface, and that in this way, a complete mapping of the stress at each point leads to a definite prediction of the total surface forces exerted by each part of the body on the other part. As it is, the lead seem to try to describe all or many aspects of stress, and ends up explaining each aspect poorly. Later sections do clarify things, but the lead would profit from a clear decision to describe one particular version of the concept, and making other versions the subjects of separate paragraphs.

Cacadril (talk) 16:52, 25 November 2009 (UTC)
 * I agree with most of what you mentioned. It is a lot to digest at once, though. I may disagree with on or two points but I will read those suggestions in more detail. I will make some of the changes that you suggested. I think your main point is that the article has to explain better surface forces, external forces, internal forces etc. I would like to mention that the idea with the introduction was to summarize the whole article to give a quick idea of what stress is about and all the aspects related to it. Kind of a map of the whole article. Then each subsequent section deals with each part of the introduction in more detail.
 * The last paragraph you wrote above can be answered with the section on Cauchy's principle, which explains the body divided into two parts by an imaginary surface.
 * I would like to add that if you want to makes some changes yourself feel free. It is easier if you make one change at a time and explain why than pointing out lots of changes that need to be made and wait for someone to make them. If you think you know a better way to explain something, or know how a particular paragraph could be improved, be bold and do it!!! :) sanpaz (talk) 03:52, 26 November 2009 (UTC)

I have taken the existing lead and moved it all to a section called "Introduction" with several sub-sections created just to break it apart in a more readable way. The new lead is taken from that existing text and stripped down to what I thought was a bare minimum. I have also avoided being overly-technical in the lead, as all the detail is below. I have also made only minimal modifications to the text as written, as I wanted to improve the structure, not change the meaning. This may all need some tweaking, but maybe its a good start. David Hollman (Talk) 11:35, 7 September 2010 (UTC)

Redundancies++
Hi all,

1. I am reading this page (thank you) and initially notice two or three paragraphs from introduction repeated verbatim in the Analysis section. The intro is rather lengthy, perhaps the Analysis paragraphs could be limited to the Analysis section.

2. In Uniaxial Analysis, it is unclear what "a metal sheet loaded on the face and viewed up close and through the cross section" means or looks like and the view of a wire (prior example) seems irrelevant to its 1d approximation. I'm s'pose to be bold so I'll go ahead and white-out that phrase.

IDave2 (talk) 05:19, 21 July 2009 (UTC)


 * The idea I had with the introduction was to summarize all aspects of the article. It is a long introduction. I do not know yet what parts of the intro to omit or simplify. sanpaz (talk) 03:37, 23 July 2009 (UTC)

Yes, the intro has everything but the kitchen sink. The pictures are awesome -- did you make these? I'm rather new to this discussion and to Wikipedia protocols and hesitate to jump right in and make large changes (i.e., changing prose organization or outline without losing any good info). I don't know if you wrote most of this or if the main authors are long deceased. Let me know what you think. I'd also appreciate your feedback on my suggestion for deformation disambiguation. Regards, IDave2 (talk) 04:57, 23 July 2009 (UTC)

Traction Vector?
My teacher was talking about this today, apparently when you multiply a stress tensor and a normal vector the answer you get is a traction vector? But when I search for Traction vector, it just sends me right back to stress.

Is there some vast store of knowledge out there some place on these mysterious Traction Vectors, that will one day be added to Wikipedia or is this something that is not really very important?StressTensor (talk) 18:05, 23 September 2009 (UTC)
 * Traction vector is another name for stress vector. See the section of Cauchy's stress principle. sanpaz (talk) 18:31, 23 September 2009 (UTC)


 * "It is also assumed that on the surface element with area $$\delta S$$, the material outside $$\mathcal R$$ exerts a force


 * $$\delta {\mathbf p}={\mathbf t}^{(n)}\delta\mathcal S$$


 * on the material inside $$\mathcal R$$. The force $$\delta\mathbf p$$ is called the surface force and $${\mathbf t}^{(n)}$$ the mean surface traction transmitted across the element of area $$\delta\mathcal S$$ from the outside to the inside of $$\mathcal R$$."


 * So think of the traction of your car's wheels on the road. Authors use many notations and lingos. Another one is British usage of couple versus American torque. Good luck! IDave2 (talk) 18:49, 23 September 2009 (UTC)



Excellent article
This is an excellent article. The concepts are very clear for a person with little background in stress mechanics, forces, elasticity, the operation of tensors, and etc., etc. Kudos and thanks to all the editors who created this article. Ti-30X (talk) 01:22, 3 October 2009 (UTC)
 * I would like to nominate this article for GA, but I think the lack of in-line citations is holding this type of nomination back. In addition, I am thinking that with in-line citations this could be nominated for FA. To the editors of this aritcle - Why not go for the gold? Ti-30X (talk) 01:34, 3 October 2009 (UTC)
 * Time I guess :). I'll try to give it a little push the next few weeks. sanpaz (talk) 03:11, 3 October 2009 (UTC)

