# 3D Printing Auxetic Materials | Two Minute Papers #96

## Метаданные

- **Канал:** Two Minute Papers
- **YouTube:** https://www.youtube.com/watch?v=5-xMV3sT3Tw
- **Дата:** 30.09.2016
- **Длительность:** 4:28
- **Просмотры:** 99,447
- **Источник:** https://ekstraktznaniy.ru/video/14768

## Описание

In this episode, we shall talk about auxetic materials. Auxetic materials are materials that when stretched, thicken perpendicular to the direction we're stretching them. In other words, instead of thinning, they get fatter when stretched.

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The paper "Beyond Developable: Computational Design and Fabrication with Auxetic Materials" is available here:
http://lgg.epfl.ch/publications/2016/BeyondDevelopable/index.php

The tendon paper, "Negative Poisson’s ratios in tendons: An unexpected mechanical response" is available here:
http://www.sciencedirect.com/science/article/pii/S1742706115002871

Our previous episode about optimization is available here:
https://www.youtube.com/watch?v=1ypV5ZiIbdA

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Sunil Kim, Julian Josephs, Daniel John Benton, Dave Rushton-Smith, Benjamin Kang.
https://www.patreon.com/TwoMinutePapers

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## Транскрипт

### Segment 1 (00:00 - 04:00) []

Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér. We are back! And in this episode, we shall talk about auxetic materials. Auxetic materials are materials that when stretched, thicken perpendicular to the direction we're stretching them. In other words, instead of thinning, they get fatter when stretched. Really boggles the mind, right? They are excellent at energy absorption and resisting fracture, and are therefore widely used in body armor design, and I've read a research paper stating that even our tendons also show auxetic behavior. These auxetic patterns can be cut out from a number of different materials, and are also used in footwear design and actuated electronic materials. However, all of these applications are restricted to rather limited shapes. Furthermore, even the simplest objects, like this sphere cannot be always approximated by inextensible materials. However, if we remove parts of this surface in a smart way, this inextensible material becomes auxetic, and can approximate not only these rudimentary objects, but much more complicated shapes as well. However, achieving this is not trivial. If we try the simplest possible solution, which would basically be shoving the material onto a human head like a paperbag, but as it is aptly demonstrated in these images, it would be a fruitless endeavor. This method tries to solve this problem by flattening the target surface with an operation that mathematicians like to call a conformal mapping. For instance, the world map in our geography textbooks is also a very astutely designed conformal mapping from a geoid object, the Earth, to a 2D plane which can be shown on a sheet of paper. However, this mapping has to make sense so that the information seen on this sheet of paper actually makes sense in the original 3D domain as well. This is not trivial to do. After this mapping, our question is where the individual points would have to be located so that they satisfy three conditions: one: the resulting shape has to approximate the target shape, for instance, the human head, as faithfully as possible two: the construction has to be rigid three: when we stretch the material, the triangle cuts have to make sense and not intersect each other, so huge chasms and degenerate shapes are to be avoided. This work is using optimization to obtain a formidable solution that satisfies these constraints. If you remember our earlier episode about optimization, I said there will be a ton of examples of that in the series. This is one fine example of that! And the results are absolutely amazing - the possibility of creating a much richer set of auxetic material designs is now within the realm of possibility, and I expect that it will have applications from designing microscopic materials, to designing better footwear and leather garments. And we are definitely just scratching the surface! The method supports copper, aluminum, plastic and leather designs, and I am sure there will be mind blowing applications that we cannot even fathom so early in the process. As an additional selling point, the materials are also reconfigurable, meaning that from the same piece of material, we can create a number of different shapes. Even non-trivial shapes with holes, such as a torus, can be created. Note that in mathematics, the torus is basically a fancy name for a donut. A truly fantastic piece of work, definitely have a look at the paper, it has a lot of topological calculations, which is an awesome subfield of mathematics. And, the authors' presentation video is excellent, make sure to have a look at that. Let me know if you have found this episode understandable, we always get a lot of awesome feedback and we love reading your comments. Thanks for watching, and for your generous support, and I'll see you next time!