Trunks and branches of trees withstand external stresses through load-adaptive growth.

Trees and bones achieve an even distribution of mechanical tension through the efficient use of material and adaptive structural design, optimizing strength, resilience, and material for a wide variety of load conditions. For example, to distribute stress uniformly, trees add wood to points of greatest mechanical load, while bones go a step further, removing material where it is not needed, lightweighting their structure for their dynamic workloads. At the scale of the cell, trees arrange fibers in the direction of the flow of force, or principal stress trajectories, to minimize shear stress. Engineers have incorporated these and other lessons learned from trees and bones into software design programs that optimize the weight and performance of fiber-composite materials. For example, car parts and entire cars designed with these principles have resulted in new vehicle designs that are as crash-safe as conventional cars, but up to 30% lighter.


“The analogy that [Claus] Mattheck wants to pursue, though, is not that between trees and other organisms, but between trees and engineered artefacts. If trees achieve longevity and structural stability, aren’t these the qualities of reliability and integrity that engineers want to design into products?

“The key to this is Mattheck’s contention that the structural optimisation in trees and apparent in other natural structures such as animal bones is all about making the external and internal stresses as uniform across the whole structure as possible. Mattheck calls this the ‘axiom of uniform stress’ and adds that, though he can cite plenty of examples of it, he cannot prove it exists…Mattheck’s contention is that trees are constantly readjusting this balance by adding more material at points of high stress and adding no material at points of low or no stress. (Bones, he contends, go one stage further by actually shrinking at points of low stress.)

“In trees, junctions between main trunks and branches, for instance, are places of concentrated stresses. Trees compensate for this extra stress by adding more material to the shoulder.” (Pullin 1998:17-18)

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The author's reply to the discussion on “A survey of X-rays in engineering and industry”Journal of the Institution of Electrical Engineers - Part I: GeneralNovember 4, 2014
V.E. Pullin

Design in Nature: Learning from TreesOctober 27, 2016
Claus Mattheck

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Teacher tree: The evolution of notch shape optimization from complex to simpleEngineering Fracture MechanicsMay 4, 2006
C. Mattheck

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Talking to the treesPullin, John

Scots PinePinus sylvestrisSpecies