Talk:Stress (mechanics)

This article sucks

for one thing, it focuses exclusively on solid material - what about fluids and gasses? For another, the most important concepts are buried under mountains of crap - the most simple, basic and important concepts, like ductile materials failing under shear and brittle failing under normal, fluids supporting normal but flowing under shear ... that should be in the intro. Instead, the article drones on and on with graduate level tensor math that should be spit into other articles. --32alpha4tango (talk) 20:59, 1 June 2011 (UTC)

Great ideas. Please add them (with references)! Mgnbar (talk) 22:22, 1 June 2011 (UTC)

This article is about the concept of stress, not about strength of materials. It is very tempting to start writing in this article about ductile materials, the mechanical behaviour of solids (metals, rock, soil) and fluids under different loads. But this is not what this article is or should be about. sanpaz (talk) 16:46, 10 September 2011 (UTC)

I agree wholeheartedly, but for different reasons. This article is focused way too much on engineering aspects, as opposed to the basic physics, and spends too much time trying to explain simple concepts in a confusing manner. Stronger emphasis needs to be placed on the general applicability of the stress tensor to continuous media, and on its physical meaning. The overall formatting is crap. Why is the basic equation $\mathbf {T} ^{(\mathbf {n} )}={\boldsymbol {\sigma }}\cdot \mathbf {n}$ in the middle of the article? Also, $\mathbf {n}$ is not explicitly defined before being used. Furthermore, for an article about the stress tensor, how come there is no link to the Cauchy momentum equation? Also, why is there no mention of the connection to non-mechanical stress tensors like the Maxwell stress tensor? Why, in many of the equations, are the individual components of the tensor written out? Either vector notation, or Einstein notation (with links to the appropriate pages in the intro) should be sufficient. I personally have never written a wikipedia article before, but this one needs some serious revision.198.125.228.16 (talk) 18:21, 2 April 2012 (UTC)

Can someone please tell me what is T₁^(e1)? — Preceding unsigned comment added by 78.45.152.147 (talk) 16:49, 15 February 2013 (UTC)

T is the stress vector. T^e1 is the stress vector associated with a plane with normal vector e1. Then, T₁^(e1) is the component (scalar) in the x1 direction of the T vector (associated with the plane with normal vector e1). sanpaz (talk) 17:06, 15 February 2013 (UTC)

Ah thank you.— Preceding unsigned comment added by 78.45.152.147 (talk) 17:33, 15 February 2013 (UTC)

In the equation stress tensor is in transpose form actually, as it is evidenced by the matrix members following. Which is same as the stress tensor itself due to its symmetry. Just the symmetry notes should be placed before the equation, not after it. So there would be no initial wondering for those like me, not well familiar with the subject. Twowheelsbg (talk) 17:22, 14 June 2013 (UTC)

Separate into Intro and Main Page

There seem to be a lot of complaints and problems with this article largely because it's too broad and too dense. I think we should try splitting it the way the entropy and special relativity articles are with a special "intro to" article that discusses a less technical and more conceptual formatting. Thoughts? Vramasub (talk) 19:20, 21 January 2012 (UTC)

Scope of this article

It seems that from time to time this article gets edits related to material engineering, strength of materials, and metal forming processes. I would like to make it clear that the scope of this article should be, and it is, about the treatment of the concept of stress within the field of classical mechanics, i.e. continuum mechanics. All those disciplines use the concept of stress, as explained in this article, to study stresses encountered in the solids under study: during forming of the solid, during shaping of the solid, during use of the solid in a structure, etc. Those findings should go into other articles related to those disciplines, not into this article. sanpaz (talk) 17:55, 10 February 2012 (UTC)

Stress has no meaning outside of its effect on material. The effects of stress on material are needed to describe what stress is.

This article is really bad. The writing is really bad. It's about as exciting as stale dogshit. It drones on and on and on with graduate level tensor math that nobody cares about or will ever use, and which should be moved to its own article. It focuses obsessively on esoteric crap while failing to describe in clear terms what stress is. The article is written like someone who understands stress is talking to themselves, instead of being written for a reader who wants to learn what stress is. How many years have you been working on this article Sanpaz? The whole article should be deleted and re-written from scratch. --Typoheaven (talk) 14:16, 21 February 2012 (UTC)

Some of your criticisms are fair. The article could certainly be improved. This is true of most Wikipedia articles. Perhaps you'd like to help improve it? You could propose a complete rewrite here, on this talk page. Please give us your text.

