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Researchers Determine 'Perfect' Stress Cloak Not Possible
August 8, 2019

Findings reported in a new study, “Nonlinear and Linear Elastodynamic Transformation Cloaking,” by researchers at the Georgia Institute of Technology (Georgia Tech) have all but shattered the dream of perfecting an ‘invisibility’ cloak for stress waves. According to information provided by Georgia Tech, the ‘perfect’ stress wave cloak would have precisely steered stress waves in the ground, like those emanating from a blast, around objects like buildings to make them “untouchable.”

However, despite casting serious doubt on dozens of theoretical papers that have pursued “elastodynamic” cloaking, the new study’s authors don’t think civil engineers should completely give up on it, just on the idea of an ideal cloak. Limited cloaking could still add a degree of protection to structures, particularly against some stress waves common in earthquakes.

“With cloaking, there is this expectation that if you get any kind of stress wave from any kind of direction, a cloak should be able to hide the object from it. We now see that it is not possible,” stated principal investigator Arash Yavari, a professor in Georgia Tech’s School of Civil and Environmental Engineering and in the George W. Woodruff School of Mechanical Engineering. “But for a large class of disturbances, namely the in-plane disturbances, you could probably design a good cloak.”

In an earthquake, in-plane disturbances are seismic waves that track along flatter and broader — or planar — paths through the surface of the Earth.

The theoretical dream of elastodynamic cloaking to steer stress waves past a structure like it isn’t even there has a lot in common with another cloaking dream — an invisibility cloak, which would bend light — electromagnetic waves — around an object then point it out the other side.

The light waves hitting the viewer’s eye would reveal what is behind the object but not the object itself. In elastodynamic cloaking, the waves are not electromagnetic but mechanical, moving through the ground. Hypothetically, cloaking the object would completely isolate it from the waves.

In an example of protecting a nuclear reactor from any stress waves traveling through the ground, whether from a natural or human-made calamity, ideally, civil engineers might lower the base of the reactor into a hole below the surface of the ground. They would build a protective cylinder or a half-spherical underground bowl around it with special materials to steer the stress waves around the circle.

However, according to Prof. Yavari, “We proved that the shape of the cloak does not matter, whether spherical or cylindrical, you can’t completely cloak.”

According to the report, a lot of theory and math from electromagnetic (light) cloaking has been transferred onto elastodynamic cloaking research, leading to the creation of an erroneous analogy.

“Many times, analogies from other fields are useful, but elasticity adds multiple physical factors that you don’t have in electromagnetism,” Prof. Yavari noted. “For example, the balance of angular momentum is being violated in much of the research literature.

Angular momentum is a property of mass in rotational motion, and it is resistant to changes.

Although it’s a wave, light is photons, which have no mass. Conversely, stress waves travel through matter — specifically, solid matter as opposed to liquid or gas — and that adds pivotal dynamics to the equation.

Those dynamics also affect that hole that hides the object. Without it, the stress waves travel pretty uniformly through a medium, but with it, stresses concentrate around the hole and destroy the neat geometry of the wave patterns.

“The math says that cloaking is not possible in the strict sense. When you understand that, you don’t waste time,” Prof. Yavari said. “You formulate problems that optimize with what you do know around targeted stresses or loads you want to protect against.”

Engineers could protect against important earthquake stresses if they use materials that have been specifically pre-stressed, have certain elastic properties and distribution of densities that are detailed in the study. A real-life cloak can fall short of an ideal and still be great.

“If instead of 100 percent of the wave energy I only feel 10 or 20 percent, it’s a huge deal because engineering is not a pursuit of absolute ideals,” Prof. Yavari said.

The new study also examined a popular idea in civil engineering that building construction using a family of materials that have a microstructure making them Cosserat solids might allow for perfect cloaking. Based on their research, the authors concluded that this also can’t work. The study did not consider so-called metamaterials, which have received attention for rerouting in particular light waves.

Supported by grants from the Army Research Office, the authors published their research in the journal Archive for Rational Mechanics and Analysis, a leading journal on theoretical solid mechanics.

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