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(19)
United
States
US
20170009036A1
(12)
Patent
Application
Publication
(10)
Pub.
No.:
US
2017/0009036A1
Xie
et
al.
(43)
Pub.
Date:
Jan.
12,
2017
(54)
STRUCTURED POROUS METAMATERIAL
(71) Applicant:
RMIT
UNIVERSITY,
Victoria
(AU)
(72)
Inventors:
Yi
Min
Xie,
Rossana
(AU);
Jianhu
Shen,
Ringwood
(AU);
Shiwei
Zhou,
Balwyn
(AU);
Xiaodong
Huang,
Kew
(AU)
(21)
Appl.
No.:
15/113,373
(22)
PCT
Filed:
Jan.
20,
2015
(86).
PCT
No.:
PCT/AU201S/OOOO25
S
371
(c)(1),
(2)
Date:
Jul.
21,
2016
(30)
Foreign
Application
Priority
Data
Jan.
24,
2014
(AU)
................................
2O1490O227
Publication
Classification
(51)
Int.
Cl.
C89/00
(2006.01)
B29C
67/00
(2006.01)
(A)
B33
W
80/00
(2006.01)
GOIN
3/08
(2006.01)
B33
W
IMO
(2006.01)
B33Y
70/00
(2006.01)
(52)
U.S.
Cl.
CPC
C08J
9/00
(2013.01);
B33Y
10/00
(2014.12);
B33Y
70/00
(2014.12);
B33
Y
80/00
(2014.12);
G0IN
3/08
(2013.01);
B29C
67/0051
(2013.01);
C08J
2383/04
(2013.01);
C08.J
2205/04
(2013.01);
B29K
2083/00
(2013.01)
(57)
ABSTRACT
A
structured
porous
metamaterial
includes
a
threedimen
sional
matrix
of
at
least
one
repeating
base
unit.
The
matrix
is
formed
from an
array
of
at
least
eight
base
units,
each
base
unit
including
a
platonic
solid
including
at
least
one
shaped
Void,
wherein
each
base
unit
has
void
geometry
tailored
to
provide
a
porosity
of
between
0.3
and
0.97,
and
to
provide
the
metamaterial
with
a
response
that
includes
a
Poisson’s
ratio
of
0
to
0.5
when
under
tension
and
compression,
or
negative
linear
compression
(NLC),
negative
area
compres
sion
(NAC),
Zero
linear
compression
(ZLC),
or
Zero area
compression
(ZAC)
behaviour
when
under
pressure.
(B)
(C)
Patent
Application
Publication
Jan.
12,
2017.
Sheet
1
of
7
US
2017/0009036A1
(A) (B) (C)
(A)
(B)
(C)
Figure
1B
Figure
2
Patent
Application
Publication
Jan.
12,
2017.
Sheet
2
of
7
US
2017/0009036A1
Figure
3A
2O
 

D2
Printing
direction
A.

. .

.
D1

1
D1
f

D1repeat
1
: ,
O 10
20
30
40
Displacement
(mm)
Figure
3B
40
Printing
direction
US
2017/0009036A1
Jan.
12,
2017.
Sheet
3
of
7
2O
Displacement
(mm)
Figure
3C
10.
Loading
along
X


Loading
along
Y
Loading
along
Z
Patent
Application
Publication
30mm
12mm
SE3mm
O.Omm
2.94
mm
SE
12mm
Figure
4
O.Omm
Patent
Application
Publication
2.0
1.6
Jan.
12,
2017.
Sheet
4
of
7
0.4
Experimental
result
(model
with
no
imperfection)
FE
result
for
model
(model
with
0.1%
imperfection,
E=1.05MPa)
FE
result
(model
with
8%
imperfection,
ends
laterally
fixed,
E=1.05MPa)
FE
result
(model
with
8%
imperfection,
roller
ends,
E=0.925MPa)
Experimental
result
(8%
imperfection)

SEO.
Omm
O.1
O2
O.3
0.4
NOminal
Strain
Figure
5
Dood
Odo'
g
i:
Oe
Osos
states
if
OOOOOOO
air
two
Yunot
up
.
f




OSS
''
OO
o
O
OC
O.
9
up
to
of
.
A
data
a
?h
Aha
A
a
a
Figure
6
US
2017/0009036A1
Patent
Application
Publication
Jan.
12,
2017.
Sheet
5
of
7
US
2017/0009036A1
Figure
7A
Figure
8B
Patent
Application
Publication
Jan.
12,
2017.
Sheet
6
of
7
US
2017/0009036A1
A.
t
...
s
,
O.
“...
A

FEStrana
.
A.

15
O
ExperimentalStrainz
'...
...
FEStraX

A
A
ExperimentalStrainX
"...
a.
O.2
s
(C)
0.25
O5
1
15
2
2.5
3.
3.5
4
4.5
5
Triaxial
pressure
(kPa)
Figure
10
Patent
Application
Publication
Jan.
12,
2017.
Sheet
7
of
7
US
2017/0009036A1
(A) (B) (C) (D)
Figure
11
(A) (B) (C) (D)
Figure
12
(A) (B) (C) (D)
Figure
13
US
2017/0009036A1
STRUCTURED
POROUS
METAMATERIAL
TECHNICAL
FIELD
0001.
The
present
invention generally
relates
to
a
three
dimensional
(3D)
structured
porous
metamaterials
with
spe
cific
deformation
pattern
under
applied
loading,
and
more
particularly
a
3D
structured
porous
metamaterials
having
a
negative
or
Zero
Poisson’s
ratio
and/or
Zero
or
negative
compressibility
(NC).
BACKGROUND
OF
THE
INVENTION
0002
The
following
discussion
of
the
background
to
the
invention
is
intended
to
facilitate
an
understanding
of
the
invention.
