Talk:Stress (mechanics)/Archive 2

Stress as a vector
In Voigt notation, stress is written formally as a column 'vector' simply to allow the fourth-order elasticity tensor to be written as a square matrix on a flat sheet of paper. However stress is a tensor and calling it a vector has misled generations of students. The sentence 'Simplifying assumptions are often used to represent stress as a vector' could simply be deleted. RDT2 10:03, 15 August 2006 (UTC)
 * I was bold and went ahead and made the change. —Ben FrantzDale 11:54, 15 August 2006 (UTC)
 * I think the reason people sometimes mistakenly believe that stress is a vector is because it's so often used that way in everyday calculations. Understanding how and why this comes about should be mentioned in the article. Maybe not in the intro though. --Duk 18:13, 14 January 2007 (UTC)

Stresses in Equilibrium
70.51.153.89 made a good point in his/her edit.

The 3-d Cauchy stress tensor shown is only valid in equilibrium, unlike the corrected:


 * $$\sigma_{ij}=

\left[{\begin{matrix} {\sigma _x } & {\tau _{xy}} & {\tau _{xz}} \\ {\tau _{yx}} & {\sigma _y } & {\tau _{yz}} \\ {\tau _{zx}} & {\tau _{zy}} & {\sigma _z } \\ \end{matrix}}\right] $$

In equilibrium, $$\tau_{yx}=\tau_{xy}$$, $$\tau_{zx}=\tau_{xz}$$, and $$\tau_{zy}=\tau_{yz}$$, so the filled matrix becomes symmetric. The article is about Stress, however, not Stress in Equilibrium.

I'll correct this tomorrow unless someone objects.

MinstrelOfC 00:06, 24 February 2007 (UTC)
 * I've made the change, and added some explanation. If someone can add how one may make the matrix symmetric when not in equilibrium, please do. About all I know is that it involves a virtual force, and expressing $$\tau_{yx}$$ (etc) as a function of $$\tau_{xy}$$. MinstrelOfC 19:20, 25 February 2007 (UTC)

Mohr's circle
Rankine the pioneer of Mohr's stress circle? See Talk:Christian_Otto_Mohr —DIV (128.250.204.118 06:42, 14 May 2007 (UTC))

Should this be a short summary of Mohr's circle and a link to the Mohr's circle page? Bradisbest 20:38, 25 October 2007 (UTC)
 * Sure. At least remove the steps and figures. -Fnlayson 20:46, 25 October 2007 (UTC)
 * Done. -Fnlayson 21:24, 25 October 2007 (UTC)

Intro cleanup
I was reading this page to look up the difference between stress and strain, since I can never remember which is which. After reading the first paragraph and getting zero understanding, I found the Strain link, and became enlightened by that page. This suggests we need a better layman's description of what stress is before jumping into tensors. Unfortunately, I don't have sufficient background to myself write something simultaneously accurate and legible. I suspect something like the second paragraph, cleaned up, would make a good intro. Given how interwoven the two concepts are, I'd also expect an early sentence about the relation between stress and strain, and particularly how they differ. Bhudson 17:11, 12 July 2007 (UTC)
 * I just added this sentence to the end of the first paragraph: "In short, stress is to force as strain is to elongation." Does that help? —Ben FrantzDale 17:28, 12 July 2007 (UTC)
 * Somewhat, but the entire article is somewhat hard to follow and not helpful in many respects. I have a degree in engineering and the leap to advanced stress concepts jumps the gun a little to fast. —Preceding unsigned comment added by Dj245 (talk • contribs)


 * I wouldn't call it perfect, but it's much better; thanks. Bhudson 19:51, 16 July 2007 (UTC)

Rearranging the whole article

 * I see a lot of things that need to be improved about this article. The first one: the logical order of sections. The article should start, after the introduction, with the Cauchy stress principle section. Here, the principle is stated and derived and the concept of stress vector is obtained. Then the the article should talk about "state of stresses at a point" in a continuum, which will lead to the definition of the stress tensor. The second section has to be the relationship between stress vector and stress tensor and the transformation of the stress tensor into other coordinate system which in fact defines it as a tensor. The Third section will the symmetry of the stress tensor, with its demonstration. The Fourth section would deal with the Stress Invariants (Principle stresses). The Fifth section would deal with the Stress Deviator Tensor. Other sections: Octahedral stresses and stresses in 2D. I know these are a lot of changes, but I think they are very necessary for the improvement of this article. Am I in the correct path here? Please comment.Sanpaz (talk) 00:39, 16 January 2008 (UTC)