Figure numbers superfluous
The wiki software makes it easy to make clear formatting that does not require figure numbers. If you need figure numbers you're doing it wrong, and not maintaining the same style as the rest of the wiki. - Craig Pemberton 07:00, 3 February 2010 (UTC)
 * I prefer figure numbers. Specially if you want to reference a figure that is in the article but not exactly next to the paragraph you are writing. If there is a figure-numbering system that is used in other wiki articles, please let me know or if you want you can edit this article and fix the formatting. Thanks. sanpaz (talk) 23:30, 3 February 2010 (UTC)


 * Personally I thought the numbering was very useful; the article is quite detailed but the numbering made it easy to match the text to the figures. Perhaps the layout could be improved somewhat (though I disagree that this is necessarily "easy") but even if it were, some figures are refered to in multiple places, etc. so the numbers are very helpful. The fact that the rest of WP does not do this could just mean that more articles would benefit from it. (Anyone know of guidelines of manual of style stuff for this?) Also note that auto-numbering features are apparently not installed on en.wikipedia which would make it easier to do so. David Hollman (Talk) 11:31, 7 September 2010 (UTC)

Maximum Shear Stress section
I just updated this section. Please, review in detailed the derivation just to make sure everything is correct. I don't think I missed anything but you never know. sanpaz (talk) 20:06, 24 February 2010 (UTC)

Changes March 2010
I added more content to the first part of the article. The intention is to explain in more detail where stress come from and what physical laws (equations of motion) are used to formulate the concept of stress.

Please review the additional content and drop any comments in the discussion page or just change the mistakes. Some issues that need to be addressed:


 * Size of the article. One issue that arises with more content is the size of the article. Right now is 103 KB in size, which according to Wikipedia guidelines should be less than 100 KB and after that should be split into several articles. To address this, I will try to merge the section on prismatic bars (first section) into the intro. This way the basic explanation on stress is contained in the introduction and no where else. I am a little bit reluctant to split the article. But if it needs to be done later then...
 * Citation. Right now I've been specifying the particular page of each reference that I have used. But I have been repeating some references that can be consolidated into one. I will try to consolidate them.
 * Consistency in the variables. Right now there are to differential elements for area (dS and dA), and two representations for body forces (Fi and bi). I will unify that.

I will work on the article a little less in the next two weeks (holidays). But I will try to add figures an other stuff before the end of this week, or else later. sanpaz (talk) 00:46, 23 March 2010 (UTC)


 * I think some sections could be moved to other articles. This would improve stress (mechanics) by maintaining its focus and abbreviating it; and would also improve other articles because the text is extremely valuable and detailed. In particular:


 * The article Euler's laws of motion is pretty sparse but seems like it deserves to stand on its own among all the CM articles; I suggest moving the "Euler's laws of motion" section fully to that article.


 * "Forces in a continuum" seems more general to CM and I suggest moving it to continuum mechanics.


 * A brief summary of this material could be added to the introduction of this article.


 * David Hollman (Talk) 11:25, 7 September 2010 (UTC)
 * Hi David. I included these topics you mentioned to this article to add completeness to the subject, giving a better foundation to the article with concepts that come from Continuum Mechanics and from classical mechanics. I also struggled with putting all the content here or in its own articles. I decided to put that content here because of time and effort to expand the other articles. I think is a good idea what you are proposing by moving some content around to other articles. Right now I am not much of a help as other stuff is keeping me very busy. But I can contribute with suggestions in the mean time. sanpaz (talk) 21:34, 8 September 2010 (UTC)
 * Thanks for your feedback (and amazing work on this article BTW). I do understand and support the broader context you were setting with those sections. IMO a summary of these topics should; with good links that should provide the same context to the reader. David Hollman (Talk) 07:29, 9 September 2010 (UTC)


 * Okay I've made these changes, leaving what I hope is a reasonable summary in this article. Iteration on that may be necessary.  David Hollman (Talk) 08:27, 9 September 2010 (UTC)


 * Incidentally, I noticed that a referenced named Slaughter was used, but there was no corresponding citation - Sanpaz can you add that one? David Hollman (Talk) 08:27, 9 September 2010 (UTC)

Sign conventions
I think someone needs to add some explanation of whether a stress expressed as a positive number is a tension or a compression. Different fields of work seem to use opposing conventions for this, apparently.Eregli bob (talk) 03:18, 27 July 2010 (UTC)
 * I just realised I raised this issue 15 months ago and I am still confused.Eregli bob (talk) 03:21, 27 July 2010 (UTC)
 * For metals and polymeric materials a positive stress usually indicates tension. For rocks, concrete, soils, and some other brittle materials the range of values that tensile stresses can take is much smaller than the range of compressive stresses.  Compressive stresses are taken to be positive for these materials.  The convention is just a matter of convenience because it's easier for people to visualize stress states in the first quadrant of a 2D coordinate system.  Bbanerje (talk) 22:28, 27 July 2010 (UTC)

Tensile and compressive stress articles
Compressive stress has its own (brief) article but tensile stress redirects here. IMO they ought to be consistent. I would propose a merge except that this article is already so long; so I'm not sure what is best but thought I should at least mention it here. David Hollman (Talk) 07:19, 7 September 2010 (UTC)


 * I redirected the compressive stress article to here, because it was redundant with this article. Wizard191 (talk) 14:26, 7 September 2010 (UTC)


 * Stress is a complex topic. Sometimes articles have to be long. Micah Schamis (talk) 01:41, September 15 2010 (UTC)

Talk archive created
I just archived all the discussions which seemed to be closed. I have left any which seemed to suggest things needing to be done, or which might require more discussion. Hope that makes this page more readable! David Hollman (Talk) 07:50, 7 September 2010 (UTC)


 * I agree with the need for an archive but I think it is okay to move posts from almost 4 years ago that are inactive into it. I will try to restore the chronological order.