However,
it
should
be
appreciated
that
the
dis
cussion
is
not
an
acknowledgement
or
admission
that
any
of
the
material
referred
to
was
published,
known
or
part
of
the
common
general
knowledge
as
at
the
priority
date
of
the
application.
0003.
A
material’s
Poisson’s
ratio
is
defined
as
the
nega
tive
of
the
ratio
of
that
materials
lateral
strain
to
its
axial
strain
under
uniaxial
tension
or
compression.
Most
materials
have
a
positive
Poisson’s
ratio
and
therefore
which
expand
laterally
under
compression
and
contract
in
the
transverse
direction
under
axial
tension.
Auxetic
materials
are
materials
with
negative
Poisson’s
ratio
(NPR).
The
materials
contract
laterally
under
compression
and
expand
in
the
transverse
direction
under
axial
tension.
0004
Compressibility
is
a
measure
of
the
relative
volume
change
of
a
Solid
or
fluid
as
a
response
to
a
pressure
change.
Usually
a
material contracts
in
all
directions
when
the
pressure
increases.
However
there
are
some
exceptional
materials
which
expand
under
hydrostatic
pressure
in
one
or
two
directions.
Such
phenomena
are
known
as
negative
linear
compressibility
(NLC)
and
negative
area
compress
ibility
(NAC),
respectively.
0005.
In
recent
years,
there
has
been
increasing
interest
in
the
negative
compressibility
behaviour,
mostly
due
to
its
many
potential
applications
such
as
sensitive
pressure
sen
sors,
pressure
driven
actuator
and
optical
telecommunication
cables.
There
are
little
artificial
metamaterials
with
NLC
or
NAC
available.
As
for
metamaterial
with
NPR,
Most
of
the
currently
available
artificial
metamaterials
have
a
represen
tative
Volume
element
having
a
complex
topology.
A
number
of
auxetic
elastomeric
materials
have
also
been
developed,
of
which
the
following
are
examples:
0006
Overvelde
et
al
(Compaction
Through
Buckling
in
2D
Periodic,
Soft
and
Porous
Structures:
Effect
of
Pore
Shape.
Advanced
Materials.
2012;
24:23372342)
teaches
two
dimensional
Soft cellular
structures that
comprise
a
solid
matrix
with
a
square
array
of
holes.
No
three
dimensional
structures
are
investigated.
The
response
of
2D
porous
structure
to
compression,
including
the
Poisson’s
ratio
of
the
material,
are
taught
as
being
designed
and
tuned
by
changing
the
shape
of
the
holes.
Structures
with
a
porosity
(p
of
between
0.4
and
0.5
were
identified
as
providing
suitable
auxetic
properties.
Structures
with
smaller
porosity
were
noted
to
facilitate
macroscopic
instability
leading
to
struc
tures
characterised
by
limited
compaction.
Structures
with
higher
levels
of
porosity
where
also
noted
as
leading
to
structures
characterised
by
very
thin
ligaments,
making
them
fragile.
0007
United
States
Patent
Publication
No.
20110059291
A1
teaches
both
two
dimensional
and
three
dimensional
Jan.
12,
2017
structured
porous
materials
having
a
porous
structure
pro
vides
a
range
in
Poisson’s
ratio
ranging
from
a
negative
Poisson’s
ratio
to
a
Zero
Poisson’s
ratio.
The
geometry
of
the
Voids
is
suggested
as
being
variable
over
a
wide
range
of
sizes
and
shapes.
However,
the
exemplar
structures
consist
of
a
pattern
of
elliptical
or
ellipticallike
voids
in
an
elas
tomeric
sheet.
The
porous
pattern
of
both
two
dimensional
and
three
dimensional
comprise
a
matrix
of
Voids
having
a
porosity
(p
of
less
than
0.5.
The
voids
are
located
in
the
matrix
as
individual
shapes
within
the
base
material,
and
are
spaced
apart
in
a
regular
pattern.
0008
Babaee
et al
(3D
soft
metamaterials
with
negative
Poisson’s
ratio.
Advanced
Materials.
2013;
DOI:
10.1002/
adma.201301986:16)
teaches
a
new
class
of
threedimen
sional
metamaterials
with
negative
Poisson’s
ratio.
A
library
of
auxetic
building
blocks
is
identified
and
procedures
are
defined
to
guide
their
selection
and
assembly.
The
taught
materials
all
comprise
a
three
dimensional
matrices
of
ball
shaped
building
block
units.
Each
ball
building
block
includes
shaped
Voids.
The
balls
are
stacked
in
a
complex
three
dimensional
array
to
form
the
metamaterial.
0009.
It
would
therefore
be
desirable
to
provide
a
new
and/or
improved
three
dimensional
metamaterials
with
negative
Poisson’s
ratio
(NPR),
negative
linear
compression
(NLC),
negative area
compression
(NAC),
Zero
linear
com
pression
(ZLC),
and/or
Zero
area
compression
(ZAC)
behav
iour
(NAC).
In
particular,
it
is
preferable
that
this
new
auxetic
metamaterial
has a
different
and/or
simpler
structure
than
the
metamaterial
taught
in
Babaee
et
al.
SUMMARY
OF
THE
INVENTION
0010.
The
present
invention
provides
in
a
first
aspect
a
structured
porous
metamaterial
comprising
a
threedimen
sional
matrix
of
at
least
one
repeating
base
unit,
the
matrix
formed from
an
array
of
at
least
eight
base
units,
each
base
unit
comprising
a
platonic
Solid
including
at
least
one
shaped
Void,
wherein
the
geometry
of
the
at
least
one
shaped
void
of
each
base
unit
is
tailored
to:
0.011
provide
a
porosity
of
between
0.3
and
0.97;
and
0012
provide
the
metamaterial
with
a
response
com
prising
at
least
one
of
0013
a
Poisson’s
ratio
of
0
to
0.5
when
under
tension
and
compression; or
0014
negative
linear
compression
(NLC),
negative
area
compression
(NAC),
Zero
linear
compression
(ZLC),
or
Zero
area
compression
(ZAC)
behavior
when
under
pressure.