 * I re-wrote the whole Cauchy's stress section. The previous version was not cohesive, stated many things without an particular order, and lacked mathematical development. I tried to include all the main things that were included in the previous version. However, somethings were left as they do not belong in this section. I am trying to include them in other parts of the article so those statements are not lost. I know it is very radical change but I think it was necessary. Please comment. Sanpaz (talk) 01:07, 30 January 2008 (UTC)


 * I deleted the section named Stress in three dimensional bodies. The reason for this is that the concepts of hydrostatic and deviator stress are already included in their respective section. And the stresses for a viscous fluid are in fact a topic related to a constitutive equation that relates stress and strains (e.g. hooke's law). In other words, this concepts do not explain what stress is but rather explain the behavior of a body subjected to loads. Therefore, it should go somewhere else (any suggestions where it can go?) Sanpaz (talk) 23:10, 9 February 2008 (UTC)


 * {| class="toccolours collapsible collapsed" width="40%" style="text-align:left"

!Cauchy stress tensor for a viscous fluid
 * For viscous fluids the Cauchy stress tensor $$ \sigma $$ is defined as:
 * $$\ \sigma_{ij}=-p\delta_{ij}+\lambda^*e_{kk}\delta_{ij}+2\eta e_{ij}$$
 * $$\ \sigma_{ij}=-p\delta_{ij}+\lambda^*e_{kk}\delta_{ij}+2\eta e_{ij}$$

If the fluid is incompressible it follows that:
 * $$p = \frac{\mathrm{tr}(T)}{3} = \frac{\sigma_{11} + \sigma_{22} + \sigma_{33}}{3} $$

If the fluid is compressible the assumption above is true, if the viscosity of compression $$\ \mu_D$$ vanishes:
 * $$ \mu_D = \lambda^*+\frac{2}{3}\eta$$


 * }


 * I deleted two sections; 1D stresses and 2D stresses. All the conntent of the 1D section is included in the new section called stress conditions. However, the content of the 2D stresses was not all included. The reason for this is that most of that section was about principal stresses which is already explain it the section Principal stresses and stress invariants; and the paragraphs about the morh circle should go in the Mohr circle section. Sanpaz (talk) 23:38, 9 February 2008 (UTC)


 * Please, review all the changes made. All of them where made with the intent of improving the development of the topic. I tried to keep all which was written before about stress in the previous articles. If I missed something, please include it in the new article. Comments? Sanpaz (talk) 23:42, 9 February 2008 (UTC)


 * I remember this article sucking the last time I viewed it. Your changes are excellent, thank you so much! &mdash; Ben pcc (talk) 19:21, 21 March 2008 (UTC)

Premature FAC withdrawn

 * Featured article candidates/Stress (physics)/archive1. Sandy Georgia  (Talk) 19:58, 23 April 2008 (UTC)

Consistency of invariants
In the section derivation of principal stresses and stress invariants, $$I_2$$ is included in the characteristic equation with a positive sign. In Invariants of the stress deviator tensor, $$J_2$$ is included with a negative sign. This introduced an sign error in the expression for $$I_2$$, which I corrected. For consistency, I feel that either the sign of $$I_2$$ or the sign of $$J_2$$ must be corrected. Yet, I feel reluctant to choose, since $$I_2 = \sigma_1 \sigma_2 \ etc.$$ seems better without a minus, and $$\sigma_e = \sqrt(3J_2)$$ too. Any input how this is in the textbooks? Martenjan (talk) 10:22, 10 June 2008 (UTC)
 * I see the mistake. Thanks for the correction. In the textbooks the characteristic equation appears with either $$-I_2$$ or $$+I_2$$. I don't have a reason to go one way or the other. Sanpaz (talk) 14:45, 10 June 2008 (UTC)
 * The signs of the equations were correct. The way the equations and the invariants are presented is a matter of choice. Some books present the characteristic equation as
 * $$\ -\lambda^3 + I_1\lambda^2 - I_2\lambda + I_3=0$$
 * or
 * $$\ +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$$
 * or
 * $$\ +\lambda^3 - I_1\lambda^2 - I_2\lambda - I_3=0$$


 * I could not tell you which one is "better" Sanpaz (talk) 20:36, 10 June 2008 (UTC)


 * Expanding the determinant $$\ \left|\sigma_{ij}- \lambda\delta_{ij} \right| \ $$ always results in a minus sign before $$ \lambda^3 $$, making the first equal signs in the second and third equation false.
 * To find the eigenvalue $$\lambda$$, this determinant needs to be zero. Then, of course,
 * $$\ -\lambda^3 + I_1\lambda^2 - I_2\lambda + I_3=0$$
 * has the same solution as
 * $$\ +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$$
 * Would we have defined $$I_2$$ with a different sign, as I presume is the case for books in favor of the third equation, then the third is correct too.
 * My solution to keep the plus sign in front of $$ \lambda^3 $$ is to use the following equation
 * $$\ -\left|\sigma_{ij} - \lambda\delta_{ij} \right| = +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$$ Martenjan (talk )(Dont' forget to sign your posts...)


