# Deformation without stress?

Elastic bodies are submit to stress whenever they are deformed. This eventually lead to break them.

However, let's consider a rope. If i stretch it, it is submit to stress and will eventually reach the break point. But I can "bend" it as much as I want --> it will deform (it is not straight anymore), however it doesn't seem to be subject to stress (in fact, it will not attempt to return to original straight configuration).

Why is that? Does it depend on the material? Can some material be deformed without being subjected to stress?

• Rigid bodies don't deform, by definition. Commented Aug 31, 2019 at 16:31
• @nicoguaro I know, but I am not talking about rigid bodies Commented Aug 31, 2019 at 17:39
• Your first sentence reads "Rigid bodies are submit [...]". Commented Aug 31, 2019 at 17:44
• Yes you are right, I used the wrong term. Edited with "elastic". However, the "rope example" does not fit into the elastic category (it does not recover his initial position after a bending). So , which category does it fit into? Commented Aug 31, 2019 at 21:55
• I mean you have to appreciate that a rope is quite a complex structure from a basic physics point of view. It is not homogeneous, has structure (it consists of fibres). So when you try to longitudinally compress a rope, even relative distances between fibers can change. You cannot directly apply elasticity theory to a rope, simply because of this internal structure. If you want to dig deeper you might want to model the "internal dynamics" of a loose rope, but it might get quite complex and there will probably pop up many "free parameters" unique to different kinds of ropes... Commented Sep 1, 2019 at 6:58

## 1 Answer

An ideal rope or string can only experience tension and not compression. That is how they are typically treated in statics and mechanics of materials problems.

A real rope will resist compression and bending, that is, will experience stress in response to force that can theoretically lead to deformation. When such a rope is "bent" it will experience tensile and compressive stresses at the extreme fibers (outside and inside surfaces of the bend). But I think it is highly unlikely (though perhaps not impossible) that such stresses will be great enough to cause a structural failure of a rope.

Perhaps someone else is aware of examples of such failures.

Hope this helps.

• The bending radius can't get much less than the thickness of the rope (because of mechanical interference of the rope pieces on either side of the bend). This limits the level of strain that can established in the outer fibers. Commented Sep 2, 2019 at 0:47