0015
The
present
invention
can
therefore
provide
two
broadly
different
properties
through
the
inventive
porous
Structure:
0016.
In
a
first
embodiment,
the
present
invention
pro
vides
a
structured
porous
metamaterial
having
a
response
under
tension
and
compression
having
a
Poisson’s
ratio
of
0
to
0.5.
This
embodiment
of
the
present
invention
comprises
a
simple
building
unit that
provides
a
large
and
tuneable
negative
Poisson’s
ratio
(NPR)
strain
range
under
both
tension
and
compression.
The
negative
and/or
Zero
Pois
son's
ratio
behavior
of
this
metamaterial
is
a
result
of
the
mechanics
of
the
deformation
of
the
voids
and
the
mechan
ics
of
the
deformation
of
the
solid
base
material.
0017.
In
these
embodiments,
the
porosity
is
preferably
between
0.30
and
0.97.
More
preferably,
the
porosity
is:
(0.018
between
0.69
and
0.97
for
a
spherical
shaped
void;
US
2017/0009036A1
(0019
between
0.30
and
0.90
for
regular
nonspherical
shaped
Voids;
or
(0020
between
0.3
and
0.98
for
optimised
shaped
voids.
0021.
In
some
forms
of
this
first
embodiment,
the
present
invention
provides
a
structured
porous
metamaterial
com
prising
a
threedimensional
matrix
of
at
least
one
repeating
base
unit,
the
matrix
formed from
an
array
of
at
least
eight
base
units,
each
base
unit
comprising
a
platonic
Solid
including
at
least
one
shaped
Void,
wherein
the
geometry
of
the
shaped
void
of
each
base
unit
is
tailored
to:
0022
provide
a
porosity
of:
(0023
between
0.69
and
0.97
for
a
spherical
shaped
void;
0024
between
0.30
and
0.90
for
regular
nonspheri
cal
shaped
Voids;
or
(0025
between
0.3
and
0.98
for
optimised
shaped
voids.
0026
provide
the
metamaterial
with
a
response
com
prising
a
Poisson’s
ratio
of
0
to
0.5
when
under
tension
and
compression.
0027.
The
inventors
have
found
that
contrary
to
the
teaching
of
the
prior
art,
the
size
and
geometry
of
the
Void
needs
to
be
configured
to
provide
a
porosity
(p
of
between
0.69
and
0.965
in
the
metamaterial
with
base
unit
compris
ing
a
cube
with
a
spherical
shaped
Void
in
order
to
provide
the
advantageous
negative
and/or
Zero
Poisson’s
ratio
behavior
for
the
defined
base
unit.
In
this
respect,
the
inventors
have
found
that
lower
porosity
values
as
taught
as
being
essential
in
US20110059291
and
Overvelde
et
al
do
not
provide
a
three
dimensional
porous
structure
which
displays
tuneable
negative
and/or
Zero
Poisson’s
ratio
over
a
large
compression
Strain,
despite
these
characteristics
being
demonstrated
as
being
displayed
in
the
two
and
three
dimensional
structures.
The
desired
properties
and
deforma
tion
characteristic
of
those
materials
can
only
be
reproduced
in
threedimensional
structure
through
significant
modifica
tion
of
the
porous
structure
and
geometry
of
the
base
unit
and
constituent
Void.
0028.
Without
wishing
to
be
limited
by
any one
theory,
the
inventors
consider
that
the
negative
Poisson’s
ratio
of
the
metamaterial
of
the
present
invention
is
achieved
through
selection
of
the
geometry
and
porosity
of
the
material
to
create
a
desired
alternating
opening
and
closing
deformation
pattern
of
the
Voids
and
a
specific
configuration
of
the
base
unit
which
on
compression
allows
spatial
rotation
and
translation
of
part
of
the
material
of
the
base
unit
accom
panied
by
the
bending
and
stretching
of
other
parts
of
the
material
of
the
base
unit.
0029.
In
a
second
embodiment,
the
present
invention
provides
a
structured
porous
metamaterial
having a
negative
linear
compression
(NLC),
negative
area
compression
(NAC),
Zero
linear
compression
(ZLC),
or
Zero area
com
pression
(ZAC)
behavior
when
under
pressure.
In
these
embodiments
of
the
present
invention,
the
metamaterial
comprise
a
simplified
building
unit
that
provides
NLC,
NAC,
ZLC,
ZAC
behaviour
under
pressure.
In
preferred
forms,
these
building
units
are
derived
from
bidirectional
evolutionary
structural
optimization
(BESO).
0030.
In
these
embodiments,
the
porosity
is
preferably
between
0.30
and
0.97.
More
preferably,
the
porosity
is
between
0.3
and
0.95
for
optimised
shaped
voids.
0031.
In
some
forms
of
this
second
embodiment,
the
present
invention
provides
in
a
structured
porous
metama
Jan.
12,
2017
terial
comprising
a
threedimensional
matrix
of
at
least
one
repeating
base
unit,
the
matrix
formed from
an
array
of
at
least
eight
base
units,
each
base
unit
comprising
a
platonic
Solid
including
at
least
one
optimised
shaped
Void,
wherein
the
geometry
of
the
at
least
one
shaped
Void
of each base
unit
is
tailored
to:
0032
provide
a
porosity
of
between
0.3
and
0.95
for
optimised
shaped
Voids;
and
0033
provide
the
metamaterial
with
a
response
com
prising
at
least
one
of
negative
linear
compression
(NLC),
negative area
compression
(NAC),
Zero
linear
compression
(ZLC),
or
Zero area
compression
(ZAC)
behavior
when
under
pressure.