Some of your criticisms are unfair. The article is not supposed to be exciting; it is an encyclopedia article, not a textbook or lecture. Lots of people care about and use the "graduate level tensor math". The article should include this technical material, as well as less-technical explanations. Mgnbar (talk) 15:26, 21 February 2012 (UTC)

Typoheaven, if you or anyone wants to understand what stress is in simple terms without going into the tensor math then you only need to read the introduction and the first two sections of the article. The rest of the article which has the math to explain stress is needed to really understand what stress is. There is no other way. That is what any book on continuum mechanics have. You cannot avoid going through the tensor math. So for you to suggest that the article should be deleted does not make sense. Not understanding a subject or thinking is too complex is not a reason to delete the content. Then again, the basic explanation of stress is in the introduction.

And to answer your question on how many years I have been working on this article, I say that is irrelevant. That is a personal attack from you that do not have any relevance to the content on the article.

The introduction and the first two sections could be improved, but the content after that will stay as is, because that is what the current knowledge of stress is.sanpaz (talk) 16:38, 21 February 2012 (UTC)

There is also the possibility to reorganize (not delete) the content, perhaps separating the Euler-Cauchy principle into its own article or something like that. But that has to be discussed and thought carefully as to keep the flow of ideas in the article intact.sanpaz (talk) 16:50, 21 February 2012 (UTC)

In my honest opinion, the article is quite good and I have gained lot of information from it. There is, of course, always room for improvement but I think we should respect the work other people are doing and try giving constructive criticism. Aarne Pohjonen (talk) 08:35, 19 December 2012 (UTC)

Scope: stress has no meaning without material. No material, no stress. Describing the effect of stress and its particular components on different materials is many times more informative than graduate level tensor math. At least for someone who wants to learn what stress is. Dump all that esoteric crap into its own article. Where's mohr's circle? That's something that's actually useful as well as illuminating to someone trying to understand stress. Again, this article reads like a graduate student talking to himself. And sorry Sanpaz, I don't mean this as a personal attack. --Typoheaven (talk) 17:04, 21 February 2012 (UTC)

Typoheaven, the reason for not including how stress relates to specific materials is that that is a specific topic on strength of materials, or metal forming, or strength of materials. Those articles should have the information on how stress develops or is present in materials. The article on stress should only include the explanation of the concept of stress, so other articles (strength of materials, metal forming, materials engineering, etc) can use it as reference to describe stress in their own context.

I understand what you are looking for. You are trying to find a space in Wikipedia where the content related to stresses in materials should be located. And when you see this article it seems like a good place to included it. But this article has a very distinctive scope, which I already explained above. One has to frame an article so it does not blow out of proportion and includes everything under the sun. Is the current scope the best? I would not put my hand on the fire for it, but I think the scope is very clear.

What I think you are looking for is a section that links this article with those other articles. A section that talks, without going into to much details, about how stress is important in those fields related to materials so the reader can go there and be more informed on stress as it relates to materials. That can be done (I'll try to do something on this too). If you want to give it a go by all means do.

And again, this article needs to keep the math which is necessary to understand stress in depth. I did not developed the math, that has been done for the last 250 years. There is no way to avoid it. It is a complex math, but that is why the first parts of the article gives and introduction in words to the reader to the concept of stress. That introduction is good enough for understanding stress and applying it to basic strength of materials etc. However, if later the reader wants to go into the details of what stress actually is (a quantity that can be "fully" described by a tensor) then he/she can follow the math.

Good point on the Mohr circle. Actually, Mohr Circle was originally included in the article a year or so ago. However, the section containing the graphical representation of stress (Mohr cirlce) was moved by other users to the article Stress Analysis. There is still a reference to the Morh cirlce in the current stress article.The section on the Mohr circle should have a more prominent location in the article. That's something else that needs to be worked on.

I accept the apology. It seems you like this topic, which is great. I also like this topic, and that is why I work on it. I, and other users, try to present the topic the best we can. We only want other people to benefit from the article. It is never easy to explain things. It is a constant iteration. That is why feedback from users like you is very important, because it shows that there are needs not met. And, I suggest never to use over the top language, such as "dog shit" etc. That does not help at all. It shows to much emotion and not much reason. Always give reasons for changes, but saying something is too complex is not a reason for removing content that is correct and verifiable. A reason for changes may be that the complex content needs better exposition or better introduction. Or that the complex content would be better placed in a separate article. With respect. sanpaz (talk) 17:59, 21 February 2012 (UTC)

Why is this article tagged "very long"?

