Frustrated by tape that won't peel off the roll in a straight
line? Angry at wallpaper that refuses to tear neatly off the wall?
A new study reveals why these efforts can be so aggravating.
Wallpaper is not out to foil you-it's just obeying the laws of physics,
according to a team of researchers from the Centre National de la
Recherche Scientifique (CNRS) in Paris, the Universidad de Santiago,
Chile, and MIT.
The report, published in the March 30 online issue of Nature
Materials, sheds light on a phenomenon many people have experienced,
which the researchers dubbed “the wallpaper
“You want to redecorate your bedroom, so you yank
down the wallpaper. You wish that the flap would tear all the way down
to the floor, but it comes together in a triangle and you have to start
all over again,” said Pedro Reis, one of the authors of the
paper and an applied mathematics instructor at MIT.
This pattern, where two cracks propagate toward each other and
meet at a point, is extremely robust. It applies not only to wallpaper
but other adhesives such as tape, as well as nonadhesive plastic sheets
such as the shrink-wrap that envelops compact discs. It even extends to
fruit: The skin on a tomato or a grape typically forms a triangle when
“This has happened to everyone. it's
frustrating,” said Reis, who collaborated with Enrique Cerda
and Eugenio Hamm of the Universidad de Santiago, Benoit Roman of CNRS
and Michael LeBlanc of the University of Chicago.
The team found that those ubiquitous triangular tears arise
from interactions between three inherent properties of adhesive
materials: elasticity (stiffness), adhesive energy (how strongly the
adhesive sticks to a surface) and fracture energy (how tough it is to
The researchers developed a formulation that predicts the
angle of the triangle formed, based on those three properties.
They also figured out just how those triangular tears arise.
As the strip is pulled, energy builds up in the fold that forms where
the tape is peeling from the surface. The tape can release that energy
in two ways: by unpeeling from its surface and by becoming narrower,
both of which it does.
In a possible industrial application, materials engineers
could use this method to calculate one of the three key properties, if
the other two are known. This could be particularly useful in
microtechnologies, such as stretchable electronics, where the
characterization of thin material properties is very difficult.
Reis, who now works in MIT's Applied Mathematics Laboratory,
and his collaborators at CNRS and Universidad de Santiago got the idea
for the project after noticing consistent tearing patterns in plastic
sheets such as the plastic wrapping of CDs.
The researchers tried controlled experimental versions of the
same process in their lab and got the same results. “This
shape is really robust, so there must be something fundamental going on
that gives rise to these shapes,” Reis said.
However, the shapes formed by tearing nonadhesive sheets
proved difficult to study because they are not perfect triangles, and
without adhesion, the physics of the problem is more complicated.
Instead, the researchers turned their attention to adhesives, which do
form perfect triangles when torn.
The triangular shapes can also be seen in the work of French
artist Jacques Villeglé. His art consists of posters taken
from the streets of Paris and other French cities, complete with the
same sort of rips that the researchers studied. One of the posters may
be featured on the cover of Nature Materials to illustrate the team's
Torn posters, tape and tomato skins may seem like strange
research topics for physicists and applied mathematicians, but it's
perfectly normal to Reis and his colleagues, who draw inspiration from
an array of everyday objects.
Such real-world applications are not only fun to study, but
“we can really learn things that will be useful for industry
and help us understand the everyday world around us. It is also a great
way to motivate students to be interested in science,” Reis