0034.
The
matrix
structure
of
the
metamaterial
of
the
present
invention
is
formed
from
repeating
adjacent
base
units.
The
metamaterial
is
formed
from
a
three
dimensional
matrix
formed
from
an
array
of
at
least
eight
base
units,
preferably
arranged
as
a
2x2x2
matrix
and
preferably
many
more
than
eight
base
units
arranged
in
a
three
dimensional
matrix.
The
shape
of
the
base
unit
is
a
platonic
solid
which
enables
the
base
unit
to
be
arranged
in
a
matrix
without
any
Voids or
gaps
between
adjacent
units.
In
preferred
embodi
ments,
the
base
unit
comprises
at
least
one
of a
tetrahedron,
cube,
cuboid,
parallelepiped,
octahedral,
dodecahedron,
or
icosahedron.
In
one
exemplary
embodiment,
the
base
unit
comprises
a
six
sided
shape,
preferably
a
cube,
cuboid,
parallelepiped,
and
more
preferably
a
cube,
more
preferably
a
cubic
symmetric
platonic
Solid.
0035
Each
base
unit
includes
a
geometric
center.
In
preferred
embodiments,
the
geometry
of
the
void
is
centered
about
the
geometric
center
of
the
base
unit,
and
more
preferably
the
geometric
center
of
each
void
is
centered
about
the
geometric
center
of
the
base
unit.
This
provides
a
regular
spacing
between
the
center
of
adjacent
void shapes
throughout
the
matrix.
0036.
The
negative
Poisson
ratio
of
the
metamaterial
can
be
tuned
by
using
different
base
shape
for
the
void
and
buckling
mode
of
the
representative
element.
For
example,
a
material
formed
from a
base
unit
including
a
void
having
a
spherical
base shape
has
a
different
negative
Poisson
ratio
to
a
material
formed
from
a
base
unit
including
a
Void
having
an
ovoid base
shape.
Similarly,
a
material
formed
from
a base
unit
including
a
Void
having
a
spherical
base
shape
or
an
ovoid base shape
has
a
different
negative
Poisson
ratio
to
a
material
formed
from a
base
unit
including
a
void
having
an
ellipsoid
shape.
0037.
The
void
or
voids
within
each
base
unit
can
have
any
suitable
shape
and
configuration.
The
base
shape
of
the
void
is
preferably
selected
to
provide
desired
tension
and
compression
properties
to
the
metamaterial.
In
some
embodiments,
wherein
the
base
geometric
shape
of
the
Voids
comprises
a
spherical
shape
or
at
least
one
regular
non
spherical
shape Such
as
ovoid,
ellipsoid
(including
rugby
ball
shaped),
cubic,
cuboid,
parallelepiped,
hyperboloid,
conical,
octahedron,
or
other
regular
3D
polygon
shape.
In
preferred
forms,
the
Void
comprises
a
spherical,
ovoid,
or
ellipsoid,
more
preferably
spherical,
or ovoid,
and
yet
more
preferably
spherical.
0038.
In
other
embodiments,
the
void
or voids
can
have
a
nonregular
shape.
For
example,
in
Some
embodiments
the
void
or
voids
can
be
formed
from
a
combination
of
inter
connected
Void
shapes
such
as
ovoid,
ellipsoid
(including
rugby
ball
shaped),
cubic,
cuboid,
parallelepiped,
hyperbo
loid,
conical,
octahedron,
or
other
regular
3D
polygon
shape.
US
2017/0009036A1
0039.
In
yet
other
embodiments,
the
base
geometric
shape
of
the
Voids
comprises
an
optimised
shape,
thus
comprising
an
optimised
shape
Void.
It
is
to
be
understood
that
an
optimised
shaped
Void
is
a
shaped
Void
having
a
configuration
and
shape
derived
from
optimization
algo
rithms,
preferably
bidirectional
evolutionary
structural
optimization
(BESO),
to
provide
the
desired
response
prop
erties.
The
void
shape
is
therefore
has
an
optimised
shape
to
provide
these responses.
Such
optimised
shaped
voids
typi
cally
have
complex
shapes
and
can
comprise
an
amalgama
tion
of
a
number
of
different
regular
shapes.
Furthermore,
optimised
shaped
Voids
can
comprise
two
or
more
separate
void
shapes
within
the
base
unit.
For
example,
a
base
unit
may
include
three
separate
Void
spaces,
the
Void
spaces
being
generally
located
at
the
sides
and one
void
around
the
geometric
center
of
the
base
unit.
Preferably,
the
void
is
shaped
to
assist
in
providing
the
metamaterial
with
at
least
one
of
a
negative
linear
compression
(NLC),
negative
area
compression
(NAC),
Zero
linear
compression
(ZLC),
or Zero
area
compression
(ZAC)
behavior
when
under
pressure.
0040.
As
noted
above,
the
porosity
of
the
metamaterial
and
constituent
base
unit
is
an
essential
factor in
the
defor
mation
characteristics
of
the
metamaterial
of
the
present
invention.
The
porosity
of
the
base
unit
is
typically
config
ured
to
be
between
0.3
and
0.97.
In
preferred
embodiments,
the
porosity
is
between
0.4
and
0.90,
and
more
preferably
between
0.50
and
0.90.
In
some
embodiments,
the
porosity
is
between
0.60
and
0.90.
In
some
embodiments,
the
poros
ity is
between
0.3
and
0.80.
In
some
embodiments,
the
porosity
is
between
0.69
and
0.90.
