- I dunno whether to
call this a structure, a mechanism, or a material. Well, I suppose it's a
material that has mechanisms embedded within it that
result in it having an interesting structure. The designer calls it a
bi-table auxetic structure, so we'll go with that,
but I don't think the name does it justice because
it does so much more than being bistable and auxetic. This video is sponsored by KiwiCo. More about them at the end of the video. Let's pick that name apart
though, bistable auxetic. You may have come across
Auxetic materials. Auxetic materials are
materials that behave in a weird way when stretched or squished. Blue Tack, for example, isn't auxetic. If you stretch Blue Tack in one direction, it gets thinner in the other direction. That's quite normal behavior. Auxetic materials do the opposite. When you stretch an auxetic
material in one direction it gets wider in the
other direction as well. And in fact, there's a whole
spectrum of possible behaviors when you squish and stretch a material. We assign a number to the
behavior of a material called the Poisson number. Normal materials have a
positive Poisson number like Blue Tach. When it's stretched in one direction, it contracts in the other. An auxetic material has a
negative Poisson number. When it's stretched in one direction, it expands in the other direction as well. But you also get materials
with a zero Poisson number. Cork, for example, has a
Poisson number of about zero. (upbeat music) Meaning if you squish it in one direction actually nothing happens
in the other direction and that makes cork really useful for stopping up wine bottles. When you press down on the cork to get it inside the neck of the bottle, it doesn't expand sideways, which is good because if it did, you wouldn't be able to
get it in the bottle. But how can a material have
a negative Poisson number? Well, it's all to do with
how smaller components of the material move around each other. See how these small triangles
hinge around each other and how that force is there to
be extra space between them. Here's another example. As I pull on this square, the smaller squares
rotate around each other according to the pattern of hinges causing the whole thing to
expand in both directions. Side note, I actually made
this contraption a while ago, and I put whiteboard
adhesive on all the squares. That's because I had this idea that I might be able to put an image on those squares that works in both
orientations of the mechanism. I never managed it, but if
you're inspired to have a play, I'd love to see what you come up with. The best place to share your creations is on the science fair project channel on my discord server linked
to the server invitation in the description. In my video about flexible polyhedra Jessen's polyhedron is auxetic. Squishing it in one
direction causes it to squish in the other direction. Actually, the other two directions. So this is auxetic material,
but it's also bistable. You encounter bistable
mechanisms all the time in your everyday life. For example, light switches. Look this light switch is
stable in the off position. If I push it a little, it returns to the off position
when I stop pushing it. But if I push it hard enough, it will flip into a
different stable state. So a light switch has
two stable configurations and I can move between them by overcoming some minimum force. This switch is constructed
of several parts all working together but it's possible to
construct a bistable mechanism from a single part so long as the material
is somewhat flexible. I printed this with a
material called PETG, and look it has two stable configurations. You could also call this
a compliant mechanism. I'll leave a link to Derek's video about that over on Veritasium. But there's something even
more interesting going on here. Not only is this material bistable, one of the stable configurations is curved into this interesting shape. It turns out it's possible
to tune the material so that the deployed state
is any shape you like. Well, almost any shape. I spoke to Tian Chen who
co-authored a paper about it. He showed me the basic building blocks of the material, and it's really clever. See when you pull on this
thing in one direction, it expands in the other direction. So if we tessellated them together, we'd have an auxetic material. But watch that animation again? And this time I want you
to focus on these cuts here marked in red. Notice how the pieces move
apart as the shape is stretched, but crucially, by the end
they have come back together. The same is true for these cuts. These parts are together at
the beginning and at the end, but they're separate in between. So what would happen if we
simply didn't make those cuts? Well, if the material
was elastic like rubber, those parts would stretch
as you pull on the material. But crucially, they would
be at a maximum stretch halfway through the sequence meaning once you've passed the middle, those stretched bits of rubber will actually be pulling the material towards the final state. In other words the material will be stable in both configurations. Just like the light switch,
it will be bistable. How cool is that? Tian Chen and his colleagues didn't actually come up with that bit. That was the work of Ahmad
Rafsanjani and Damiano Pasini. They saw some interesting
geometric tiling in Iran and wondered how a
rubber sheet would behave if it was cut according to the tiling. And it turned out to be
by stable and auxetic, though the material remains
flat in both stable states. So how do you make it pop
out into three dimensions? Well, what Tian Chen did was
to look at one of the triangles that makes up the hexagonal lattice unit. And actually there are
a couple of parameters you can play with. You can vary the length of this line. Let's call that length T. So there's a whole range