 * Phancy Physicist (talk) 14:11, 28 December 2010 (UTC)

An Newtonian approach is perhaps a more accessible way of mathematically de-construct materials
I have browsed through the content in the Wikipedia article "Stress (mechanics)" and it is most intriguing with a lot of fine approaches to describe and model the very essences of material behaviour.

However, I do think it´s important to acknowledge the fact that materials behave differently in dynamic deformation compared to models based on an mathematical emulative static average. Or in other words, a crystal matrix or a solid amorphous state have the ability to phase transform and behave differently with regards to stress, (or quantified pressure in the system).

The ability to phase transform and changes in properties make all attempts to create a mathematical model describing materials deformation abilities extremely difficult. The only solution I can see, is to drop all previous models based on tensile- or shear-stresses or other know present vectorial approaches, because they all lack the ability to adapt according to the materials ability to phase transform. It is doubtful to create a model based on elements that are static in nature regarding deformation properties when the procedure is clearly dynamic.

My humble suggestion, to an alternative solution, is to watch the material from a in the box perspective. The box wraps around all moving or deformed material and the exhibited stresses or internal pressures found within the box must have a minimum limit which is connected to the surrounding material, where there is no noticeable deformation or movement of mass present. The limit or boundary around a deformed area is thereby given by a very consistent and exact material parameter, because non-moving material is static in nature and measurements are relativity easy to obtain. The tricky part is to deduce the energy distribution or internal stresses within the deformed area, because this must be relative to the geometry (size and shape) and the velocity of the tool or solid-body responsible for the deformation of the deformed area.

For example. In the seemingly "one dimensional" tensile stress=σ (see Figure 1.2 Axial stress in a prismatic bar axially loaded in the article), the applied force clearly have a connection to the fracture mechanism because if the force is large and instantly applied there will be less amount of plastic flow and the fracture mechanism would mostly consists of brittle fracture. In other words, tensile stress=σ is relatively connected to time and amount of the applied force and the circumstances regarding the tool that applies the force.

In compressive stress and frictional contact are the pressure or energy density relatively connected to the penetrating objects geometry (size and shape), nominal penetration velocity which gives the size of the plastic zone and deduce acceleration and deceleration of the deformed mass. In other words, the acceleration and deceleration of material is relative to the nominal penetration velocity and the size of the plastic zone, (the size is given by the geometry of the penetrating object).

I would be happy to discuss the above notion and hopefully the Newtonian approach might make material science allot more accessible with an all-embracing(Box-approach), although very crude and incomplete description of material behaviour. For more information and a snap shoot of empiric observations that supports the above description read the article galling. --Haraldwallin (talk) 14:17, 15 December 2010 (UTC)
 * iMechanica is probably a better place to discuss such issues. Bbanerje (talk) 02:14, 16 December 2010 (UTC)


 * I think I understand what you are getting at, but I don't think much of that belongs here. As I understand it, what you are getting at includes dynamics, nonlinear stress–strain relationships, and stress localization. While important and interesting, that seems largely out of the scope of this page. It could be mentioned, but as links elsewhere. For example, the dynamics of loading a member will certainly create microscopic local regions that experience high stress briefly (see contact mechanics), but at every point in the member there will still be stress that is well described, at least so long as the stresses are low enough for continuum mechanics to apply.
 * With dynamics, are you trying to get at the fact that the stress on a volume element should include stresses from neighboring volume elements accelerating? If so, that seems a bit esoteric for this page. Perhaps there is a continuum dynamics page that could address that stuff?
 * Or am I missing something? —Ben FrantzDale (talk) 14:08, 16 December 2010 (UTC)

First I want to thank "alias Ben" for the above answer. Unfortunately I´m not quite convinced that we use the same terminology or nomenclature and therefore I wan´t to obviate or pree-prevent any existing or eventual developed misunderstandings between us by making a request of goodwill and understanding with regards to that. With this said there are some words in your, "alias Ben", text I need to have clarified.

continuum mechanics or stress systems in a solid materials such as crystalline or amorphous entities are to me very much dynamic in nature, because the very word "continuum" are to me referred to as a "undiscrete" sequence or in other words a sequence or a successive occurrence without stops. I can be wrong about this and if so it´s god to know.

Secondly, you "alias Ben" use the word member in such a way that it can be translated to what is referred to as a bar in the Wikipedia article "Stress (mechanics),Figure 1.2 Axial stress in a prismatic bar axially loaded". I hope you don´t do this type of misspelling as a joke, with the intention to compromise my own sometimes misleading or inadequate spelling that I do in good faith due to incorrect translation by various translation appliances or simply human error. However, if "member" is the accepted word for a particular mechanical phenomenon or defined mechanical occurrence, I would be much obliged to acknowledge and respect your basis of expression.

