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The mathematics of trees. Claus Mattheck

"Nature never uses leftover material in their structure"

It’s no secret that the history of humanity has maintained throughout the years, a close relationship with the trees, from which we have benefited in different ways. Trees have given us plenty of fruits, leaves, flowers and roots with both food and medicinal properties. We have offered wood that make tools, weapons and toys, in addition to houses, fences, boats and bridges. But perhaps most significant of all is the infinite source of knowledge that we might offer them.

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Claus Mattheck, german physicist awarded numerous honors in science and literature applied, proposes several methods to achieve structural optimization, extracting it of the structure of trees: the Computer Aided Optimization (CAO), the Visual Tree Assesment (VTA ) or the Soft Kill Option (SKO).
The first idea is to simulate the form of organic growth which occurs in natural materials. In this way you can avoid stress concentration in nodes to optimize the geometry that defines his shape. Not having such concentration efforts, we can reduce the amount of material of the structural element.

"Trees are not only living biological entities but also mechanical load-bearing structures."

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The second method, proposed by Mattheck and Breloer and published in the book "The body languages of trees" 1994, is based on identifying external symptoms due to internal abnormalities of wood, something that is only possible with experience and knowledge of the processes of growth of each species.

In a first phase a visual inspection of defects and vitality, after a confirmation of suspected defects is performed, which can be used for easy handling apparatus to verify resistance to penetration of wood or pulse rate is performed sound, among others. The study concludes with the evaluation of the resistance (failure criteria), which plays an important role flow cup forces the roots.

Finally, the third method mentioned above, (the Soft Kill Option) is based on extracting the sub-material being worked within a structural element, that is, which is underutilized.

Nature never uses leftover material in their structures and this is what you want to achieve with the methods Mattheck posed.

For more information, attached below some of the latest books dedicated to the understanding of this biomechanical optimization of shapes.

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