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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)
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:
In equilibrium, , , and , 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)
Rankine the pioneer of Mohr's stress circle? See Talk:Christian_Otto_Mohr#Rankine —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)
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)
Cauchy stress tensor for a viscous fluid |
---|
For viscous fluids the Cauchy stress tensor is defined as:
If the fluid is incompressible it follows that: If the fluid is compressible the assumption above is true, if the viscosity of compression vanishes: |
In the section derivation of principal stresses and stress invariants, is included in the characteristic equation with a positive sign. In Invariants of the stress deviator tensor, is included with a negative sign. This introduced an sign error in the expression for , which I corrected. For consistency, I feel that either the sign of or the sign of must be corrected. Yet, I feel reluctant to choose, since seems better without a minus, and too. Any input how this is in the textbooks? Martenjan ( talk) 10:22, 10 June 2008 (UTC)
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 [1]
Falk H. Koenemann
Aachen, Germany, 1 July 2008 —Preceding unsigned comment added by 217.250.179.59 ( talk) 08:29, 1 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)
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)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 |
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)
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:
In equilibrium, , , and , 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)
Rankine the pioneer of Mohr's stress circle? See Talk:Christian_Otto_Mohr#Rankine —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)
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)
Cauchy stress tensor for a viscous fluid |
---|
For viscous fluids the Cauchy stress tensor is defined as:
If the fluid is incompressible it follows that: If the fluid is compressible the assumption above is true, if the viscosity of compression vanishes: |
In the section derivation of principal stresses and stress invariants, is included in the characteristic equation with a positive sign. In Invariants of the stress deviator tensor, is included with a negative sign. This introduced an sign error in the expression for , which I corrected. For consistency, I feel that either the sign of or the sign of must be corrected. Yet, I feel reluctant to choose, since seems better without a minus, and too. Any input how this is in the textbooks? Martenjan ( talk) 10:22, 10 June 2008 (UTC)
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 [1]
Falk H. Koenemann
Aachen, Germany, 1 July 2008 —Preceding unsigned comment added by 217.250.179.59 ( talk) 08:29, 1 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)
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)
![]() | This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |