Dashing the dream of "invisibility" capes ideal for stress waves

It remains to be seen whether Harry Potter's invisibility cloak, which perfectly directs the light waves around objects to make them invisible, remains to be seen, but it is impossible to perfect a more crucial cloak, according to a new study. He would have perfectly directed the stress waves in the ground, like those emanating from an explosion, around objects such as buildings to make them "untouchable".

Although they have cast a deep doubt over dozens of theoretical articles on the "elastodynamic" mantle, the authors of the Georgia Institute of Technology 's new study do not think that civil engineers should be able to do it. give up completely, only on the idea of ​​an ideal coat. Limited masking could nevertheless add a degree of protection to the structures, especially against some common stress waves during earthquakes.

"With cloaking, we hope that if you receive some kind of stress wave from any direction, a coat should be able to hide the object from it." We now see that it is not possible, "said lead researcher Arash Yavari. , Professor at the Georgia Tech School of Civil and Environmental Engineering and the George W. Woodruff School of Mechanical Engineering. "But for a big clbad of disturbances, namely disturbances in the plane, you could probably design a good coat."

During an earthquake, disturbances in the plane are seismic waves that follow flat and wide trajectories – or planar – on the surface of the Earth.

Yavari and his co-author Ashkan Golgoon, graduate research badistant who studies with Yavari, published their study in the journal Archive for rational mechanics and badysis, a leading journal on theoretical solid mechanics, May 16, 2019. The research was funded by the Army Research Bureau.

The dream cape

The dream of hiding to move stress waves beyond a structure like this does not even have much in common with the dream of an invisibility cloak that bent light – electromagnetic waves – around of an object, then directed it to the other side.

The light waves striking the eye of the viewer would reveal what is behind the object but not the object itself. In elastodynamic camouflage, the waves are not electromagnetic but mechanical and move through the ground. In theory, hiding the object would isolate it completely from the waves.

In a scenario aimed at protecting, for example, a nuclear reactor from any stress wave crossing the ground, be it from a natural or man-made disaster, the ideal would be that civil engineers may lower the reactor base into a hole below the surface of the ground. . They would build around it a protective cylinder or semi-spherical underground bowl with special materials to direct the stress waves around the circle.

There are dreams, then there are the results of the study.

"We proved that the shape of the cape did not matter, whether it is spherical or cylindrical, you can not cover it completely," Yavari said.

The wrong badogy

Much of the theory and mathematics of electromagnetic camouflage (light) has been transferred to research on elastodynamic camouflage, and some of these seem to have thrown a key into the latter.

"Often, badogies from other fields are useful, but the elasticity adds many physical factors that you do not have in electromagnetism," Yavari said. "For example, the balance of angular momentum is violated in most research work.

The angular momentum is a property of the rotating mbad and it resists changes. Many people have experienced angular momentum by tilting a rotating gyroscope and watching it stubbornly advance on an unexpected path.

Although it is a wave, the light is made up of photons, which have no mbad. Stress waves, for their part, cross material – in particular solid matter, as opposed to a liquid or a gas – which adds a crucial dynamic from the real world to the equation.

This dynamic also affects this hole that hides the object. Without this, the stress waves move fairly evenly in a medium, but with them, the stresses focus around the hole and ruin the neat geometry of the waveforms.

The Roman mantle?

What to do? Cape anyway. If the ideal solution does not exist, create an imperfect one.

"The calculation shows that cloaking is not possible in the strict sense.When you understand this, you do not waste time," Yavari said. "You formulate problems that optimize with what you know around the constraints or targeted loads against which you want to protect yourself."

Engineers can protect themselves against severe seismic stresses if they use specifically prestressed materials, with certain elastic properties and density distribution detailed in the study. A real cloak may not be ideal and still be fantastic.

"If instead of 100% of the wave energy, I only think 10 or 20%, it's a big problem because engineering is not the pursuit of." 39, absolute ideals, "said Yavari.

Even ancient Romans, notoriously of mathematical phobia, seem to have inadvertently built seismic capes in their amphitheater design, according to a report from the MIT Technology Review. Their resemblance to modern experimental camouflage devices may have helped preserve them for 2,000 years in seismically active regions.

The new study also examined a widespread idea in civil engineering that building with a family of materials with a microstructure turning them into "Cosserat solids" could allow for a perfect lap. The authors concluded that this too could not work. The study did not take into account the so-called metamaterials, which have attracted attention for the rerouting of certain light waves.