With regards to the above consideration and reservation I would like to answer your reflection and question of fact, with the following argument.

You, (alias Ben), have almost point out exactly what I´m getting at, the stress on a single volume element inside the "member" or bar is always deduced by the acceleration of it´s neighbouring volume elements and even the total amount of moving volume elements in the whole system. If I understand you correctly your statement is that, in every point the stresses are known and well described as long as the stresses are low enough. But is this really true? I don´t think so because stress isn't equally distributed even in the elastic region. Some parts of a "member" or bar have higher concentration of stress due to inclusions, stress-plans or grain boundaries or other factors. My initiative is to merge all kinds of material stress behaviour into one single model by first setting a system boundary around the "member" or bar. Then attempt to describe the interior with regards to acceleration of mass and as a consequence the material dependent coefficients, that represent the strength of bounds between atoms and the phase constitution, are thereby stress assorted and of course non-linear due to any eventual phase transition, almost exactly like changes in viscosity when fluids are exposed to cavitation when they turn from fluids(l=liquid) into gas(g).

As an example. In the seemingly "one dimensional" tensile stress=σ (see Figure 1.2 Axial stress in a prismatic bar axially loaded in the article), the applied force can be derived from the tool that are fixed to the bar that pulls it apart. Even this tensile stress material parameter is a consequence of friction between the tool and the bar. In my notion to emulate the material behaviour, the system boundary is set around the interface between the tool and the bar. In other words, I don´t recommend to conduct an investigation on only a single cross section or stress-plan inside the bar and use this in association with the strain or yield as a base for the material parameter, as is presently the case. On the contrary, any developed tensile stress found inside the rod is a consequence of friction stresses between the tool and the bar and therefore should an investigation include the whole course of events and the material parameter be described as a function or at least with "attendant very defined circumstances" attached to it. Notably, there is very little visible plastic deformation between the tool and the bar and investigations almost always concentrate on the plastically deformed area when they determine material parameters such as tensile stress =σ. And the acceleration or the action of pulling the bar apart is forgotten or considered unimportant. But is the acceleration of the pull really unimportant? I think you can agree to the fact that the acceleration determine the exact stress distribution from the interface between the tool, bar and outwards to the bars plastic region where the actual fracture is developed.

Hope this clarify some of my notion and perhaps you might find something to remark on, I would be happy to continue this discussion. --Haraldwallin (talk) 11:27, 17 December 2010 (UTC)


 * Yes, "member" is not a joke; it is common parlance in English engineering language to describe a part, generally with nondescript shape, I think.
 * Again, I overall agree with what you are saying. You are absolutely right that continuum models don't properly describe polycrystals. In fact, part of my master's research was in multiscale simulation working to address exactly that.
 * You are right that in a polycrystaline part that is not annealed, doing just about anything to it will cause some local plastic deformation (1) because some tiny differential elements are already stressed to their yield stress (e.g., at grain boundaries or around dislocations) and (2) because of surface contact including friction&mdash;just look at surface marring on the head of a brand new bolt just after tightening it for the first time. But in both cases, at a large scale, these effects can be ignored in most cases. (Although precision engineering generally assumes a much smaller plastic-yield stress than the usual numbers.)
 * All that said, I don't see how these observations are actionable for this page. If we are trying to explain stress, I think it makes the most pedagogical sense to gloss over real-world complexities. This is much as Newton's laws generally get explored first in the context of point masses on frictionless surfaces.
 * What change are you proposing for this page? Or, are you proposing another page going into these details? —Ben FrantzDale (talk)

Hi Ben, thanks for your reply. I apologise for my incomplete vocabulary and I’m going to immediately incorporate common terminology/nomenclature in my translation appliances to avoid similar misunderstandings in the future. However, we still seems to have trouble of understanding each others argumentation with regards to context or "the full meaning of the argument". But I hope and believe that I understand you correctly and making a request of goodwill, if not.

(1) I fully support your basis of opinion and conclusion regarding polymers and other materials with no or insignificant elastic properties, where movements of dislocations or parallel changes in bonds between atoms/molecules are light and frequent.

(2) I respect your opinion, and I agree to some extant that in large scale examination of material properties, these effects can be ignored and are ignored. (3) My reference to an Newton approach was due to the connection between deformation of materials and acceleration of mass. I have once again read through the Wikipedia article "Stress (mechanics)" and I find references to acceleration of mass and stress/pressure assorted material behaviour in the introduction chapter and "Theoretical background", but this is not to my opinion, exhibited in the following mathematical discussion??

