Talk:Contact mechanics

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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 (talkcontribs) 21:24, 8 September 2015 (UTC)