In
some
embodiments,
the
porosity
is
between
0.50
and
0.97.
In
some
embodi
ments,
the
porosity
is
between
0.60
and
0.97.
0041.
However,
it
should
be
appreciated
that
the
effective
porosity
varies
with
the
shape
of
void
in
the
building
cell.
In
embodiments,
the
void
geometry
of
the
base
unit
is
prefer
ably
be
tailored
to
provide
a
porosity
of
0042
between
0.69
and
0.97
for
a
spherical
shaped
void;
0043
between
0.30
and
0.90
for regular
nonspherical
shaped
Voids;
or
0044)
between
0.3
and
0.98
for
optimised
shaped
voids.
0045.
In
those
embodiments
in
which
the
metamaterial
comprises
a
cubic
base
unit
with
a
spherical
Void,
the
porosity
is
preferably
between
0.69
and
0.97.
In
those
embodiments
in
which
the
metamaterial
comprises
a
cubic
base
unit
with
an
ellipsoid
void,
the
porosity
is
preferably
between
0.3
and
0.875.
In
those
embodiments
in
which
the
metamaterial
includes
an
optimised
shaped
Void
the
porosity
is
between
0.3
and
0.97
for
optimised
shaped
voids,
pref
erably
between
0.40
and
0.90,
and
more
preferably
between
0.50
and
0.90.
0046.
The
base
unit
comprises
a
platonic
solid.
For
optimised
shaped
voids,
the
shaped
void
or
voids
in
the
base
unit
form
spaces
within
that
platonic
solid
which
cut
out
or
shape
the
solid
material
in
the
unit
cell
into
the
required
form
to
provide
the
desired
NLC,
NAC,
ZLC
or
ZAC
property.
For
example,
where
the
base
unit
comprises
a
cube,
opti
mised
shaped
voids
geometries
are
determined
using
opti
mization
algorithms,
for
example
bidirectional
evolution
ary
structural
optimization
(BESO),
to
provide
a
unit
cell
structure
with
those
properties.
0047.
The
base
unit
typically
includes
a
width,
height
and
length.
In
some
embodiments,
at
least
one
dimension
of
the
Jan.
12,
2017
base
geometric
shape
of
the
Void
is
larger
than
at
least
one
of
the
width,
height
or
length
of
the
base
unit.
In
such
embodiments,
the
Void
comprises
a
truncated
form
of
a
base
geometric
shape.
For
example,
where
the
base
geometric
shape
of
the
Void
comprises
a
sphere
and
the
base
unit
comprises
a
cube,
the
diameter
of
the
sphere
can
be
greater
than
the
width, height
and
length
of
the
cubic
base
unit.
Similarly,
where
the
base
geometric
shape
of
the
void
comprises
an
ellipsoid
and
the
base
unit
comprises
a
cube,
selected
diameters
of
the
ellipsoid
can
be
greater
than
the
width, height
and
length
of
the
cubic
base
unit.
The
shape
of
the
void
will
then
be
a
truncated
ellipsoid
shape.
0048.
The
truncation
of
the
base
geometric
shape
forms
openings
in
the
side
of
the
base
unit
shape.
In
preferred
embodiments,
the
Void
includes
an
opening
in
at
least
one,
preferably
two
sides
of
the
base
unit.
For
example,
where
the
base
geometric
shape
of
the
Void
comprises
a
sphere
and
the
base
unit
is
cubic,
the
base
spherical
geometric
shape
would
form
circular
openings
in
each
of
the
side
walls
of
the
cubic
base
unit.
More
preferably,
the
Void
includes
an
opening
in
at
least
two
opposing
sides
of
the
base
unit.
In
this
way,
the
void
space
of
a
first
base
unit
is
interconnected
to
the
void
space
of
at
least
two
adjacent
base
units.
In
some
embodi
ments,
the
Void
includes
at
least
one
opening
in
each
(all)
sides
of
the
base
unit.
0049.
For
the
first
embodiment
of
the
present
invention,
the
configuration
of
the
base
unit,
void
geometry
and
pattern
of
the
matrix
formed from
the
base
units
can
be
tailored
using
a
buckling
mode
obtained
through
Finite
Element
analysis,
so
that
it
provides
a
means
to
control
the
initial
value
of
Poisson’s
ratio
ranging
from 0
to
0.5.
In
this
respect,
the
desired
deformation
state
of
the
material
com
prises
adjacent
voids
being
alternatively
open
and
closed
throughout
the
matrix.
It
can
be
advantageous
to
pattern
the
voids
into that
deformation
pattern
in
order
to
force
the
voids
to
take
that
configuration
when
the
material
is
subject
to
tension
or
compression.
Accordingly,
in
Some
embodiments
the
base
geometric
shape
of
the
Void
comprises
shape
having
a
greater
central
length
than
central
height,
the
shape
having
a
central
length
axis,
the
matrix
of
base
units
being
arranged
such
that
the
central
length
axis
of
the
void
of
each
base
unit
is
perpendicular
to
the
central
length
axis
of
the
void
of
each
adjoining
base
unit.
Preferably,
the
Void
shape
comprises
an
ovoid
or
an
ellipsoid,
more
preferably
an
ovoid.
0050.
In
some
embodiments,
the
metamaterial
can
com
prise
a
threedimensional
matrix
of
at
least
two
different
repeating
base
units,
comprising
a
first
base
unit
comprising
a
platonic
Solid
including
at
least
a
first
shaped
Void
and
a
second
base
unit
comprising
a
platonic
solid
including
a
second
shaped
void.
The
first
base
unit
and
second
base
unit
are
preferably
arranged
in
a
pattern,
preferably
a
regular
pattern
in
the
threedimensional
matrix.