Don´t get me wrong here, I just want to point out what I think and hopefully come to an agreement and perhaps an eventual development and incorporation of clarifications through an discussion with others. My notion is to watch the system in a similar way as you do, but incorporate the use of acceleration and mass in the mathematical discussion. And the "mass" component is of course tricky to introduce in a "two dimensional" or "one dimensional" system. But, the foremost issue is to come to some agreement to the influence of acceleration in plastic deformation of materials. --Haraldwallin (talk) 21:08, 1 January 2011 (UTC)


 * Hi, Haraldwallin. I'm not qualified to comment on the substance of your comments, but please keep in mind Wikipedia's policies on original research and verifiability. This is not a forum for figuring out new treatments of stress or materials science, but rather a forum for writing the article Stress (mechanics) using verifiable sources. I think that both Bbanerje and BenFrantzDale have alluded to this issue. Regards, Mgnbar (talk) 14:47, 2 January 2011 (UTC)


 * I admit I haven't done much with continuum dynamics. My sense is that it is a fairly advanced topic and can lead to subtleties such as asymmetry of the stress tensor (since force balance isn't maintained). There certainly is literature on it, but as Mgnbar points out, keep any additions well-referenced. Feel free to propose language you'd like to add. —Ben FrantzDale (talk) 12:59, 3 January 2011 (UTC)

Hi again Ben and once again, thanks for your reply. I wrote my discussion on this page to announce my intention to change some aspects of the article. My changes might of course annoy previous writers if they don’t agree to the content of my changes. My thought was to be polite and discuss my concerns in the discussion page in accordance whit Wikipedia's policies. This procedure worked pretty well for other articles related to this subject. I´m not really going to figure out something, My intention is to correct some minor details or more or less incorporate some explanation and references that in my opinion might make this article and subject accessible and connected to a broader scientific field and comprehensible for wider audience.

The main issue is of course to use an acceleration component, rather than an entity such as the force. --Haraldwallin (talk) 09:44, 10 January 2011 (UTC)


 * You're right; major changes to an article are often best discussed first. However, it is difficult to evaluate the changes you want to make without seeing the specific text and references that you want to use. An approach that has worked for me in the past is to start composing text on the talk page, in an "isolation box" (see below), and then to have other editors comment on it. Mgnbar (talk) 14:24, 10 January 2011 (UTC)

[write your proposed article text here?]

Hi alias Mgnbar. I´m sorry that I haven´t answered your comment earlier. Regarding your request. I must admit It will take some time before I write something, because the article in it´s present form is quite "divided", perhaps do to several authors. In other Wikipedia articles where I contributed. I took control of the total picture or layout, meaning a total rewrite of the whole Wikipedia article or section. I´m sorry to say but this is perhaps needed in this article as well, no offence. And I´m not sure if I´m the man to do it.

Because continuum mechanics only resembles my own expertise and the articles nomenclature contains "some" expressions or mathematical expressions that I need to explore before knowing what to do whit it and the lay out of the article. I my do a rewrite of the article later, but It will take me more time than I expected and quite frankly I have other things on my mind for the moment. --Haraldwallin (talk) 17:35, 24 January 2011 (UTC)


 * I understand, and I would take no offense even if I had edited this article. The distributed nature of Wikipedia editing makes it difficult to produce coherent text in a single voice. And complete rewrites can take a while, and must be done diplomatically. Anyway, best wishes. Mgnbar (talk) 19:45, 24 January 2011 (UTC)

Ok, I will make an attempt to rewrite the whole article of, Stress (mechanics), in the Wikipedia archives.

However, I can’t do it on this discussion page due to format issues, so I will make changes directly in the original article. And it will take a considerable amount of time, so please don’t be extremely angry if things aren’t perfect at once. Others can of course make changes but I will probably delete or rework them as they appear. I have of course no owner ship of Wikipedia but I believe I can make changes that make everybody happy as the rewrite progresses.

The fundamental issue is to develop the expressions and “physics” in such a way that it becomes more accessible and in point of view more useful. If I do something wrong about the physics, please discuss it with me and explain why I’m wrong. I will start the work when I feel for it, but it wont take long. Politely, Harald W --Haraldwallin (talk) 15:54, 2 February 2011 (UTC)


 * I'm strongly against non-standard interpretations of Cauchy stress in an article that talks about the Cauchy stress. The stress that you are talking about is a different concept and probably falls into the category of stresses in Cosserat/ micromorphic materials.  Stresses and deformations in the context of phase transformations have been studied extensively and continue to be a topic of active research.  Since Wikipedia is not a forum for original research, I'd suggest that you look into the literature for studies that reflect your ideas and create a new article on that interpretation of stress.  If you don't find any, I'd suggest that you publish your ideas in the peer-reviewed literature before writing the Wikipedia article.  Bbanerje (talk) 19:46, 2 February 2011 (UTC)

Hi, alias Bbanerje. My primary objective is to rewrite the article in such away that certain aspects of plastic deformation are included or amplified. The article already mention important aspects but dosen´t in my opinion, sufficiently emphasize on the subject. I think I mentioned this in my previous discussion.

Regarding the cosserat modelling of heterogeneous materials. I´m no expert on this cosserat modelling so take no offence, it seams that the model is based on evaluation of generalized "static" strain between unit cells, this is ok but shouldn't it also include acceleration of mass as a factor of resistance? My opinion are in other words. The wave function included in the cosserat model, perhaps should somehow be connected or assorted to the size of the whole system or more precisely the size of the effected volume. If this is done the wave function incorporates "or exclude the need for", a acceleration component. The way of making a homogeneic (one big material piece), mathematical simplification is perhaps a productive way of doing it. I can´t say becouse I don´t know whats better. But my instinctive thought is that it might be easier to use use a "discrete" finite element method (FEM, Allot of small material cells after one another).

