For light, such transformations are based on the mathematics of transformation optics. So far, however, it has been impossible to transfer this principle to real materials and components in mechanics. The mathematics made impossible requirements on the material.
To overcome these difficulties, researchers of the KIT Institute of Applied Physics around first author Tiemo Bückmann found a new, simple method. “We imagined a network of electric resistors,” Bückmann explains. “The wire connections between the resistors may be chosen to be of variable length, but their value does not change. Electric conductivity of the network even remains unchanged, when it is deformed.”
The researchers transferred this thought experiment to practice. “In mechanics, this principle is found again when imagining small springs instead of resistors,” Tiemo Bückmann says. “We can make single springs longer or shorter when adapting their shapes, such that the forces between them remain the same. This simple principle saves computation expenditure and allows for the direct transformation of real materials.”
The researchers tested their method in a model experiment with a material made of printed polymer. A stable hexagonal honeycomb structure was provided with a hole. Due to its reduced stability, the distorting forces first caused an error of more than 700 percent. After application of the newly developed transformation, the error amounted to 26 percent only. The results have just been published in the proceedings of the National Academy of Sciences (PNAS).
Applications are manifold, as the new method can be used to calculate known composite materials or mechanical support constructions. Even special designs will react as stably as possible to external forces – as if the support construction would not have been deformed.
Karlsruhe Institute of Technology (KIT) is a public corporation pursuing the tasks of a state university of Baden-Wuerttemberg and of a national research center of the Helmholtz Association. The KIT mission combines the three core tasks of research, higher education, and innovation. With about 9,400 employees and 24,500 students, KIT is one of the big institutions of research and higher education in natural sciences and engineering in Europe.