In
some
embodi
ments,
the
first
shaped
void
has
a
different
shape
to
the
second
shaped
Void.
0051.
The
voids
can
have any
suitable
form.
In
some
embodiments,
the
Voids
comprise
an
empty
space
framed
by
the
material
of
the
base
unit.
In
other
embodiments,
the
Voids
are
composed
of a
compressible
material,
preferably
having
a
high
compressibility.
In
yet
further
embodiments,
the
voids
include
at
least
one
fluid,
preferably
at
least
one
liquid.
0052.
Where
the
voids
hold
a
fluid,
it
is
preferred
for
the
geometry
of
the
voids
in
the
base
unit
is
configured
to
allow
the
fluid
flow
through
the
voids
in
the
matrix.
In
some
US
2017/0009036A1
applications
of
the
metamaterial
of
the
present
invention,
filling
such
voids
with a
fluid
where
the
fluid
acts
as
a
dampening
mechanism.
0053.
The
base
unit
material
can
be any
suitable
base
material.
In
some
embodiments,
the
base
unit
material
comprises
a
polymeric
material.
Exemplary
polymeric
mate
rials
include
at
least
one of
an
unfilled
or
filled
Vulcanized
rubber,
natural
or
synthetic
rubber,
crosslinked
elastomer,
thermoplastic
Vulcanizate,
thermoplastic
elastomer,
block
copolymer,
segmented
copolymer,
crosslinked
polymer
ther
moplastic
polymer,
filled
or
unfilled
polymer
or
epoxy.
In
other
embodiments,
base
unit
material
comprises
metallic
and
ceramic
and
composite
materials.
Exemplary
metals
include
aluminium,
magnesium,
titanium,
iron
and
alloys
thereof.
0054.
In
some
embodiments,
the
base
unit
material
com
prises
a
biocompatible
material,
preferably
a
biocompatible
polymeric
material.
0055.
The
structure
and
configuration
of
the
metamaterial
of
the
present
invention
can
be
determined
using
a
number
of
methods.
In
some
embodiments
of
the
present
invention,
the
configuration
of
a
structured
porous
metamaterial
according
to
the
present
invention
is
determined
using
structural
optimisation
algorithms,
such
as a
bidirectional
evolutionary
structural
optimization
(BESO)
modelling
techniques.
0056.
A
second
aspect
of
the
present
invention
provides
a
method
of
determining
the
configuration
of
a
structured
porous
metamaterial
comprising
a
threedimensional
matrix
of
at
least
one
repeating
base
unit,
comprising:
0057
determining
a
base
unit
topology
using
a
struc
tural
optimization
algorithm,
each
base
unit
comprising
a
platonic
Solid
including
at
least
one
shaped
Void,
the
geometry
of
the
at
least
one
shaped
Void
of
each
base
unit
being
tailored
to
provide
a
metamaterial
with
a
porosity
of
between
0.3
and
0.97
and
a
response
comprising
at
least
one
of
0058
a
Poisson’s
ratio
of
0
to
0.5
when
under
tension
and
compression;
or
0059
negative
linear
compression
(NLC),
negative
area
compression
(NAC),
Zero
linear
compression
(ZLC),
or
zero
area
compression
(ZAC)
behaviour
when
under
pressure;
and
0060
simplifying
the
configuration
of
the
at
least
one
shaped
void
of
each
base
unit
to
form
a
structural
base
unit;
and
0061
forming
a
threedimensional
matrix
from
an
array
of
at
least
eight
structural
base
units.
0062.
Whilst
a
number
of
any
suitable
structural
optimi
sation
algorithm
or
techniques
could
be
used,
in
preferred
embodiments,
the
configuration
of
the
shaped
Voids
within
each
base
unit
is
derived
from
a
bidirectional
evolutionary
structural
optimization
(BESO)
model.
0063.
The
step
of
simplifying
the
configuration
of
the
at
least
one
shaped
Void
of
each
base
unit
is
aimed
at
simpli
fying
and/or
optimizing
the
configuration
of
the
base
unit
and
resulting
matrix
for
3D
printing
construction.
This
step
therefore
preferably
comprises
reconfiguring
the
topology
of
the
shaped
Void
or
voids
to
have
a
more
regular
geometric
shape.
This
simplified
configuration
is
typically
more
Suit
able
for
3D
printing
construction.
0064.
It
should
be
appreciated
that
this
method
is
suitable
for
forming
a
structured
porous
metamaterial
according
to
the
first
aspect
of
the
present
invention.
The
method of
this
Jan.
12,
2017
second
aspect
is
particularly
suitable
for
forming
metama
terial
of
the
second
embodiment
of
the
first
aspect
of
the
present
invention
comprising
optimised
shaped
Voids
which
provide
a
structured
porous
metamaterial
having
a
negative
linear
compression
(NLC),
negative
area
compression
(NAC),
Zero
linear
compression
(ZLC),
or
Zero
area
com
pression
(ZAC)
behavior
when
under
pressure.
0065.
The
metamaterial
of
the
present
invention
has
potential
to
be
used
as
a
mechanism
for
redistributing
the
base
material
of
the
metamaterial
according
to
the
external
loads
so
as
to
support
external
loading
more
effectively.
Such
a
designed
structural
anisotropy
can
guide
the
loading
into
certain
directions.
Thus,
this
type
of
metamaterial
could
be
designed
to
create
complex
stressstrain
paths
to
protect
a
certain
internal
Volume.
0066.
The
tunable
Poisson’s
ratio
and/or
compressibility
of
the
present
invention are
a
result
of
determining
the
deformation
characteristics
of
the
metamaterial during
buck
ling
of
the
structure
when
a
force,
preferably
a
compression
force
or
pressure
is
applied
to
the
material.