 * The different equations (with different signs) are not "False". All of them are correct. The only difference between them is how you present the result of the different coefficients($$\ I_2=\sigma_1\sigma_2+\sigma_2\sigma_3+\sigma_1\sigma_3$$ or $$\ I_2=-(\sigma_1\sigma_2+\sigma_2\sigma_3+\sigma_1\sigma_3)$$), or if you multiply the equation by -1 or not. But I would suggest using the first equation with the sign (-) first as this is how you solve first the determinant The (+) equation is fine by me.Sanpaz (talk) 13:28, 11 June 2008 (UTC)

Refutation of Cauchy stress
The theory of stress based on Euler & Cauchy is now refuted. The profound incompatibility of this theory with the rest of physics, especially the theory of potentials and the theory of thermodynamics, has been documented in

Koenemann FH (2001) Cauchy stress in mass distributions. Zeitschrift für angewandte Mathematik & Mechanik (ZAMM) 81, suppl.2, pp.S309-S310

Koenemann FH (2001) Unorthodox thoughts about deformation, elasticity, and stress. Zeitschrift für Naturforschung 56a, 794-808

Furthermore, three articles are due to appear in print in the International Journal of Modern Physics B (accepted for publication May 2008, expected publication date August 2008).

In the first paper "On the systematics of energetic terms in continuum mechanics, and a note on Gibbs (1877)" I show that the First Law of thermodynamics has been routinely turned upside-down in continuum mechanics.

In the second paper "Linear elasticity and potential theory: a comment on Gurtin (1972)" I show that a well-known continuum mechanicist must have discovered the fatal flaw in the Euler-Cauchy theory in 1972, but he did his best to mislead his readers.

In the third paper "An approach to deformation theory based on thermodynamic principles" I give an outline of the new approach, which is basically a transformation of the theory of thermodynamics from the scalar form (implying that it is isotropic) into vector field form, in order to consider anisotropic boundary conditions and/or materials. Fully satisfactory predictions for a number of phenomena are presented which were considered unsolved so far, such as kinematics of plastic simple shear, cracks in solids, turbulence in viscous flow, elastic-reversible dilatancy and others.

The new theory has no precursors, except for two papers by Rudolf Clausius (1870) and Eduard Grueneisen (1908) which were completely ignored by the continuum mechanics professional group. The Clausius paper is essentially a modern counter-proposition to the Navier-Stokes equations.

All the papers mentioned above, including the Clausius and Grueneisen papers (in English), can be downloaded from my homepage, see

Falk H. Koenemann

Aachen, Germany, 1 July 2008 —Preceding unsigned comment added by 217.250.179.59 (talk) 08:29, 1 July 2008 (UTC)


 * Sounds very interesting. So I would suggest that you open a new section about the inconsistencies of the Cauchy theory with thermodynamics explaining this new approach and making the proper references to your published papers. I am not sure about wikipedia's policies about writing about one's own work even if is published...any one knows this? - Sanpaz (talk) 18:10, 1 July 2008 (UTC)


 * For a discussion of Koenemann's misconceptions about stress and continuum mechanics in general see http://www.imechanica.org/node/3570. Bbanerje (talk) 21:14, 22 July 2008 (UTC)


 * Sanpaz—No_original_research details Wikipedia's policy about such things. Papna (talk) 22:01, 22 July 2008 (UTC)
 * Bbanerje, I read the imechanica discussion about these papers. I have not read Koenemann papers so I cannot comment about them. But the discussion in imechanics made something clear about the "new" ideas: -let's wait for the paper to be published, and more discussion needs to happen before these ideas can be incorporated into this Wikipedia article. Sanpaz (talk) 22:20, 22 July 2008 (UTC)

Hello Koenemann, some good policy to review is WP:COS and WP:SPA, the first policy is citing ones self, and it is OK as long as you do it in the third person, the second one is policys regarding experts in a certain field who specialze in a certain topic. Please review these policies and by all means contribute to wikipedia, you have much to offer, thanks for discussing this with us.StressTensor (talk) 18:06, 22 September 2009 (UTC)

Plane stress
When defining the Plane stress, a coordinate system should be defined too. I came to the page to understand the Plane stress but I leave without...Kotecky (talk) 11:44, 26 September 2008 (UTC)