Whether designing a window in an airliner or a cable conduit for an engine, manufacturers devote a lot of effort to reinforcing openings for structural integrity. But the reinforcement is rarely perfect and often creates structural weaknesses elsewhere.
Now, engineers at Princeton and Georgia Institute of Technology have developed a technique that can maintain structural integrity by essentially hiding the opening from the surrounding forces. Rather than reinforcing the opening to protect against a few select forces, the new approach reorganizes nearly any set of forces that could affect the surrounding material to avoid the opening.
In a May 5 article in the Proceedings of the National Academy of Sciences, the researchers said they surrounded openings with microstructures designed to protect against many loads — external forces that cause stress, movement or deformation. The microstructures' shape and orientation are calibrated to work with the most challenging loads facing the structure, allowing designers to counter multiple stresses at once.
"Think about a plate with a hole in it. If you put it under stress, if you pull on it, you are going to get a concentration of stress where the plate fails sooner than it would without the hole," said Emily D. Sanders, an assistant professor of mechanical engineering at Georgia Tech and one of the authors. "We want to design something around this hole, or defect, so it seems like the hole does not exist."
Glaucio Paulino, a principal author and the Margareta Engman Augustine Professor of Engineering at Princeton, said designers typically reinforce the structure at openings like windows or tunnels. But he said that by increasing structural strength in one direction, reinforcement can introduce other problems by creating new stress in a different direction. The goal of the cloaking technique is to protect the structure by redirecting the force without creating new or undesirable stress levels.
The researchers were inspired by knots in trees, where it seems like microstructures in tree knots direct force around the site of intrusions like branches or roots and maintain structural strength. The researchers wanted to know if they could engineer structures to do the same thing in manufactured materials.
Paulino said the technique relies on two optimization problems, which are designed to select the best solutions from a range of choices. The first problem uncovers the loads that will produce the greatest challenge to the object's structure. This is more challenging than it sounds because loads on a structure or a machine can change with circumstances.
"Any structure can potentially have an infinite number of loads. Every time you drive your car, the loads are different, the wind may blow in different directions, or the temperature may fluctuate" Paulino said.
The researchers found that calculating 6-10 of the worst-case loads for a structure yields the most effective results. With that information, they run a second optimization problem to find the most effective way to create and deploy microstructures surrounding the window or conduit.
"The optimization technique introduced by the authors represents a breakthrough methodology for achieving the invisibility of a defect, irrespective of the direction of any externally applied force," said Davide Bigoni, a professor of solid and structural mechanics at the Universita' di Trento in Italy. "This results in omnidirectional cloaking, a property with broad applications. These include ensuring mechanical stress neutrality in organ tissue replacement, modifying structural elements to facilitate the passage of installations in machinery or civil infrastructure, and enhancing the restoration of artwork."
The idea is similar to cloaking techniques that have been developed to hide objects on the electromagnetic spectrum such as stealth aircraft. Paulino explained that the equations for solid material can be more challenging than those for electromagnetism. But he said the goal is the same.
"Any elastic disturbance is hidden by the cloak," he said. "It is like it does not exist."
The article, Unbiased Mechanical Cloaks, was published in the journal PNAS on May 5. Besides Paulino and Sanders, it was co-written by Fernando Vasconcelos Senhora, of Georgia Institute of Technology. Support for the project was provided in part by the National Science Foundation and the Princeton Materials Institute (PMI). https://doi.org/10.1073/pnas.2415056122
