- 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.
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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)