Talk:Contact mechanics: Difference between revisions
←Created page with 'I am wondering about the coordinate system in the Chapter "Loading on a Half-Plane". The coordinate z seems to be the direction normal to the surface (as also in th…' |
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{{WikiProject Physics|importance=High}} |
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== Too technical == |
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In my opinion the page is too technical, I added the technical template to the top of the page. |
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* The introduction is quite long, and already contains a lot of details. It might try to focus more on the essential ideas. |
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* The distinction between non-adhesive and adhesive contact might be introduced separately. |
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* Classical solutions could be an entire top-level section by itself. |
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* Analytical and numerical solution techniques could also be discussed separately. |
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* The purposes, strengths and weaknesses of the various adhesive contact theories could be introduced in more general terms, before the theories are discussed in detail. |
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[[User:Edwinv1970|Edwinv1970]] ([[User talk:Edwinv1970|talk]]) 09:20, 22 March 2011 (UTC) |
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== Line contact on a plane section == |
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I think the integral formulas given in line contact on a plane section are incorrect. The dimensions don't match. Can someone confirm? I was reading contact mechanics by johnson and the formulas look a little different there. [[User:Blooneel]] 24 June, 2010 |
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: Johnson's book assumes a left-handed coordinate system with the <math>z</math>-axis pointing down. The results given in this article assume that the <math>z</math>-axis points up. That leads to the different relations. See Barber's book on elasticity for the form given in this article. [[User:Bbanerje|Bbanerje]] ([[User talk:Bbanerje|talk]]) 03:45, 25 June 2010 (UTC) |
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::There seems to be an inconsitency between the (x,y) directions shown on the diagram and the use of z in the formulas. It needs to be clear what the directions are.[[User:Eregli bob|Eregli bob]] ([[User talk:Eregli bob|talk]]) 04:37, 30 August 2010 (UTC) |
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== Coordinate system == |
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I am wondering about the coordinate system in the Chapter "Loading on a Half-Plane". |
I am wondering about the coordinate system in the Chapter "Loading on a Half-Plane". |
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The coordinate z seems to be the direction normal to the surface (as also in the chapter before). |
The coordinate z seems to be the direction normal to the surface (as also in the chapter before). |
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For the same reason y should also be replaced by z in the sentence following the formulae : ''"for some point, (x,y), in the half-plane. "'' |
For the same reason y should also be replaced by z in the sentence following the formulae : ''"for some point, (x,y), in the half-plane. "'' |
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[[User:B Sadden|B Sadden]] ([[User talk:B Sadden|talk]]) 14:57, 30 May 2009 (UTC) |
[[User:B Sadden|B Sadden]] ([[User talk:B Sadden|talk]]) 14:57, 30 May 2009 (UTC) |
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== Error in sphere on half-space? == |
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I may be wrong, but I believe that there is a mistake here; the radius of the contact area is quoted as being sqrt (R * d), I think (from a bit of cursory mathematics) that is should actually be sqrt (2 * R * d), can anyone confirm this, I may be mistaken so I won't change this unless someone else confirms... |
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thanks, |
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Mike Strickland <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/152.78.178.59|152.78.178.59]] ([[User talk:152.78.178.59|talk]]) 16:59, 27 July 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--> |
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: The Hertz solution for the elastic displacements in the region of contact is |
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::<math> |
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u_1 + u_2 = \delta - A x^2 - B y^2 |
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</math> |
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:where <math>x,y</math> are coordinates of the contact surfaces projected on to the <math>x-y</math>-plane. For a circular contact area with radius <math>a</math>, |
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::<math> |
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A = B = \tfrac{1}{2}\left(\tfrac{1}{R_1} + \tfrac{1}{R_2}\right) |
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</math> |
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:If the second surface is a half-plane, <math>R_2 \rightarrow \infty</math> and we have |
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::<math> |
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A = B = \tfrac{1}{2 R_1} = \tfrac{1}{2R} |
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</math> |
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:Therefore, |
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::<math> |
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u_1 + u_2 = \delta - \tfrac{1}{2 R} r^2 |
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</math> |
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:where <math>r</math> is the radial distance to a point in the contact region from the center of contact. The Hertzian pressure distribution |
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::<math> |
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p = p_0 \left[ 1 - (\tfrac{r}{a})^2\right]^{1/2} |
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</math> |
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:leads to the displacement field |
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::<math> |
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u_1 = \left(\tfrac{1-\nu_1^2}{E_1}\right)\left(\tfrac{\pi p_0}{4a}\right)\left(2 a^2 - r^2\right) ~;~~ |
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u_2 = \left(\tfrac{1-\nu_2^2}{E_2}\right)\left(\tfrac{\pi p_0}{4a}\right)\left(2 a^2 - r^2\right) |
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</math> |
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:Plugging these into the relation for <math>u_1+u_2</math> gives |
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::<math> |
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\left(\tfrac{1}{E^*}\right)\left(\tfrac{\pi p_0}{4a}\right)\left(2 a^2 - r^2\right) = \delta - \tfrac{1}{2 R} r^2 |
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</math> |
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: At <math>r = 0</math> |
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::<math> |
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\delta = \tfrac{\pi p_0 a}{2 E^*} |