Is there a point to leave the tag alone? Seriously, there is nothing wrong about this article's length. What are specific issues that brought you into tagging this article as "very long"? --George Ho (talk) 17:39, 11 May 2012 (UTC)

The tag is apparently gone, but the article is indeed to long:

• The Cauchy stress tensor deserves its own article.
• There is some repeated material, in the article and across articles.
• Proofs should be trimmed or moved to a Wikibook.

--Jorge Stolfi (talk) 03:22, 6 February 2013 (UTC)

Built-in stress is stress, sometimes important

The article states that

The stresses considered in continuum mechanics are only those produced during the application of external forces and the consequent deformation of the body; that is to say, relative changes in deformation are considered rather than absolute values. A body is considered stress-free if the only forces present are those inter-atomic forces (ionic, metallic, and van der Waals forces) required to hold the body together and to keep its shape in the absence of all external influences, including gravitational attraction.[1][2] Stresses generated during manufacture of the body to a specific configuration are also excluded.

This is not true. Stress by definition includes any built-in stress. Only in some applications, where one can assume linearity, it is possible (but optional) to leave out built-in stress. In some applications (such as prestressed concrete, polarization, crack propagation, tempered glass) the built-in stress is critical. --Jorge Stolfi (talk) 22:44, 31 January 2013 (UTC)

• Fixed. --Jorge Stolfi (talk) 14:40, 6 February 2013 (UTC)

Stress can exist without deformation

The article also states that

The stresses considered in continuum mechanics are only those produced during the application of external forces and the consequent deformation of the body; that is to say, relative changes in deformation are considered rather than absolute values.

This too is incorrect. Stress can be generated without any deformation or external forces, e.g. by change in temperature or chemical structure. In piezoelectric materials the stress is generated directly by applying an external field, and one can arrange the field so that there is stress but no deformation. Also in flowing viscous liquid or vibrating viscoelastic solid that is momentarily going through its rest (zero-strain) state there will be viscous stress without any deformation. --Jorge Stolfi (talk) 22:50, 31 January 2013 (UTC)

• Fixed. --Jorge Stolfi (talk) 14:41, 6 February 2013 (UTC)

The statement was/is correct. The statement is not saying stress is not present in bodies withoug external loads. What the statement is saying is that for the the field of continuum mechanics what is of interest is stresses produced by loads. sanpaz (talk) 19:38, 7 February 2013 (UTC)

That can't be correct. For example, for the design of prestressed concrete and analysis of fractures in tempered glass the built-in stress is all-important. In woodworking, a straight board becomes bent when humidity changes, or when it is cut in half. A telescope mirror deforms with changes in temperature. Stresses and strains go on dancing in a sound wave even when there is no external load. Shouldn't those phenomena be studied in continuum mechanics?
Perhaps that statement applies to continuum mechanics as it is taught in certain areas of engineering? --Jorge Stolfi (talk) 03:37, 8 February 2013 (UTC)

The statement was taken from the book of Atanackovic (see reference section). The cases you suggested are all examples of materials being affected by loads: the stresses the pre-stressed concrete has are reached by applying a load (tension tendons) on the concrete; when you cut a piece of wood you are unloading the wood. The statement is trying to make it clear that stresses produced during manufacturing are not the scope of continuum mechanics (that is the scope of other fields). The mathematical body of continuum mechanics does not have the tools to analyze those inter-atomic forces (ionic, metallic, and van der Waals forces) required to hold the body together and to keep its shape in the absence of all external influences, including gravitational attraction. The statement is correct, it comes from a reference, and frames the study of stress from the perspective of continuum mechanics, which is the treatment of this article.sanpaz (talk) 16:33, 8 February 2013 (UTC)

Not everything that comes from a reference is correct 8-).
I am confused: since the internal stress in the wood example is "unloaded" by cutting, then isn't it to be considered a "load"?
Another example of stress without external load: a throbbing blob of water floating in the Space Station. The viscous forces inside the blob are definitely within the scope of C.M. but are not due to any external load. C.M. does not even assume that there were any external forces in the past that set the blob in motion.
Perhaps what the author really wanted to say is: continuum mechanics studies all the forces and stresses in a material, internal or external, whatever their causes; but is not concerted with the causes themselves? In particular, C.M. does cover built-in stress (and must do so when things get non-linear), but not its physical causes? All the best, --Jorge Stolfi (talk) 00:54, 9 February 2013 (UTC)

Another sentence that gives an overly narrow definition of CM:

Following classical Newtonian and Eulerian dynamics, the motion of a material body is produced by the action of externally applied forces.