This
can
be
determined
using
a
standard
buckling
analysis
of
the
mate
rial,
in
which
the
deformation
mechanism
is
determined.
The
deformation
characteristics
at
buckling
are
termed
the
“buckling
mode'
of
the
base
unit.
The
buckling
mode
provides
the
structure
of
deformation
of
the
material.
Once
the
buckling
mode
is
determined,
the
structure
of
the
base
unit
and
more
preferably
of
the
void
can
then
be
modified
to
change
(enhance
or
inhibit)
the
initial
microstructure
of
the
initial
metamaterial
and
thus
change/tune
properties
of
the
metamaterial
such
as
the
value
of
Poisson’s
ratio,
effective
strain
range
and/or
compressibility
for
the
desired
NPR,
NLC,
NAC,
ZLC,
and/or
ZAC
behaviour
of
the
material.
0067.
The
present
invention
provides
in
a
third
aspect,
a
method
of
tuning
the
value
of
Poisson’s
ratio
and
effective
strain
range
of
a
metamaterial
according
to
the
first
aspect
of
the
present
invention.
The
method
includes
the
steps
of:
0068
identifying the
localized
buckling
mode
of
the
metamaterial
under
compression
through
standard
buckling
analysis;
0069
determining
the
representative
volume
element
of
the
metamaterial
and
the
deformation
mechanism
thereof
during
buckling;
0070
determining
a
range
of
values
of
shape
change
of
the
representative
volume
element
which
modify
the
defor
mation
mechanism
thereof;
0071
modifying
the
original
base
unit
by
superposition
of
the localized
buckling
mode
of
the
metamaterial
with
a
selected
magnitude
of
shape
change
in
the
representative
volume
unit
thereby
enabling
the
value
of
the
Poisson’s
ratio
and
effective
strain
range
of
the
metamaterial
to
be
tuned
to
a
desired
value.
(0072
Preferably,
the
shape
of
the
void
of
the
base
unit
is
altered
to
modify
the
configuration
of
the
base
unit.
BRIEF
DESCRIPTION
OF
THE
DRAWINGS
(0073.
The
present
invention
will
now
be
described
with
reference
to
the
figures
of
the
accompanying
drawings,
which
illustrate
particular
preferred
embodiments
of
the
present
invention,
wherein:
0074
FIG.
1A
provides
the
geometric
configurations
for
a
comparative
three
dimensional
structure
porous
material
without
negative
Poisson’s
ratio
showing
(A)
the
base
cell
unit;
(B)
a
block
of
the
comparative
material
comprising
an
US
2017/0009036A1
8x8x8
matrix
of
the
base
unit;
and
(C)
representative
Volume
unit
of
the
comparative
material.
0075
FIG.
1B
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
according
to
the
first
embodiment
of
the
present
invention
showing
(A)
the
base
cell
unit;
(B)
a
block
of
the
inventive
metamaterial
comprising
an
8x8x8
matrix
of
the
base
unit;
and
(C)
representative
volume
unit
of
the
inventive
metamaterial.
0076
FIG. 2
provides
photographs
of
samples
of
the
metamaterial
shown
in
FIG.
1B
(A)
with
supporting
material
fabricated
using
3D
printing
and
(B)
without
Supporting
material
fabricated
using
3D
printing.
0077
FIG.
3A
shows
the
deformation
patterns
and
thus
buckling
model
for
materials
with
(A)
comparative
a
face
centred
cubic
cell
(volume
fraction:
51.0%)
and
(B)
a
cubic
building
cell
according
to
the
present
invention
(volume
fraction:
12.6%).
0078
FIG.
3B
provides
a view of
forcedisplacement
response
of
inventive
metamaterial
in
two
different
direc
tions
D1
and
D2.
007.9
FIG.
3C
provides a
comparison
of
nominal
stress
strain
curve
of
comparative
structure
porous
material
with
facecentred
cubic
cell
along
three
different
loading
direc
tions.
0080
FIG.
4
provides a
comparison
of
deformation
pat
tern
of
inventive
metamaterial
(volume
fraction:
12.6%,
load
direction:
D2
(FIG.
3),
strain
rate:
10
s)
between
(A)
experiment
and
(B)
finite
element
model.
0081
FIG.
5
provides
a
comparison
of
nominal
stress
strain
curve
of
inventive
metamaterial
between
experiment
and
finite
element
model
for
spherical
voids
and
slightly
ovoid
shaped
Voids
shaped
(spherical
with
imperfection).
0082
FIG.
6 provides a
comparison
of
deformation
pat
tern
of an
embodiments
of
the
inventive
metamaterial
including
slightly
ovoid
shaped
Voids
(Volume
fraction:
12.6%,
strain
rate:
10s)
between
(A)
experiment
and
(B)
finite
element
model.
0083
FIG.
7A
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
tetrahedron
in
cube
building
cell,
showing
(A)
the
base
cell
unit;
(B)
a
block
of
the
inventive
metamaterial
comprising
an
8x8x8
matrix
of
the
base
unit;
and
(C)
an
isometric
view
of
the
representative
volume
unit
of
the
inventive
metama
terial.
0084
FIG.
7B
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
ellipsoid
in
cube
building
cell,
showing
(A)
the
base
cell
unit;
(B)
a
block
of
the
inventive
metamaterial
comprising
an
8x8x8
matrix
of
the
base
unit;
and
(C)
an
isometric
view
of
the
representative
volume
unit
of
the
inventive
metama
terial.
I0085
FIG.
8A
provides
the
deformation
pattern
for
the
metamaterial
shown
in
FIG.
