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

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**Elena Davidson** - 1 month ago
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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!

We are back! Thanks so much for your patience. ðŸ™‚

In the face deformation example I wonder whether it's possible to put singularities such that certain structures keep their mesh around. I.e. if you look carefully how the eyes of one face morph into the other, it looks like they are actually replaced by what previously was cheeks whereas the eyes become the brow, and the nose undergoes a similar such uncanny transformation.

I wonder if that's "fixable".

Meanwhile, in CG this would make an excellent method to depict a person morphing into another if it is

meantto be uncanny.And of course, the materials that could be made from this are also sure to be highly interesting. I bet something similar could be achieved with sheets of graphene.

someone plz apply this to UV mapping. Big money to be got, many human lives to be bettered.

BMW 100 VISION

I had no idea what auxetic was, now I'm sure to lose a couple hours on wikipedia.

This is great.

a very fine example indeed

very simply explained. loved the video…. congrats

Am I the only one who thought the initial parts of the video with the sphere and hands was 3D rendered as well?

so it's just uv unwrapping and then cutting it out from auxetic material

Amazing, mindblowing – overused.

Thank you!! this video is very understandable!!

Thank you very much for this video and especially for the explanations. I'm studying flexure structures and also the chiral auxetic cellular and you open my mind a little more.

Just a very big thank you because every millimeter that allows the elevation of the spirit and true knowledge and a victory against obscurantism.

Pierre

how do you build this structure in 3d software?

Where can you buy such material ,,,?,

Or how to generate it from 3D software? Is anyone making it for sale? .. if so, where?

—Finally sent to lasser court …—Thanks

The episode was very understandable but I would have liked a bit more explanation of the math and methods.

is that hungarian english? better than italian english.

so we are finally getting textures in rl xD

Did I understand that correctly? So this allows us to calculate the shapes we need to cut into a solid, flat material to form it into body armor? Like solid steel body armor that perfectly fits the shape of your body?

I see a lot of skin pinching in the future of clothing

Please can you fix your microphone or talk less close to it as it distorts my speakers

Need the stl for my printer ðŸ˜€

So the tech that will lead to clothes that can change shape?

Dear algorithm THANK YOU

So basically they had to make algorithm to UV map the objects before they could print the structure? slightly alter that and you could have a very useful tool for 3d artists. All the automatic UV tools i've tried produce undesirable results, and doing it by hand is tedious.

I watch your channel whenever I feel like spitting my drink on my computer

can you guys train you AI to come up with auxetic material that would expand in every direction if pressure is applied from every direction?

Product-idea:

Auxetic kitchen strainer — expands when filled — washes and stores flat.

This is first to me to see you to making video without AI topic ðŸ˜‚

So its basically a hair removal system. Cool.

i'm currently studying product design, i definetly using this on my next project, grazie mille

Spacesuit gloves: still needs to be solved kids.

so basically, UV unwrapping irl

Am I understtand right? Auxetic more about geometry tweacks in some material than about material itself? This "supported materials" conclude me to some missunderstand I supose.

they should reconfigure it such a way that its can be applied to the joints of robotic arms or prothetics

Shoes for fat people… Well, they can go fit themselves.

FOUR MORE TILL 100!!!