The main issue is to understand the implication of mass-acceleration with regards to scale. And this can be done with a non-static approach. Materials dosen´t have a minimum scale or a smallest "cell element" and the resistant due to acceleration of mass is amplified when the scale is smaller. Thus all generalized material parameters measured at a macro scale lose their validity in micro or nano scales circumstances. It is clear that material distributed in smaller bits all together are stronger, than the same amount fused tougher in a single structure. One example are the metal cable and the metal bar, the stress distribution are different in a dynamic (acceleration) aspect. If acceleration of mass is investigated with regard to scale, there is a possibility to make staggering discoveries.

This is not a joke or a "new" scientific discovery in any way. It´s only a rearrangement, modification and clarification of existing models. But I agree to that if the problem is expleined correctly, the practical impact "might" be huge.

It will also make strange mechanical issues and other things much more easy to understand. And if I just rearrange some structure issues in the article, it can´t be that bad? If you think differently you can change it back, easy. --Haraldwallin (talk) 21:47, 5 February 2011 (UTC)
 * Once again, before you go and change the article, write up your version in a separate article in your user page and ask for some feedback. I've suggested earlier that you present your ideas to iMechanica and see if they stand scrutiny from professional mechanicians.  You should first publish your ideas before adding them to Wikipedia.  I have nothing more to say.  Bbanerje (talk) 03:05, 6 February 2011 (UTC)


 * I have alreday changed the article in two sections and descibed how “Geometrical constraints” do implicate on acceleration of deformed material, my changes have been approved buy other editors and are allready publiched, see reference--Haraldwallin (talk) 15:18, 3 November 2011 (UTC)


 * Wallin H. 2008, 129 p: An investigation of friction graphs ranking ability regarding the galling phenomenon in dry SOFS contact : (Adhesive material transfer and friction), A free pdf document available here or www.diva-portal.org found here or at www.uppsok.libris.kb.se here use search words:"galling & Harald Wallin" or the direct libris link here

Stress tensor is (2, 0), (1, 1), or (0, 2)?
This article is pretty sloppy in its use of superscripts and subscripts, right? It is hard to tell whether the stress tensor is of type (2, 0), (1, 1), or (0, 2). I know that we can raise and lower indices pretty freely in Euclidean space, but Wikipedia can and should be clear and definitive about the exact types of tensors here, to facilitate non-orthogonal coordinate changes, generalization to curved spaces, etc.

The "Stress modeling (Cauchy)" section says that the stress tensor $$\sigma$$ is of type (0, 2), and consistently uses double subscripts.

The "Cauchy’s stress theorem – stress tensor" section has equations such as $$T_j = \sigma_{ij} n_i$$. This equation is "incorrect" in that (1) it violates tensor notation conventions (contracting upper against lower indices, etc.) and (2) T is supposed to be a vector, so its index should be a superscript. Depending on whether n should be of type (0, 1) or (1, 0), the equation can be corrected to either $$T^j = \sigma^{ij} n_i$$ or $$T^j = \sigma^j_i n^i$$, from which we deduce that $$\sigma$$ is of type (2, 0) or (1, 1).

Is it true that n is of type (0, 1) and $$\sigma$$ is of type (2, 0)? If not, then what's right? If it helps, the Stress-energy tensor article writes that stress tensor as (2, 0), while the Maxwell stress tensor article writes that stress tensor as (0, 2). Mgnbar (talk) 17:26, 16 January 2011 (UTC)


 * The article is consistent in the sense that rectangular Cartesian coordinates are assumed whenever components of the stress tensor are introduced. There is no distinction between covariant, mixed, or contravariant components in that situation and (2,0), (1,1), (0,2) lead to identical results.  The use of the (0,2) format is standard in solid mechanics and is not incorrect because summation is over repeated indices and the use of upper/lower indices just complicates things.   You can see the discussion at imechanica.org/node/4356 for more thoughts on the matter and issues that arise when one moves from Euclidean space to Riemannian manifolds.  Bbanerje (talk) 22:28, 16 January 2011 (UTC)


