Why (and How) Does Paper Crumple?

It turns out that thin, bendy sheets like paper crumple in predictable ways -- and we can learn a lot from the process. Learn more about the protective physics of crumpling in this episode of BrainStuff, based on this article: https://science.howstuffworks.com/crumple-theory.htm

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Episode Transcript

Speaker 1 (00:01):
Welcome to Brainstuff, a production of iHeartRadio, Hey brain Stuff,
lor and Vogel Bomb. Here pop quiz in case you
didn't read this episode title, But what do a sheet
of paper being crushed into a ball and tossed into
a waste basket, The front end of a car forming
in a crash, and the Earth's crust gradually forming mountains

(00:23):
over millions of years all having common They're all undergoing
a physical process called crumpling, which occurs when a relatively
thin sheet of material, one with a thickness that's far
less than its length or its width, has to fit
into a smaller area. And while it's easy to imagine

(00:43):
crumpling as mere disarray, scientists who have studied crumpling have
discovered that it's anything but The crumpling turns out to
be a predictable, reproducible process governed by math. A recent
breakthrough at our understanding was described in a paper published
in Nature Communecations in twenty twenty one, in which researchers
describe a physical model for what happens when thin sheets

(01:06):
are crumpled, then unfolded, and recrumpled. For the article, this
episode is based on how Stuffwork. Spoke via email with
Christopher Ryecroft, the paper's corresponding author, who's Associate professor in
the John L. Paulson School of Engineering and Applied Sciences
at Harvard University. He said, from an early age, everyone

(01:26):
is familiar with crumpling a sheet of paper into a ball,
unfolding it, and looking at the complicated network of creases
that form on the surface. This seems like a random,
disordered process, and you might think it's difficult to predict
anything at all about what happens. Suppose now you repeat
this process, crumple the paper again and unfold it. You

(01:46):
will get more creases. However, you won't double the number
because the existing creases already weakened the sheet and allow
it fold more easily the second time around. That idea
formed the base of experiments performed several years ago by
another of the papers authors, former Harvard physicist Schumel M.
Rubinstein and his students. Rubinstein and his team crumpled a

(02:10):
thin sheet repeatedly and measured the total length of the
creases on that sheet, which they called mileage. Ryecroft said
they found that the growth of mileage is strikingly reproducible,
and each time the accrual of new mileage would get
a little less because the sheet is progressively getting weaker.

(02:32):
That finding stumped the physics community, hence the more recent research.
A Ryecraft said, we found that the way to make
progress was not to focus on the creases themselves, but
rather to look at the undamaged facets that are outlined
by the creases. Houstuffworks also spoke by email with the
more recent papers lead author Yovanna A. And Jyevic, a

(02:54):
Harvard doctoral candidate. She said, in the experiment, thin sheets
of mylar, a thin film that crumples similarly to paper,
were systematically crumpled several times, developing some new creases with
each repetition. In between crumples, the sheets were carefully flattened
and their height profiles scanned using an instrument called a profilometer.

(03:15):
The profilometer makes measurements of the height map across the
surface of the sheet, which allows us to calculate and
visualize the locations of creases as an image. Because creasing
can be messy and irregular, it generates noisy data that
can be tough for computer automation to make sense of.
To get around that problem, Andreavic hand traced the crease

(03:38):
patterns on twenty four sheets using a tablet, PC, Adobe illustrator,
and photoshop. That meant hand recording twenty one thousand, one
hundred and ten facets in total. Thanks to Andreevic's labors
and image analysis, the researchers could analyze how many facets
of different sizes were created as the crumpling progress. They

(04:01):
found that the size distributions could be explained by fragmentation theory,
which looks at how objects are ranging from rocks and
glass shards to volcanic debris and icebergs, break up into
small pieces over time. Ryecroft said that same theory can
accurately explain how the facets of the crumpled sheet break

(04:22):
up over time as more creases form. We can also
use it to estimate how the sheet becomes weaker after crumpling,
and thereby explain how the accumulation of mileage slows down.
This allows us to explain the mileage results and the
logarithmic scaling that we're seen in the twenty eighteen study.
We believe that the fragmentation theory provides a perspective on

(04:44):
the problem and is especially useful to model the accumulation
of damage over time. But okay, let's back up a second.
Why do some objects crumple in the first place, as
opposed to simply breaking apart into a lot of little pieces.
It has to do with how flexible a material is.
Things like paper and milar are very easy to bend,

(05:06):
so they're not very likely to break when you apply pressure,
But things like rock and glass don't bend easily, so
force can make them break. Andreevic explained a crumpling and
breaking are quite distinct processes, but there are some similarities
we can recognize. For example, both crumpling and breaking are
mechanisms of relieving stress and a material. The idea of

(05:31):
creases protecting other regions of a sheet from damage refers
to damage being localized to very narrow ridges in the sheet.
In fact, the sharp vertices and ridges that form when
a sheet crumples are localized regions of stretching in the sheet,
which are energetically unfavorable. As a result, the sheet minimizes

(05:51):
those costly deformations by confining them to very narrow regions,
protecting the rest of the sheet as much as possible. Furthermore,
your research showed that the more a sheet is crumpled,
the more it resists further compression, so that increasingly more
force is required to compress it. The ridges seem to

(06:11):
line up and act as pillars that increase the strength
of the crumpled sheet. There's still a lot that needs
to be learned about crumpling. For example, it's not clear
whether different types of crumpling of using a cylindrical piston,
for example, rather than your hand it results in a
different type of crease pattern. A Ryecroft said, we'd like

(06:34):
to understand how general our findings are. In addition, researchers
want to learn more about the actual mechanisms of how
creases form and to be able to take measurements during
the process rather than just examining the end result. A
Ryecraft explained. To get around this, we're currently developing a
three D mechanical simulation of a crumpled sheet, which can

(06:56):
allow us to observe the entire process already our simulation
and can create creased patterns that are similar to those
seen in the experiment, and it provides us with a
much more detailed view of the crumpling process. But all right,
why does crumple theory matter? Gaining insights about crumpling is

(07:16):
potentially really important to all sorts of things in our
modern world. Ryecroft said, if you're using a material in
any structural capacity, it is critical to understand its failure properties.
In many situations, it's important to understand how materials will
behave under repeated loading. For example, aircraft wings vibrate up

(07:37):
and down many thousands of times over their lifetime. Our
study of repeated crumpling can be viewed as a model
system for how materials are damaged under repeated load. We
expect that some core elements of our theory about how
materials are weakened by fractures increases over time may have
analogs in other material types, and sometimes crumpling might actually

(08:02):
be utilized technologically. For example, crumpled graphene sheets have been
suggested as a possibility for making high performance electrodes for batteries. Really,
crumple theory provides insights into all sorts of phenomena, from
how insects wings unfold to how DNA packs into a
cell nucleus, all of which could be used to build

(08:24):
more efficient machines. In the future. Today's episode is based
on the article crumple theory. We can learn a lot
from how paper crumples on how stuffworks dot com, written
by Patrick J. Higer. Brain Stuff is production of by
Heart Radio in partnership with how stuffworks dot Com and
is produced by Tyler Klang. For more podcasts on iHeartRadio,

(08:46):
visit the iHeartRadio app, Apple Podcasts, or wherever you listen
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