Talk:Strain (mechanics)

This page is the counterpart to stress (mechanics) and needs to explain the basic physics for those who are not specialists in mechanical engineering. A page on deformation is not appropriate for this purpose because most people will not be familiar with the use of that word.Trojancowboy (talk) 19:48, 6 May 2009 (UTC)

There is no reason to have two articles talking about the same concept. Deformation is the phenomenon, and strain is just a way to represent it. Strain is already explained in the Deformation (mechanics) page. Sorry for the roll back. sanpaz (talk) 21:30, 6 May 2009 (UTC)

Stress and Strain

Stress and strain go together. Deformation is the movement which is referred to as strain see Stress–strain curve. I have yet to see a deformation curve. This page needs to instruct someone in the basics, not be full of obscure mathematics. Whatever needs to be moved from other pages needs to go here. —Preceding unsigned comment added by Trojancowboy (talk • contribs) 22:01, 6 May 2009 (UTC)

I agree with you in that the Deformation article may need to be improved for non-mechanic people to understand. However, that is no reason for creating another article. sanpaz (talk) 22:08, 6 May 2009 (UTC)

I question this article's distinction between 3 types of strain theory

UPDATE: I reverted the comment that I placed (as a footnote) in the article. I still intuitively believe that the division into three types of strain theories is not important. But Wikipedia has never had a rule against stating what is not important! So read this comment at your own risk. I would delete it, but that would be slightly dishonest. And maybe I am right.--Guy vandegrift (talk) 23:03, 29 January 2024 (UTC)

Figure 3

Hi. I have a Ph.D. in physics, lots of teaching experience, but am a novice to deformation theory. In my effort to understand this theory (I'm retired with little else to do), I wrote Wikiversity:Strain for scientists and engineers. Here is an excerpt:<s

Three types deformation theories are listed (in Wikipedia's Strain (mechanics)):

1. Finite strain theory deals with deformations in which both rotations and strains are arbitrarily large.
2. Infinitesimal strain theory is valid when both strains and rotations are both small. In this case, the undeformed and deformed configurations of the body can be assumed identical.
3. Large-displacement or large-rotation theory assumes small strains but large rotations and/or displacements.

Figure 4. Use Eulerian perspective for fluids, but Lagrangian for deformation of solids.

Figure 5. Deformation of a square to a trapezoid requires a tensor field

WARNING: I question the distinction between #2 and #3 on this list, because I don't see any reason why the rotations and displacements must be small in the linearized theory. Looking at figures 3 and 4, it seems likely that infinitesimal strain theory applies when the rotations are large.

My intuition is is that it is important to distinguish between two types of rotation in infinitesimal strain theory. The large scale rotation and displacement in figure 4 is allowed and does not preclude the use of infinitesimal strain theory. On the other hand, in figure 3, the splitting of ${\underline {\nabla }}\,{\underline {u}}$ into a rotation and a deformation (i.e. symmetric and antisymmetric parts), is a different matter. It must be small, since the "rotation" is only a linear approximation to a true rotation, as can be seen in the approximations $\cos \theta \approx 1$ and $\sin \theta \approx \theta .$ The cosine approximation suggests that there is a small (second order) expansion in this so-called "rotation". That expansion releases or absorbs energy, and is ignored by the symmetrical strain tensor. Also, figure 5 shows how an arch can be constructed using infinitesimal rotations; the trick is to not excessively bend each square into a trapezoid, and allow the Lagrangian coordinate transformation to do the heavy lifting when it comes to large-scale rotations and deformations.

I'm not saying that the list of three types of deformation theory is wrong, but it is misleading because types #2 and #3 involve almost the same mathematical structure. If I am right about this, let me know, and I will make the edits. Guy vandegrift (talk) 10:21, 20 January 2024 (UTC)