7A
under
load,
showing
(A)
deformation
pattern
for
bulk
material
(8x8x8)
in
XZ
plane;
(B)
deformation
pattern
for
bulk
material
(8x8x8)
in
yZ
plane;
(C)
deformation
pattern for the
representative
volume
unit
(2x2x2)
in
XZ
plane;
and
(D)
an
isometric
view
of
the
deformation
pattern
of
the
representative
volume
unit
(2x2x
2).
I0086
FIG.
8B
provides
the
deformation
pattern
for
the
metamaterial
shown
in
FIG.
7B
under
load,
showing
(A)
deformation
pattern
for
bulk
material
(8x8x8)
in
XZ
plane;
(B)
deformation
pattern
for
bulk
material
(8x8x8)
in
yZ
plane;
(C)
deformation
pattern for the
representative
volume
Jan.
12,
2017
unit
(2x2x2)
in
XZ
plane;
and
(D)
an
isometric
view
of
the
deformation
pattern
for the
representative
volume
unit
(2x2x2).
I0087
FIG.
9
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
NLC
according
to
the
second
embodiment
of
the
present
inven
tion
showing
(A)
the
optimised
building
cell
from
BESO;
(B)
the
simplified
building
cell
unit;
and
(C)
a
block
of
the
comparative
material
comprising
an
8x8x8
matrix
of
the
building
cell
unit.
I0088
FIG.
10
provides
a
comparison
of
deformation
pattern
of
inventive
NC
metamaterial
with
NLC
shown
in
FIG.
9
between
(A)
experiment
and
(B)
finite
element
model;
and
(C)
Comparison
of
strainpressure
history
between
FE
results
and
experimental
data
for
NLC
material
under
pressure.
I0089
FIG.
11
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
NAC
according
to
the
second
embodiment
of
the
present
invention
showing
(A)
the
optimised
half
building
cell
from
BESO;
(B)
the
optimised
building
cell
from
BESO;
(C)
the
simplified
building
cell
unit;
and
(D)
a block
of
the
material
comprising
an
8x8x8
matrix
of
the
building
cell
unit.
0090
FIG.
12
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
ZLC
according
to
the
second
embodiment
of
the
present
inven
tion
showing
(A)
the
optimised
half
building
cell
from
BESO;
(B)
the
optimised
building
cell
from
BESO;
(C)
the
simplified
building
cell
unit;
and
(D)
a block
of
the
material
comprising
an
8x8x8
matrix
of
the
building
cell
unit.
0091
FIG.
13
provides
the
geometric
configurations
for
a
three
dimensional
structure
porous
metamaterial
with
ZAC
according
to
the
second
embodiment
of
the
present
inven
tion
showing
(A)
the
optimised
half
building
cell
from
BESO;
(B)
the
optimised
building
cell
from
BESO;
(C)
the
simplified
building
cell
unit;
and
(D)
a block
of
the
material
comprising
an
8x8x8
matrix
of
the
building
cell
unit.
DETAILED
DESCRIPTION
0092.
The
present
invention generally
relates
to
a
series
of
3D
structured
porous
metamaterial
with
specific
defor
mation
pattern
under
applied
loading,
and
more
particularly
a
3D
structured
porous
metamaterial
having
at
least
one
of
0.093
a
negative
Poisson’s
ratio
under
uniaxial
tensile
or
compression; and/or
0094
Zero
or
negative
compressibility
under
uniform
pressure,
such
as
negative
linear
compressibility
(NLC),
negative
area
compressibility
(NAC),
Zero
lin
ear
compressibility
(ZLC)
and/or
Zero area
compress
ibility
(ZAC).
0.095
The
initial
design
of
the
microstructure
of an
auxetic
metamaterial
form
of
the
present
invention
origi
nates
from
using
a
threedimensional
repeating
matrix
formed
from
a
base
unit
comprising
a
platonic
solid
Such
as
a
cube
having
a
shaped
Void
space
Such
as
a
sphere
or
ellipsoid.
The
platonic
solid
provides
a
repeatable
and
stackable
base
structure,
and
the
shaped
Void
imparts
the
required
characteristic
to
the
Void
space
and
the
Surrounding
base
unit
framework
structure
(around
the
Void).
The
void
geometry
of
each base
unit
is
tailored to
provide
a
porosity
of
between
0.3
and
0.97;
and
provide
the
metamaterial
with
a
response
under
tension
and
compression
having
a
Pois
son's
ratio
of
0
to
0.5.
The
specific
porosity
depends
on
the
type
of
shaped
void
used.
Therefore
the
porosity
is
typically
US
2017/0009036A1
between
0.69
and
0.97
for
a
spherical
shaped
void;
between
0.30
and
0.90
for
regular
nonspherical
shaped
voids;
or
between
0.3
and
0.97
for
optimised
shaped
voids.
Further
more,
as
will
be
explained
in
more
detailed
below
with
reference
to
specific
example
material
configurations,
this
structure
imparts
a
tailored
deformation
character
to
the
material,
with
the
negative
Poisson’s
ratios
achieved
through
the
a
specific
deformation
characteristic
of
the
voids
(alternating
opening
and
closing
pattern
of
adjacent
voids)
in
the
material
combined
with the
spatial
rotation
and
transla
tion
of
a
rigid
part
of
base
unit
material
accompanied
by
the
bending
and
stretching
of
the
thinner
or
more
flexible part
of
the
base
unit
material.
0096.
The
initial
design
of
the
microstructure
of
the
Zero
or
negative
compressibility
(NC)
metamaterial
form
of
the
present
invention
originates
from
using
a
threedimensional
repeating
matrix
formed
from a
base
unit
comprising
a
platonic
Solid,
such
as
a
cube,
having
one
or
more
shaped
void
spaces.
The
shape
of
the
voids
within
that
base
unit
and
thus
the
topology
of
those
building
unit
is
derived
from
a
bidirectional
evolutionary
structural
optimization
(BESO)
model
formed