Again, continuous materials can have motion without external force; for example, sound waves, thermal expansion, viscous relaxation of compressed memory foam These are squarely within the domain on CM. Perhaps this too applies to stress analysis in engineering, specifically, rather than CM? --Jorge Stolfi (talk) 04:20, 10 February 2013 (UTC)

Topics that are missing

In spite of its length, the article manages to be rather incomplete and narrow. There should be more material about, say:

• The molecular physics of stress
• Historical information
• Pragmatics, e.g.
  • Why heated glass shatters
  • Measuring stress
  • Stress in buildings, structures, furniture
• Stress in biology, anatomy, geology
• Stress in composites

Et coetera... --Jorge Stolfi (talk) 03:27, 6 February 2013 (UTC)

• There is now the germ of an History section. If you know more, please contribute... All the best, --Jorge Stolfi (talk) 01:00, 9 February 2013 (UTC)

General revision

The "Introduction" section (now "Overview") has gone through a general revision. Hopefully not too many errors were added and the notation was not messed up too much. I plan to work a bit more on this article over the next couple of days. --Jorge Stolfi (talk) 04:03, 7 February 2013 (UTC)

As your revision included most of the text already in existence, it will take some time to see if some of the text removed is missing in the new revision. At first glance, I noticed you removed the figure that appeared in the introduction. This figure is very useful to show the concept of an infinitesimal element and the stress tensor associated with it. I will include the figure again. sanpaz (talk) 19:42, 7 February 2013 (UTC)

That figure seemed too detailed for the needs of the head section. Isn't the "double bubble" picture (below the protractor photo) sufficient for that section? --Jorge Stolfi (talk) 03:08, 8 February 2013 (UTC)

Perhaps it is too detailed for the introduction. However, I think it is very useful in later section. I'll think about where to place it.sanpaz (talk) 16:19, 8 February 2013 (UTC)

Continuing with the general revision, I noticed that the section "stress (mechanics)#Stress analysis" was almost a verbatim copy of part of the stress analysis article. Some duplication between articles is unavoidable and even good, but verbatim copy is annoying to readers and demands twice as much work from editors. So I trimmed that section of this article, and moved to the stress analysis article some material from stress (mechanics)#Mathematical background that seemed to belong there. I hope I did not do much damage in the process. --Jorge Stolfi (talk) 03:31, 10 February 2013 (UTC)

Jorge, are you planning on moving a lot of the content of stress (mechanics) to other articles (stress analysis, Euler-Cauchy stress principle) and leave this article dealing with stress in a general sense? I think that would be a good idea.sanpaz (talk) 18:21, 11 February 2013 (UTC)

I am tempted to do that, but I do not know whether I will have the energy. 8-) --Jorge Stolfi (talk) 01:25, 12 February 2013 (UTC)

What does it mean here stress tensor is type (0-2) - covariant ? Because in article for Caushi stress tensor is stated contravariant tensor, which I interpret as type (2-0). Twowheelsbg (talk) 18:58, 14 June 2013 (UTC)

CM can handle rigid materials too

This sentence was taken from from stress (mechanics)#Mathematical background:

Continuum mechanics deals with deformable bodies, as opposed to rigid bodies.

