The Tension Triangle as a Bionic Stabilization Principle

The founding charter of Karlsruhe Polytechnical College in 1825 states the aim of the new institution as being to convey knowledge, in order to “generate the largest effects by the smallest means.” This principle is an underlying motivation in the engineering sciences, now mostly pursued with mathematics, computers, and rigorous experiments at testing stations. Claus Mattheck, during his tenure at KIT’s Institute of Materials Science II from 1980 to 2012, followed an alternate research path in bionics. By studying trees and other living organisms and inanimate natural structures, he gleaned insights into optimization. Mattheck identified one crucial principle: the omnipresence of tension triangles in the stabilization of notches. Unlike conventional engineering practices of reinforcing right-angled joints with quarter circles set at angles, Mattheck recognized that there is a better design in nature: tension triangles. These structures, pervasive in organic growth, provide robustness and efficiency. Mattheck’s result, derived from observing nature, is easy to implement because a simple triangular-shaped protractor (a Geodreieck) is all you need to construct with tension triangles. Mattheck’s insights inspired the drafting of engineering guidelines issued by the Association of German Engineers (VDI). By 2016, his principles were codified as the standard DIN ISO 18459 “Bionics – Bionic Structural Optimization.” His research group’s publications, translated into numerous languages including Korean and Japanese, underscore the global impact of his work. kn