2. Folding
in
Nature:
Protein
Folding
from
random
coil
(wikipedia)
Extreme
Mechanics
Geological
fold
in
Poland.
Manufacturing
:
Microrobo,cs
Lab
Whiteside
Lab
What
Drives
Blooming,
or
Leaves
shape
?
Liang
and
Mahadevan.
Growth,
geometry,
and
mechanics
of
a
blooming
lily.
ONAS
2011
Incorporate
foldable
structure
with
electronics
Biological
Tissues
:
Gut,
intes,ne,
brain
folds
Adv.
Funct.
Mater.
2010,
20,
28–35
Savin
et
al.
On
the
growth
and
form
of
the
gut.
PNAS
2011
3. lgorithms of resolution of the individual elements (tiles) and the number of
gning the elements that can be effectively combined in a single sheet. First,
an object the resolution of the tiles is limited by the scalability of each
he stickers element. The current materials and methods use to create the
substrate can be reasonably shrunk to create tiles on the order
Folding
in
Manufacturing
and
Engineering
of a few millimeters in largest dimension. Below this threshold,
lithography and micromolding techniques (for example, molding
described elastomers using capillary action (25)) could be used to reduce
ty-two-tile feature sizes further. Scaling of actuation has two considerations:
Folding
in
Engineering
:
Foldable
Robo,cs
Foldable
Solar
Cells
Foldable
BaZeries
Paper
Based
Electronics
…..
own in lower right—mm:ss.s) of a self-folding “boat.”(A). All actuators receiving current
boat on side (D).
Programmable
Magne,c
Self-‐assembly
Hawkes et al.
PNAS
∣
July
13,
2010
∣
vol.
107
∣
no.
28
∣
Appl. Phys. Lett. 96, 071902 ͑2010͒
071902-2 Myers, Bernardi, and Grossman Appl. Phys. Lett. 96, 071902 ͑2010͒
hematics of 3DPV structures: ͑a͒ GA-optimized
Foldable
3DPV
4 triangles inside the bounding box; ͑b͒ funnel, a
GA-optimized structures that retains their supe-
Solar
Cells
Inexpensive
Deployment
of
Solar
Cells
FIG. 2. ͑Color online͒ Schematics of 3DPV structures: ͑a͒ GA-optimized
structure shown with all 64 triangles inside the bounding box; ͑b͒ funnel, a
er shapes.
More
than
2/3
of
the
cost
of
PV
systems
is
simplified version of most GA-optimized structures that retains their supe-
rior performance over other shapes.
gredients ofMarch
15,
2005
vol.
102
no.
11
PNAS
the complicated GA struc- in
deployment
cost.
contains most key ingredients of the complicated GA struc-
tures.
e energy generated byppl.
Phys.
LeZ.
96,
071902,
2010
Myers,
et
al.
A simple open-box
We compared the energy generated by simple open-box
l structures through a figure of merit M,
shapes and the funnel structures through a figure of merit M,
4. How
Auxe,cs
(NPR)
Materials
work
news and views
Unstretched Stretched Daedalus
a
The a
ν
=
–et/el
=
–(ΔD/D)/
(ΔL/L)
The librar
only by co
b
crumbling
So Daedal
Two
dimensional
structures:
closed boo
should be
books ont
transfer th
a)
Honycomb
cells
A pape
typical inf
of fibres o
should be
b)
Inverted
honycomb
cells
wavelengt
wavelengt
Figure 1 Positive and negative Poisson’s ratios. Stretching these two-dimensional hexagonal distinguis
structures horizontally reveals the physical origin of Poisson’s ratio. a, The cells of regular side. A pu
Miura-‐ori
fold
honeycomb or hexagonal crystals elongate and narrow when stretched, causing lateral contraction
and so a positive Poisson’s ratio. b, In artificial honeycomb with inverted cells, the structural
launched
or bottom
elements unfold, causing lateral expansion and a negative Poisson’s ratio. simultane
page only,
Proper,es:
so the overall Poisson’s ratio is almost always membranes. The overall elasticity of a cell page was a
positive. membrane results from both the protein A suffi
Absorb
Energy,
resist
fracture.