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</math> |
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: For <math>r = a</math> plugging in the expression for <math>\delta</math> gives |
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::<math> |
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a = \tfrac{\pi p_0 R}{2 E^*} |
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</math> |
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: Therefore |
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::<math> |
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\tfrac{a}{\delta} = \tfrac{R}{a} \Leftrightarrow a^2 = R\delta \implies a = \sqrt{R\delta} \quad \square |
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</math> |
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:[[User:Bbanerje|Bbanerje]] ([[User talk:Bbanerje|talk]]) 00:00, 28 July 2010 (UTC) |
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== Error in rigid conical indenter and an elastic half-space? == |
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The German Wikipedia has a and d switched in this formula: <math> a=\frac{2}{\pi}d\tan\theta </math>. And indeed, if one lets theta get towards 90° then only the switched version makes sense (radius gets towards 0). [[User:Peterthewall|Peterthewall]] ([[User talk:Peterthewall|talk]]) 17:55, 28 February 2013 (UTC) |
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== Hertz Model for Sphere on Plane is Parabola Approximation == |
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I would like to point out that the sphere on a plane section is for a parabola. Many make the no-slip assumption for a spherical indenter so they can approximate the sphere for a parabola. JPK instruments has a decent read on this in terms of AFM on cells: |
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www.jpk.com/jpk-app-elastic-modulus4.download.5fb2f841667674176fd945e65f073bad |
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They have the sphere on |
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force=E/(1-v^2)*(((a^2+R^2)/2)*ln((R+a)/(R-a))-a R) |
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where a=(R*d)^1/2 (I think) |
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E is Young's Modulus |
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v is Poisson's Ratio |
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d is indentation of plane |
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I think it would be good to at least state somewhere that it is an approximation. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:EvanN90|EvanN90]] ([[User talk:EvanN90|talk]] • [[Special:Contributions/EvanN90|contribs]]) 21:24, 8 September 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--> |
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== dxe == |
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The description for "Adhesive surface forces" is "dxe" which, according to [[Dxe|this article on wikipedia]] is related to animal rights. |
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This should be corrected. |
Latest revision as of 06:52, 12 January 2024
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Too technical
[edit]In my opinion the page is too technical, I added the technical template to the top of the page.
- The introduction is quite long, and already contains a lot of details. It might try to focus more on the essential ideas.
- The distinction between non-adhesive and adhesive contact might be introduced separately.
- Classical solutions could be an entire top-level section by itself.
- Analytical and numerical solution techniques could also be discussed separately.
- The purposes, strengths and weaknesses of the various adhesive contact theories could be introduced in more general terms, before the theories are discussed in detail.
Edwinv1970 (talk) 09:20, 22 March 2011 (UTC)
Line contact on a plane section
[edit]I think the integral formulas given in line contact on a plane section are incorrect. The dimensions don't match. Can someone confirm? I was reading contact mechanics by johnson and the formulas look a little different there. User:Blooneel 24 June, 2010
- Johnson's book assumes a left-handed coordinate system with the -axis pointing down. The results given in this article assume that the -axis points up. That leads to the different relations. See Barber's book on elasticity for the form given in this article. Bbanerje (talk) 03:45, 25 June 2010 (UTC)
- There seems to be an inconsitency between the (x,y) directions shown on the diagram and the use of z in the formulas. It needs to be clear what the directions are.Eregli bob (talk) 04:37, 30 August 2010 (UTC)
Coordinate system
[edit]I am wondering about the coordinate system in the Chapter "Loading on a Half-Plane". The coordinate z seems to be the direction normal to the surface (as also in the chapter before). Does this chapter present a 3D solution for a point load given in the plane y=0? Than the term "Loading on a Half space" would be better. Or is a plane strain (plane stress) solution presented?
In any case: the appearance of the y coordinate in the figure ( (x,y) and σy ) is misleading. For the same reason y should also be replaced by z in the sentence following the formulae : "for some point, (x,y), in the half-plane. " B Sadden (talk) 14:57, 30 May 2009 (UTC)
Error in sphere on half-space?
[edit]I may be wrong, but I believe that there is a mistake here; the radius of the contact area is quoted as being sqrt (R * d), I think (from a bit of cursory mathematics) that is should actually be sqrt (2 * R * d), can anyone confirm this, I may be mistaken so I won't change this unless someone else confirms...
thanks,
Mike Strickland —Preceding unsigned comment added by 152.78.178.59 (talk) 16:59, 27 July 2010 (UTC)
- The Hertz solution for the elastic displacements in the region of contact is
- where are coordinates of the contact surfaces projected on to the -plane. For a circular contact area with radius ,
- If the second surface is a half-plane, and we have
- Therefore,
- where is the radial distance to a point in the contact region from the center of contact. The Hertzian pressure distribution
- leads to the displacement field
- Plugging these into the relation for gives
- At
- For plugging in the expression for gives
- Therefore
- Bbanerje (talk) 00:00, 28 July 2010 (UTC)
Error in rigid conical indenter and an elastic half-space?
[edit]The German Wikipedia has a and d switched in this formula: . And indeed, if one lets theta get towards 90° then only the switched version makes sense (radius gets towards 0). Peterthewall (talk) 17:55, 28 February 2013 (UTC)
Hertz Model for Sphere on Plane is Parabola Approximation
[edit]I would like to point out that the sphere on a plane section is for a parabola. Many make the no-slip assumption for a spherical indenter so they can approximate the sphere for a parabola. JPK instruments has a decent read on this in terms of AFM on cells: www.jpk.com/jpk-app-elastic-modulus4.download.5fb2f841667674176fd945e65f073bad
They have the sphere on
force=E/(1-v^2)*(((a^2+R^2)/2)*ln((R+a)/(R-a))-a R)
where a=(R*d)^1/2 (I think) E is Young's Modulus v is Poisson's Ratio d is indentation of plane I think it would be good to at least state somewhere that it is an approximation. — Preceding unsigned comment added by EvanN90 (talk • contribs) 21:24, 8 September 2015 (UTC)
dxe
[edit]The description for "Adhesive surface forces" is "dxe" which, according to this article on wikipedia is related to animal rights. This should be corrected.