 * Thank you for the link; it's a treasure trove that I haven't yet fully absorbed.
 * My background is in pure math, so I'm not entirely comfortable with the conventions of the mechanics community, but this article should certainly follow mechanics. The section "Transformation rule of the stress tensor" says, "It can be shown that the stress tensor is a contravariant second order tensor..." (i.e. a (2, 0)-tensor), and then goes on to give the transformation law for (2, 0)-tensors. Have I made a mistake? If not, then what is the mechanical view of such a statement? Is it meaningless? (Is it even possible to prove that something is (2, 0), as opposed to (0, 2)?) Is it meaningful and consistent with double subscripts? Is it inconsistent and needing removal? Mgnbar (talk) 15:35, 17 January 2011 (UTC)
 * You're right. That part is confusing and does not add to the reader's understanding of stress.  My feeling is that the text should be simplified to "The stress tensor is a second order tensor."  The reason for that can also be added, i.e., the stress is a linear transformation that takes a direction to a force (per area) and the transformation rule for second-order tensors holds.
 * Making a distinction between contravariant and covariant tensors in Euclidean space is pointless. Just saying that the tensor is second order is good enough.  The article needs a separate section where these distinctions are discussed.  One source of information on that is Theodore Frankel's "The Geometry of Physics" which has an appendix that discusses stress from a differential geometry point of view.    Bbanerje (talk) 21:21, 17 January 2011 (UTC)
 * For what it's worth, Abraham, Marsden, and Ratiu: Manifolds, tensor analysis, and applications (which I tracked down from the link you posted above) defines the Cauchy stress tensor (p. 586) and the electromagnetic stress tensor (p. 604) as being (2, 0)-tensors (which I've always favored), but in another place (p. 341) mentions the stress tensor as being a "2-tensor". I take this as evidence that one could develop mechanics paying careful attention to the types of tensors (as I've asserted), but that mechanicists typically do not (as you've argued). Regards, Mgnbar (talk) 17:51, 20 January 2011 (UTC)
 * In the mid 1900s, some mechanics textbooks (e.g., Green and Zerna) were written with careful consideration to the location of the indices. Such an approach tended to obfuscate rather than illuminate the physical principles involved.  That has been superseded by direct tensor notation (one hopes).  The differential geometry approach (pioneered by Marsden and others) has never really caught on because it hasn't led directly to many major insights yet.  But the Marsden approach has the potential of cleaning up some sloppy thinking regarding integrations over deforming domains.  Bbanerje (talk) 21:34, 23 January 2011 (UTC)

Formatting of "Euler–Cauchy stress principle" Section
I feel that the section entitled "Euler–Cauchy stress principle" is not visually well laid-out compared with other sections in the article. The appearance of a large number of inline graphics, in my view, hinders readability.

As an example, consider this segment: "The force distribution is equipollent to a contact force $\Delta \mathbf F\,\!$ and a couple stress $\Delta \mathbf M\,\!$, as shown in Figure 2.1a and 2.1b. Cauchy’s stress principle asserts that as $\Delta S\,\!$ becomes very small and tends to zero the ratio $\Delta \mathbf F / \Delta S\,\!$ becomes $d \mathbf F/dS\,\!$ and the couple stress vector $\Delta \mathbf M\,\!$ vanishes."

This appears difficult to read, to my eyes, and also suffers from a lack of punctuation. I am struggling a little to put my finger on exactly what I mean as I write this, but I also think that this sentence is a good example of one which could be expanded to several sentences for clarity. It seems to "hit you all at once", so to speak.

I also feel that some sentences lack clarity of expression, and should be rewritten. As an example of what I mean, consider the following text:

"To explain this principle, we consider an imaginary surface $S\,\!$ passing through an internal material point $P\,\!$ dividing the continuous body into two segments, as seen in Figure 2.1a or 2.1b (some authors use the cutting plane diagram and others use the diagram with the arbitrary volume inside the continuum enclosed by the surface $S\,\!$)."

I would like to hear the thoughts of others on this topic, especially if there are specific comments regarding potential improvements.

I am happy to 'fix' the section should the community agree that it needs to be tidied, however I am not an expert wikipedian and may struggle somewhat, so if someone else has a desire and an ability to amend the section then please do so.

Chrislaing (talk) 22:50, 7 February 2011 (UTC)


 * I agree, in this and other sections. Here's the kind of change you want: $$\Delta \mathbf F$$ to &Delta;F. If you would take this upon yourself to fix, then it would be much appreciated. Mgnbar (talk) 16:31, 9 February 2011 (UTC)
 * Regarding The force distribution is equipollent to a contact force $$\Delta \mathbf F\,\!$$ and a couple stress $$\Delta \mathbf M\,\!$$, as shown in Figure 2.1a and 2.1b. Cauchy’s stress principle asserts that as $$\Delta S\,\!$$ becomes very small and tends to zero the ratio $$\Delta \mathbf F / \Delta S\,\!$$ becomes $$d \mathbf F/dS\,\!$$ and the couple stress vector $$\Delta \mathbf M\,\!$$ vanishes.:
 * More common words could be used instead of "equipollent", the couple $$\Delta M$$ should remain a couple and not be converted to a stress before the limit is taken. The same information can be expressed more clearly in mathematical notation as is done later in the article.
 * I think that the convoluted language that we see in the article is the result of an attempt to explain limits and other mathematical concepts in everyday language while trying to keep the length of the article reasonably short.  Bbanerje (talk) 22:34, 9 February 2011 (UTC)


 * I've gone through the "Euler-Cauchy stress principle" section and performed a slew of formatting changes. I think it looks much better. I also added some punctuation and made a few tiny wording changes, just to make the text grammatical. In my opinion, some of the notation employed is pretty ugly, but I have tried not to change the notation, because I don't know how standard it is in the mechanics culture. I am also not qualified to improve the substance of the text. Mgnbar (talk) 17:02, 16 February 2011 (UTC)


 * Your changes vastly improve the article. Sorry I didn't do it myself, I ended up becoming rather busy with the Christchurch earthquake. I'm also not particularly familiar with the notation used the the mechanics community. Coming at this from the purely mathematical perspective, I think the notation could use some changes, but like you I am not well qualified for improving the substance of the text. Thanks for the great edit :-) Chrislaing (talk) 21:49, 18 March 2011 (UTC)

