# Scientists shed light on 'the wallpaper problem'

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London, March 31 : You must have wondered several times as to why a sheet of wallpaper refuses to tear neatly off the wall, or why people often find it difficult to peel the tape off the roll in a straight line. Well, an international team of researchers perhaps knows the answer.

The research team - comprising researchers from the Centre National de la Recherche Scientifique (CNRS) in Paris, the Universidad de Santiago, Chile, and MIT - says that the phenomenon "the wallpaper problem" is based on the laws of physics.

"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," Nature Materials quoted Pedro Reis, an applied mathematics instructor at MIT, as saying.

The researchers say that the pattern where two cracks propagate toward each other to meet at a point is extremely robust, and it applies not only to wallpaper, but also to other adhesives like tape, as well as non-adhesive plastic sheets like the shrink-wrap that envelops compact discs.

The researchers say that this phenomenon even extends to fruit, as the skin on a tomato or a grape typically forms a triangle when peeled off.

According to them, the 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 rip).

Based on the three properties, the research team developed a formulation that predicts the angle of the triangle formed. Their work proved helpful in understanding how the triangular tears arise.

The researchers say that 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.

"This shape is really robust, so there must be something fundamental going on that gives rise to these shapes," Reis said, who now works in MIT's Applied Mathematics Laboratory.

However, the researchers found it difficult to study the shapes formed by tearing non-adhesive sheets because they were not perfect triangles, and without adhesion, the physics of the problem is more complicated.

Torn posters, tape and tomato skins may seem like strange research topics for physicists and applied mathematicians, but Reis says: "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."

ANI