Twisting and Bending of Biological Beams: Distribution of Biological Beams in a Stiffness Mechanospace

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Abstract
Most biological beams bend and twist relatively easily compared to human-made structures. This paper investigates flexibility in 57 diverse biological beams in an effort to identify common patterns in the relationship between flexural stiffness and torsional stiffness. The patterns are investigated by mapping both ideal and biological beams into a mechanospace defined by flexural and torsional stiffness. The distribution of biological beams is not random, but is generally limited to particular regions of the mechanospace. Biological beams that are stiff in bending are stiff in torsion, while those that bend easily also twist easily. Unoccupied regions of the mechanospace represent rare combinations of mechanical properties, without proving that they are impossible. The mechanical properties of biological beams closely resemble theoretical expectations for ideal beams. Both distributions are potentially being driven by the interdependence of the material and structural properties determining stiffness. The mechanospace can be used as a broadly comparative tool to highlight systems that fall outside the general pattern observed in this study. These outlying beams may be of particular interest to both biologists and engineers due to either material or structural innovations.