This may be a phylosophical quibble; but fluid dynamics has no problem dealing with pressure in flows of incompressible liquids. Now, pressure is to stress like is change of volume is to strain. So it seems quite reasonable to study "rigid" materials in CM Those would be materials so stiff that the strain can be considered zero, even though the stress is not. Makes sense? --Jorge Stolfi (talk) 04:14, 10 February 2013 (UTC)

Be careful with what "rigid body" means. In physics, a rigid body is that which is assumed not deforming when loads are applied. It is not talking about actual objects (there is no such thing as a pure rigid body). Newtonian mechanics and analytical mechanics deals with the kinematics and kinetics of rigid bodies. CM, however, deals with deformable bodies, not "rigid bodies". The statement is correct.sanpaz (talk) 18:20, 10 February 2013 (UTC)

I understand the physics sense of "rigid", but it is just like "incompressible" for fluids. No real fluid is incompressible, yet in CM one can and does model them as such --- and still have well-defined stress fields in them, including stress waves, etc.. The point is that stress can be modeled in CM without assuming the existence of strain. But I will now quibble more about that. --Jorge Stolfi (talk) 03:38, 11 February 2013 (UTC)

Incompressible fluids still have flow and motion, they still deform(?) (change configuration/placement). The intent of the statement is to show that CM does not deal with the rigid body motion of objects, that is the scope, like I said before, of Newtonian mechanics and analytical mechanics. For example, the rotation of a rigid body around an axis is not a problem for CM. It is true that rigid bodies have built-in stresses, but when a load is applied on a 'rigid body' the state of stresses does not change. If they do change, then it is not a rigid body. I would prefer to have a statement in the lines of: Continuum mechanics deals with the motion of deformable bodies, as opposed to the motion of rigid bodies. But perhaps this statement is more suited for the CM article. The statement is not a deal-breaker for this article on stress, though. sanpaz (talk) 18:19, 11 February 2013 (UTC)

Theory sections have been split off

The main theoretical sections were way too long and dense. They have been split off to Cauchy stress tensor and Euler-Cauchy stress principle, where they will be hopefully easier to read and edit. Of course, summaries of those sections should remain here with wikilinks to those articles. I will try to do that in the coming days, but please help. --Jorge Stolfi (talk) 22:14, 23 February 2013 (UTC)

"Further reading" section needs trimming

The "Further reading" list seems way too long, and some of the entries seem rather specialized (e.g. specific to soil mechanics and geology). Some entries have been already moved to the split-off articles Cauchy stress tensor and Euler-Cauchy stress principle, but the list still needs some trimming IMHO. Perhaps move some enrties to continuum mechanics? --Jorge Stolfi (talk) 22:19, 23 February 2013 (UTC)

This (previously excellent) article has REALLY deteriorated in quality, rigor, completeness, accuracy and organization

Key ideas such as the Euler-Cauchy stress principle have been banished to other pages. The definition of the Cauchy stress tensor is gone. The excellent figures demonstrating the balance of internal forces are gone. There is a new and rather confused section on stress analysis. There is a considerable amount of redundant material. There are absurd references to "particles" midway in the article, which defeats the whole purpose of introducing a continuum framework to define stresses, to begin with. And what purpose does that picture of a tank car serve?

Dr. Stolfi, no doubt your edits were made with the intention of improving things but excuse me when I say that they have really hurt the article. The previous version was excellent, rigorous, comprehensive and of high quality overall (thanks to the tireless efforts of editors Sanpaz and Bbanerje, who are both experts in continuum mechanics). Watching it over the years, it had also reached a degree of stability. Unfortunately, I have neither the time nor the energy to make the extensive edits this article needs. Commutator (talk) 05:34, 25 March 2013 (UTC)

Please provide diffs. Or just revert back to the version you preferred. KatieBoundary (talk) 10:50, 25 March 2013 (UTC)

I think it is clear that this article has changed in scope. It went from addressing stress from the continuum mechanics perspective, to a addressing stress in a more general sense. I do not think this is a bad approach. What has happened is that the old article got the Cauchy stress tensor portion (continuum mechanics component) removed from it and sent to a separate article, leaving the current article with the a general explanation of stress. What perhaps needs to be done in this article to further improve it is to make sure it covers all aspects of stress and also highlights the links to the most relevant related articles (Cauchy stress tensor, Stress analysis, Mohr's circle, Cauchy's equations of motion, Euler's laws of motion etc.)sanpaz (talk) 01:54, 12 June 2013 (UTC)

Sign convention?

Is there a convention for the sign of simple uniaxial stress σ, or did I miss it in my reading of the article? Although I didn't see it stated anywhere, it looked to me from the direction of the force vectors that in the equation F/A = σ, tensile stress is positive (σ > 0) while compressive stress is negative (σ < 0). --Chetvorno^TALK 20:38, 17 April 2013 (UTC)

Confusing and Ambiguous Notation and Pictorial Discriptions

No fault to the authors. This seems to be an historical problem guaranteed to confuse initiates to the subject.

