# Folding a paper

I have always amused at the how things are able to retain their shape

For example

A paper that has been rolled up for a long time tries to retain its form when straightened

A paper rolled/folded along one line in a direction resists folding or rolling in the opposite direction

A crumpled paper is difficult to straighten

A bent rod straightens itself

I believe all of it is somehow related to elasticity

And again I fail to imagine why all of them should attain a new shape if sufficient force is applied I dont understand why elasticity fails to restore their shape after if they are sufficiently stretched even after the stretching force stops acting

Thank you.

If I understood the question correctly it can be rephrased as "Why do materials permanently attain a new shape when an applied force is above the yield strength?". The wording "yield strength" in material science is the point where a material start to deform plastically instead of elastically. Why does this happen? Let's first think about why do materials elastically deform? When a force is applied and a material starts to deform then the bonds between either atoms or molecules start to expand and if you apply a force small enough so to not break the bonds then they will go back to their original distance due to attraction of electromagnetic force. However if one apply a sufficiently large enough force then some or all of the bonds start to break or it can break and create a new bonds at a different place. If this is the case then the material has plastically deformed.

• Is the tearing of the paper along the fold line after a long time related to the same thing? Commented Aug 17, 2021 at 12:42
• I know this question is not related but Commented Aug 17, 2021 at 12:42
• I do not understand your question. Can you try to rephrase it?
– ludz
Commented Aug 17, 2021 at 17:59
• Sorry, My bad When we keep a paper folded for a long time (say inside a book), it begins to tear along that line. So is it somehow related to this Commented Aug 17, 2021 at 20:11
• My knowledge about how specifically paper tear works with its fibers is small. I would guess that the fibers get ripped (breaking bonds) when you fold the paper. And if you continue to fold back and forth then eventually you have ripped all the fibers and it tears off. What I can tell you with more certainty is that it's about breaking and perhaps also creating new bonds that takes place.
– ludz
Commented Aug 18, 2021 at 6:17

You have a limit of elasticity in every material. Best example is a spring, you can extend it quiet a bit an if you release it goes back to its initial length. but if you extend it more and more the elasticity steps and it just deforms without ever going back.paper has a very, very low limit of elasticity, so it stays in the crumpled state.