of cuts to explore there. And then you've got this angle. Let's call that theta. So you've got all these cuts to explore. You can vary T and theta independently, and you get different properties. For example, on the left, the length T is long and
the angle theta is large. Whereas on the right, T is
short and theta is small. They're both bistable auxetic structures, but one expands more than the other. And so then you say suppose I want this sheet
to turn into a dome. Well, then you need the
middle of the rubber sheet to expand more than the
perimeter of the rubber sheet. So you start off with
your pattern of triangles. It's the same across
the whole rubber sheet. And then you tweak those
two parameters, T and theta until you get just the
desired amount of expansion at every point on the sheet
so that it becomes a dome. And that's what you have here. Isn't that amazing? By the way, you could also
just make the triangles in the middle bigger to
get more expansion there. That's demonstrated with
this non bistable material. See how it collapses when the
deploying force is removed? But in general, the issue with just making
the triangles bigger in the areas where you want
more expansion is that, well, the computation becomes harder, but also you might end up
with really big flat bits and really small complex bits. Here's a question though. How do you decide which
parameter to change? And by how much? Because you've got T and theta. You can vary either of them to get the amount of
expansion that you want. So how do you choose? Well, this here is a heat map showing how much does the rubber
sheet expand as you vary T, which is shown on the vertical axis and theta on the horizontal axis. Lighter regions on the heat
map show more expansion. So if you want a specific
amount of expansion, say this much. Well, actually you've
got a whole line here of possible pairings of T
and theta to choose from that will give you that much expansion. So the way you pick is, well, basically you do a load of modeling in a computer to show you how
stable the structure will be for all these different values after it's deployed into
the dome shape or whatever. See in this simulation as
the sheet is being stretched, the graph shows how hard
it is to stretch it. And actually it's this graph that tells us that it's bistable. You've got these two energy minima. If you can put enough
energy into the system to overcome this hump, then
you'll land in this valley. So when we're thinking about what values of T and Theta to choose, we're
thinking about this graph. If we want this structure to be stable, which is to say if we
don't want it collapsing back to that flat state then we want to maximize this distance. We need to make the
valley as deep as possible to make it harder to get out of. And so you create another heat map, but this time showing how
deep this energy well is for different values of T and theta. So going back to this heat map, you have the curve of
possible T and theta values in yellow that gives you the
amount of expansion you want. You overlay that yellow
curve onto this heat map, and you pick the point along that curve that gives you the deepest valley. Interestingly, the structures
aren't that easy to undeploy. You have to kind of
massage the thing all over to get it flat again. So it might be that T and
theta are too optimized. You might be asking what sort
of applications there might be for a material like this. Well, one obvious one is medical stents. At the moment, stents
deploy into straight tubes, but arteries aren't always straight. Wouldn't it be great if
we could design a stent that grows to the exact
right size and shape when it's deployed? Also noteworthy is the fact that a self assembling
auxetic protein lattice has been developed. It works in a very similar way to my linked squares actually. How cool would it be
to play with a material that's auxetic and bistable
at the molecular level, a material that snaps between two sizes? Maybe one day. Guess what came today? - [Child] What? - KiwiCo. (kids screaming) I've been getting KiwiCo for
my kids for a long time now, and I've noticed something
really interesting. So KiwiCo is this subscription
service for STEM projects. Every month you get a crate in the post, and it has everything you need for a really fun hands-on STEM project. And the thing that I've noticed is this, there are nine different lines
for every possible age group. And typically I'll get a box that's above the age of my kids, and I'll do the project with them. And one thing you discover as a parent is human beings have to
learn absolutely everything. It's like kids don't know how
to use a spoon to eat cereal. Like they're not born with that skill. And you watch your kids
at a very young age, but failing at something
really simple like that. And so with KiwiCo, I'm showing them like this
is how you use a screwdriver. You know, this is how you
join two things together in this particular way or whatever. Here's this lever mechanism. Now it's been so long
they've been doing KiwiCo, they're really proficient in
all these things like tool use, ideas about mechanics and
engineering and electronics. They have a bit of an
intuition for this stuff now. They think like makers. KiwiCo isn't just a
subscription service by the way. You can also get one-off
crates from KiwiCo store which is perfect for the holiday season. The other thing that I
really like about KiwiCo is the replay value. Like my son has been
playing with this crane for days now and to the
point where it's annoying. Like you know, it is
time to tidy up the mess that they've made and it
takes him about an hour because he's tidying up using the crane. If you're interested in KiwiCo, then the promotion on
this one is really good. If you go to KiwiCo.com/stevemold and use promo code STEVEMOULD at checkout, you'll get 50% off your first month. The link is also in the description so check out KiwiCo today. I hope you enjoyed this video. If you did, don't forget to hit subscribe, and the algorithm thinks
you'll enjoy this video next. (upbeat music)
