Explain 'wallpaper problem'

Are you frustrated when the tape doesn't stick off the roll in a straight horizontal line? Are you angry when you can't tear the wallpaper neatly? A new study has discovered why efforts to do that can worsen the initial state.

Pedro Reis, adjunct professor of applied mathematics at MIT.(Photo: Donna Coveney)

Wallpaper cannot be torn as you like - because it only follows the laws of physics . This conclusion was made by a team of researchers from the National Center for Scientific Research in Paris (CNRS) - French Republic, University of Santiago - Chile, and Massachusetts Institute of Technology (MIT).

The article, published on March 30, on the Natural Material website, sheds light on the strange phenomenon many people have encountered, researchers have called it a "post-wall paper".

'You want to redecorate your bedroom, so you need to tear off the old wallpaper. You want all pieces of paper flap to tear in a straight line down the floor, but they tear in a triangle so you have to tear it up and down again, 'said Pedro Reis, one of the authors of the paper. The newspaper and currently an assistant professor of applied mathematics at MIT.

The type of double tearing in two diagonal lines facing each other and meeting at one point is extremely sustainable. It appears not only in wallpaper but also in adhesives such as sticky tape as well as non-stick plastic pieces like plastic covering in compact discs. Even tearing patterns with characteristic triangular shapes also appear in some types of fruits when peeled: like tomatoes or grapes.

'This happens to everyone and annoys them,' Reis said. Other collaborators include Enrique Cerda and Eugenio Hamm of Santiago University, Benoit Roman of CNRS and Michael LeBlanc of the University of Chicago.

The researchers found triangular torn pieces that are everywhere, caused by the interaction of three inherent properties of matter: elasticity (hard), adhesion energy (paste how to adhere to a sustainable surface) and energy to break (how difficult it is to tear).

The tape when torn off the tape will form a triangle and end at one point.(Photo: Donna Coveney)

Based on these 3 properties, researchers have developed a formula that can predict the angle of a formed triangle. They also calculate very precisely the cases where the triangular torn piece will appear. Because when the wallpaper strip was jerked, energy accumulated in the form of buckles. Paper strips can release energy in two directions: resist the process of separation from the surface & become narrower, that is both directions occur with the piece of wallpaper.

In industrial applications, material designers can use this method to calculate one of the three key properties when knowing the other two properties. It can also be particularly useful in micro-technology industries, such as the manufacture of elastic, electric wires, as the description of the properties of small-diameter materials is difficult. towel.

Reis - currently working at the Applied Mathematics Laboratory (MIT) - and collaborators from CNRS and University of Santiago had the idea of ​​pursuing research to predict dense patterns in the a piece of plastic like a plastic layer covering the surface of the CD.

Researchers try to control the patterns that occur in practice according to the same process in the laboratory & have received the same results."This kind of tearing is really powerful, so there must be a fundamental principle that controls the process of spawning and spreading torn lines," Reis said.

The process of forming triangles by tearing the surface of a piece of paper (left to right) (Video: Pedro Reis, MIT)

However, the shapes formed from the tearing of non-sticky plastic pieces are difficult to study because they do not produce torn pieces with perfect triangles. Because there is no involvement of adhesion force, it is very complicated to consider the phenomena that occur in a physical perspective. Instead of this research direction, scientists have turned their attention to sticky plastics, the material that when torn will produce perfect triangles.

Triangles can be seen in the work of the French artist, Jacques Villeglé. His work includes posters from the streets of Paris and many other cities in France, which have been partially perfected to the research that scientists have carried out to tear pieces of paper. One of those posters can convey the characteristics of Natural Materials, which helps illustrate the research paper.

The pieces from the posters, adhesive tapes and tomato peels seem to be eccentric topics for physicists and applied maths, but are very normal for Reis and colleagues, sympathetic seekers. inspired by everyday phenomena.

Researching real-world applications is not just for fun but 'we can find things that are really useful for the industry and better understand the world around us. It's also a good way to motivate students to be interested in science, ' Reis said.