Virial stress
A merge of virial stress has been shoehorned into this article under "Normal, shear stresses and virial stresses" (sic). It really does not belong in this section, imo it was better off in its own article. It should be unmerged with just a link here, or at least moved to its own section.  Sp in ni ng  Spark  08:02, 8 March 2011 (UTC)


 * I agree. Mgnbar (talk) 14:01, 8 March 2011 (UTC)
 * As no one else has commented, done.  Sp in ni ng  Spark  13:28, 27 March 2011 (UTC)

Second invariant
Can someone explain why different definition of tensor invariant is used for stress tensor and for its deviator tensor. Using principial component in first case correct formula according tensor math is used: I2 = s1*s2 + s1*s3 + s2*s3 in case of deviator tensor second invariant is: I2 = - s1*s2 - s2*s3 - s1*s3 Using second looks good in context of article, but not for math point of view. — Preceding unsigned comment added by 212.5.210.202 (talk) 13:35, 18 July 2011 (UTC)


 * I suspect that this inconsistency, if it is an inconsistency, has crept in due to multiple authors. Is the math even correct? I haven't taken the time to check. If you would check the correctness of the math, that would be a big help; then we could improve the presentation. Mgnbar (talk) 15:47, 18 July 2011 (UTC)


 * The math is correct. I do not understand where the inconsistency he is referring to is. I think he is confusing J2 with I2. sanpaz (talk) 16:57, 10 September 2011 (UTC)
 * The point that User talk:212.5.210.202 is trying to make is that the article defines the invariants $$I_1,I_2,I_3$$ using the characteristic equation $$\lambda^3-I_1\lambda^2+I_2\lambda-I_3=0$$ while the invariants $$J_1,J_2,J_3$$ are defined using $$\lambda^3-J_1\lambda^2-J_2\lambda-J_3=0$$. Notice that the sign of $$I_1$$ is different from that of $$J_2$$.  That's the inconsistency in the article.  I prefer the form used for the $$I$$s. Bbanerje (talk) 22:07, 31 October 2011 (UTC)
 * Ah, I see now. Sure, the other way with the second term as negative can be used. I'll change it.sanpaz (talk) 22:14, 31 October 2011 (UTC)
 * Consistency is not necessarily a good thing in this case because the definition of $$J_2$$ will change to $$J_2 = - s_{ij} s_{ij}/2 $$ which is contrary to convention. Bbanerje (talk) 22:26, 31 October 2011 (UTC)
 * I got the original formulation with the minus sign in J2 from Chen, but the other formulation with the plus sign in J2 can be found in Mase. If you think one is more common than other let me know. I really do not know which one is more common. sanpaz (talk) 02:06, 1 November 2011 (UTC)
 * The form $$J_2 = + s_{ij} s_{ij}/2 $$ is widely used in plasticity in the definition of yield surfaces and flow rules. I can't think of any field where the negative form is used.  So it's probably better to keep the article in its original form and add a note that explains the choice of sign for $$J_2$$ (with references if possible).  Bbanerje (talk) 02:28, 1 November 2011 (UTC)

Confusing paragraph (for editing)
This paragraph was included at the beginning of the article. It does not have references nor it is clear what it has to say. I suggest to edit this paragraph here until it is properly written:


 * However, models of continuum mechanics which explicitly express force as a variable generally fail to merge and describe deformation of matter and solid bodies, because the attributes of matter and solids are three dimensional. Classical models of continuum mechanics assume an average force and fail to properly incorporate "geometrical factors", which are important to describe stress distribution and accumulation of energy during the continuum.

For example, what is the meaning of the last phrase: "stress distribution and accumulation of energy during the continuum"?. Is it trying to say "...throughout the continuum"? More importantly, if this paragraphs tries to say the weaknesses of the mathematical model of stress, then it surely needs references, or else sounds like an opinion. sanpaz (talk) 21:29, 4 November 2011 (UTC)


 * Now I understand a little better the situation with this paragraph (going through the history). The reference given for this paragraph is from a Thesis. That is not a proper reference. Wikipedia is not the place to peer-review or validate concepts from a thesis. That is the job of recognized Journals. Unless there is a legitimate reference to this paragraph, there is no way it can go into this article. sanpaz (talk) 22:13, 4 November 2011 (UTC)

What is internal forces?
In the very first part of this article, it is mentioned that:

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body.

Then, it is explained that:

 These internal forces are a reaction to external forces applied on the body.

and

''External forces are either surface forces or body forces. ''

However, nothing about internal forces is given.

And in physics, internal forces means

the forces that can never change the total mechanical energy of an object, but rather can only transform the energy of an object from potential energy to kinetic energy (or vice versa)

So, it is not adequate to use internal force in the definition of stress.

If it is necessary, then the definition of internal force must be given specifically. — Preceding unsigned comment added by Valuexu (talk • contribs) 10:46, 21 December 2011 (UTC)
 * As the article states, in the context of continuum mechanics, internal forces are those produced as a reaction to external forces (body or surface forces). That is the explanation. I do not see your point. Could you please provide the reference or source for your definition of internal forces? by knowing the source I can perhaps understand your point.sanpaz (talk) 18:10, 21 December 2011 (UTC)