One of the first things I ask is, "What are the units of the quantities involved?"

Stress is identified as having units of pressure in the Units section. "The dimension of stress is that of pressure...". Within the Cauchy Stress Tensor section, the unit vector is said to have units of length. Therefore the stress tensor has units of force per unit volume.

The unfortunately named stress tensor does not have units of stress if we are to believe the references.

It should be most important to clarify this to new travelers.

In places, pressure is identified with the letter T. In other text and pictorials it has the symbol sigma, confusing it with the stress tensor. This should not occur within a single article.

In pictorials the two index stress tensor is drawn as a vector as if it has a direction and magnitude! This is sure to befuzzle anyone.

I am new to this subject and having a difficult time untangling the, apparently traditional, mess. Anyone attempting to understand this subject must carefully read each line of text, checking for errors, inconsistency and misdirection. Craigde (talk) 15:32, 18 January 2015 (UTC)

I believe that the author of the "Cauchy stress tensor" section means that the normal vector has a length of 1 ("unit length") in dimensionless units. The rest of the article has been modified arbitrarily by several people over time and needs to be re-examined by someone who understands the subject. Bbanerje (talk) 08:58, 20 January 2015 (UTC)

Thank you. This addresses one point. However, I don't think the author(s) gave it much thought at all or they would not have used the term "unit length" to describe something you say might be unitless.

To keep it simple, the stress tensor is only a multilinar map from from an area element to a vector valued pressure. It should not be confused with pressure itself. More, I find the mathematical modeling, even in tensor notation, an ill marriage with the physics. It cannot survive in any other then 3 spatial dimensions. The reason for this is the area normal obtained through an implicit cross product. I'm still looking for the mathematics that will properly model stress in a coordinate and dimension free way. 2001:5B0:2BFF:3EF0:0:0:0:36 (talk) 11:50, 20 January 2015 (UTC)

I'm not an expert on this subject, but I think that you need to carefully distinguish between the stress tensor and the traction vector. You get the latter by applying the former to a surface element, or equivalently its scaled normal vector.

You are right that a lot of this subject is specific to three (or two) dimensions. For example, the crucial Cauchy momentum equation is derived using the divergence theorem, which relates three-dimensional bodies to their two-dimensional surfaces. The divergence theorem has analogues in every dimension (see Stokes theorem), but the notation changes, and I've never seen the topic presented in that generality. Anyway, maybe this gives you an idea of how to generalize? Mgnbar (talk) 14:19, 20 January 2015 (UTC)

One possibility: Differential k-forms using the wedge (outer product) and Hodge star and sans inner products, with the unit area 2-from replacing the unit (or unitless) area normal vector. But this would be going too far engineers and students of classical physics, even if it could be done. Furthermore, no one would like it and there are no reference sources. Consider it a mathematical challenge. — Preceding unsigned comment added by 2001:5B0:2BFF:EF0:0:0:0:3C (talk) 01:51, 22 January 2015 (UTC)

For an old reference that uses the differential geometry perspective, see Mathmatical Foundations of Elasticity by Marsden and Hughes. A lot of recent research also takes a geometric approach. However, there are numerous unsolved problems in 3 and 3.5 dimensions and k (smooth) dimensions is not a priority from an engineering perspective. Bbanerje (talk) 07:22, 24 January 2015 (UTC)

Thanks for that. It is for that sort of perspective, that might be generalized to relativity, that I came to this article. Craigde (talk) 19:56, 24 January 2015 (UTC)

Redundant Picture

I think that the picture of the car window is not helpful for the article and should be removed. The resons are: 1. At the beginning of the article, there is already a picture clearly showing the visual effect of stressed materials when viewed through a polarizing filter 2. The most dramatic changes between the two views of the car window are not caused by the stress internal to the material, but by the reflection properties of its surface. With this I refer mostly to the transparency of the window when viewed with the polarizing filter. The finer structure caused by the material intrinsic stress is only visible when the picture is view in screen size and is much fainter than the one described above. Don't get me wrong, I think the picture is technically advanced , but I also think it illustrates the change of transparency much better than the effect of stress.
132.187.199.137 (talk) 11:25, 6 July 2015 (UTC)