The elastic behaviour of the membranes skeleton and the high lipid content, but the trace a sin
studied by Bowick et al.1 is said to be ‘uni- relative contributions are not yet known. letters fro
versal’ because the authors require only a Even so, Bowick and colleagues’ results are
Some
applica,ons:
body
armor,
an opaque
sparse set of assumptions to predict the provocative. If our usual expectations about absorb th
Poisson’s ratio. They start with a simple net- how things deform do not apply to biological
shock
absorber,
packing
material,
sharp atte
work of nodes, resembling a fishing net with membranes then we may need to reconsider or ‘echo’ c
,
fixed connections, which they model using the influence of membrane mechanics7 on letter. A b
knew
and
elbow
pads,
sponge
a Monte Carlo simulation. Bowick et al. the shape of cells, the formation of vesicles, the stream
show that a negative Poisson’s ratio is a uni- and the deformation of cells during life photocell
mops.
versal property of such systems, whether the processes. For example, red blood cells are Unfort
membrane is dominated by rigid bonds that routinely deformed when they pass through both sides
resist bending or by ‘self-avoiding’ inter- fine blood capillaries. As they deform, the may be in
silver.neep.wisc.edu/~lakes/Poisson.html
atomic forces that prevent portions of the membrane skeleton can unfold, which both of wh
structure overlapping.
This unusual form of elasticity may also
Metallic
Foam
might help to transport large molecules or
expose reactive chemical groups. Similar
But this is
come in. E
5. Poisson
Ra,o
is
a
very
important
mechanical
REVIEW ARTICLE NATURE MATERIALS DOI: 10.1038/NMAT3134
proper,es
a
0.6
Liquids
Lead Rubber
0.4 Dental composites
Metallic glasses
Steel
ty
Gels Oxide glasses
i
tiv
0.2 Concrete Zeolites
c
Cartilage
ne
Bone Honeycomb
in g
on
0.0 Cork Gases
dc
ck
pa
e
Carbon nanotube Laminates
as
er
re
sheets
ns
–0.2
Inc
De
α-cristobalite
Unscreened metals Bi, As
–0.4 Laser-cooled crystals
Colloidal crystals
–0.6
Re-entrant polymer foams
–0.8
Critical fluids
–1.0
–1.2
0.001 0.01 0.1 1 10 100
B/G
b
Bulk modulus B c
bulk
modulus
B
BMG hange
in
size
-‐
c
• ν
=
[3(B/G
–
2)]/[6(B/G
+
2)]
400 fcc
Unstable by
domain
Rubbery Stiff
350
shear
modulus
G
–
change
in
shape
Ductile
bcc
ν = 1/2 ν = 0.3 Brittle
ν
=
[1⁄2(Vt/Vl)2
–
1]/[(Vt/Vl)2
–
1]
formation
• 300
B/G = 2.4 hcp
Stable
• isotropic
range
of
–1
≤
ν
≤
1⁄2
for
0
≤
B/G
<
∞
at
small
strains
250
B (GPa)
ν=0 Fe–
450 Ni– Unreachable
• Nonlinear
regime
ν
<
-‐1.
Spongy
Anti-rubbery 200 Pd–
Ideal isotropic solid
Dilational
ν = –1 150 Cu– B/G = 5/3
Auxetic
Foam
Structures
wν2= –2
Nega*ve
Poissson's
Ra*o.
Lakes.
science.
1987.
ν =
ith
a Shear modulus G 100 RE- fcc metals
–4G/3 < B < 0 Zr– bcc metals
Unstable by volume change
ν=1 50 hcp metals
Poisson’s
ra*o
and
modern
materials.
Nature
Materials.
G.
N.
Greaves,
but stable if constrained Mg–
A.
L.
Greer,
R.
S.
Lakes
and
T.
Rouxel
24
Oct
2011
0
0 50 100 150 200 250
6. Project
• Make
Mouri-‐Ori
Fold.
• Vary
angle
to
vary
mechanical
proper,es.
• How
does
the
rela,on
look
like.
• Measure
Poisson
ra,os.
Miura-‐ori
paZern
is
a
Rhomboidal
(2
angles
,
2
lengths).
• They
developed
computa,onal
tool
to
simulate
the
stretching,
bending
and
folding
of
thin
sheets
of
material
to
predict
its
mechanical
proper,es.
Pleated
and
Creased
Structures.
Levi
Dudte,
Zhiyan
Wei,
L.
Mahadevan.
APS
2012
Mee,ng.
2:30
PM–5:30
PM,
Tuesday,
February
28,
2012
Room:
153C
8. Possion
ra,o
measurements
Strain
Vs.
strain
plots
for
SU-‐8
microstructures
to
measure
NPR
(no
varying
of
angles)
~100
μm
Adv.
Mater.
1999,
11,
No.
14
9. Acknowledgment
• Applied
Math
Lab
– Advisor
and
PI:
L.
Mahadevan
–
Levi
Dudte
–
Zhiyan
Wei
• Microrobo,cs
Lab
– PI:
Robert
Woods
– Lab
Manger:
Michael
Smith.
11. Problems
faced
• Project
start
Monday,
Feb
6
2012:
17
days
only
and
talked
to
students
much
later.
• No
sotware
access
(Corel
Draw,
AutoCAD)
• Hard
access
to
Laser
Lab
• Access
to
lab
to
measure
passion
ra,o.
