U.S. Patent Oct. 18, 2022 Sheet 18 of 19 US 11,475,185 B2

E Unpruned: Pruned tnstromented (A)
406 , as OA 3e drop mass
E & & Shore-A 70 ‘
30E
‘ E j Sample
20: Y "
be : Force
TEe* transducer
0 /
z =

Transmitted Force, P

0 0.02 0.04 0.06 0.08
Time, ¢ (s)

FIG. 18


U.S. Patent Oct. 18, 2022 Sheet 12 of 19 US 11,475,185 B2

(B)

FIG. 12

(A)


US 11,475,185 B2

5
DETAILED DESCRIPTION.

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion,

It has been discovered that an inverse design machine
produces a designer impact-mitigating architectured isotro-
pic structure for a manufactured article that is made by a
manufacturing machine. The designer impact-mitigating
architectured isotropic structure is an aperiodic structure that
has tunable global mechanical properties. The inverse
design machine and method of operating the manufacturing
machine for the manufactured article with the aid of the
inverse design machine provides rapid discovery and gen-
eration of such designer materials for impact mitigation
applications.

In the designer impact-mitigating architectured isotropic
structure, the aperiodic arrangement of elastic elements
provides impact-mitigating propertis
machine and processes herein use an inverse design
approach for determining the designer impact-mitigating
architectured isotropic structure, wherein the impact-miti-
gating properties can include materials properties such as a
Young’s modulus, shear modulus, bulk modulus, Poisson’s
ratio, density, acoustic impedance and the like. The designer
impact-mitigating architectured isotropic structure is deter-
mined via selective pruning to produce designer impact-
mitigating architectured isotropic structure with the impact-
mitigating properties that is used to produce the
manufactured article with the designer impact-mitigating
architectured isotropic structure via additive manufacturing.

Selective pruning subjects a disordered primary structure
that includes a network of nodes connected by bonds with an
intrinsic set of primary properties that are characterized by
potential energy density functions of bond stretching and
bond bending. A structure adjuster prunes primary structure
by removing specific bonds that contribute, e.g., to bulk
modulus of manufactured article, providing designer
impact-mitigating architectured isotropic structure with the
isotropic mechanical properties referred to as impact-miti-
gating properties.

Inverse design machine 214 is used in making manufac-
tured article 208 that includes designer impact-mitigating
architectured isotropic structure 200. In an embodiment,
with reference to FIG. 4, primary designer 217 provides
ptimary structure 207 and manufactured article 208 that
includes the primary structure 207 to inverse design machine

214 that produces designer impact-mitigating architectured °

isotropic structure 200 from structural analysis of manufac-
tured article 208 with primary structure 207 and adjustment
of to produce designer impact-mitigating architectured iso-
tropic structure 200. Manufacturing machine 224 receives

The inverse design 2

&

&

designer impact-mitigating architectured isotropic structure

200 and manufactures manufactured article 208 that
includes designer impact-mitigating architectured isotropic
structure 200 instead of primary structure 207. Accordingly,
manufactured article 208 has greater impact mitigation with
designer impact-mitigating architectured isotropic structure
200 than with primary structure 207.

In an embodiment, with reference to FIG. 4 and FIG. 5,
inverse design machine 214 includes: input unit 215 that
receives primary structure 207; primary structure analyzer
219 in communication with input unit 215 and that receives
primary structure 207 from input unit 215 and determines

6

primary properties 220 of primary structure 207 from pri-
mary structure 207; structure adjuster 221 in communication
with primary structure analyzer 219 and that receives pri-
mary properties 220 from primary structure analyzer 219,
receives impact-mitigating properties 222 from structural
property manager 223, and produces designer impact-miti-
gating architectured isotropic structure 200 for manufac-
tured article 208 from primary properties 220 and impact-
mitigating properties 222; and structural property manager
223 in communication with structure adjuster 221 and that
provides impact-mitigating properties 222 to structure
adjuster 221. According to an embodiment, inverse design
machine 214 includes primary designer 217 in communica-
tion with input unit 215 and that produces primary structure
207.

In an embodiment, inverse design machine 214 includes
manufacturing machine 224 in communication with struc-
ture adjuster 221 of inverse design machine 214 and that
receives designer impact-mitigating architectured isotropic
structure 200 from structure adjuster 221 and produces
manufactured article 208 including designer impact-mitigat-
ing architectured isotropic structure 200 from inverse design
machine 214. It is contemplated that manufacturing machine
224 includes a three-dimensional printer that three-dimen-
sionally prints manufactured article 208 from designer
impact-mitigating architectured isotropic structure 200 pro-
vided by inverse design machine 214. Moreover, manufac-
tured article 208 can include, e.g., a polymer printed by
manufacturing machine 224.

In an embodiment, with reference to FIG. 3, manufac-
tured article 208 includes disordered-network mechanical
material 236 that includes bonds 237 and nodes 238. With
reference to FIG. 2, primary structure 207 provides a three-
dimensional reticulated structure of nodes 201 intercon-
nected by bonds 202 with interstitial spaces 203 separating
proximate nodes 201 interconnected with bonds 202 in
disordered-network mechanical material 236. Although
manufactured article 208 can be made from primary struc-
ture 207, under that circumstance, manufactured article 208
has mechanical properties of primary structure 207 that are
referred to as primary properties 220. To increase impact
mitigation of manufactured article 208, primary structure
207 is replaced by designer impact-mitigating architectured
isotropic structure 200 in manufactured article 208, wherein
designer impact-mitigating architectured isotropic structure
pact-mitigating properties 222 that have greater
ation than primary properties 220. With refer-
ence to FIG. 1 and FIG. 2, designer impact-mitigating
architectured isotropic structure 200 also includes a three-
dimensional reticulated structure of nodes 201 intercon-
nected by bonds 202 with interstitial spaces 203 separating
proximate nodes 201 interconnected with bonds 202 in
disordered-network mechanical material 236, wherein cer-
tain bonds 202 in primary structure 207 are pruned to arrive
at designer impact-mitigating architectured isotropic struc-
ture 200.

Manufactured article 208 with designer impact-mitigating
architectured isotropic structure 200 provides impact miti-
gation to an object (e.g., a 3D structure fabricated from a
polymeric, metallic, ceramic, or composite materials)
designed to protect either individual (e.g., human or animal)
ora physical object (protective structures to be integrated in
vehicles, buildings, packaging materials) on which manu-
factured article 208 is disposed. Manufactured article 208
with designer impact-mitigating architectured isotropic
structure 200 instead of primary structure 207 can be
selected to be various types of articles including body armor,



U.S. Patent Oct. 18, 2022 Sheet 3 of 19 US 11,475,185 B2

FIG. 3


US 11,475,185 B2

27

6. The method of claim 5, wherein the manufactured
article comprises a polymer that is printed by the manufac-
turing machine.
7. The method of claim 6, wherein the manufacturing
machine comprises a three-dimensional printer.
8. A method of operating a manufacturing machine for
manufactured article with aid of an inverse design machine,
comprising:
providing the inverse design machine with a primary
structure for a manufactured article and with impact-
mitigating properties for the manufacturing machine,

the primary structure comprising a plurality of structural
members arranged in the primary structure that collec-
tively provide primary properties to the manufactured
article and that comprise a primary shear modulus and
a primary bulk modulus that provide a primary tor-
sional rigidity and a primary compression rigidity of
the manufactured article being made by the manufac-
tured article; and

10

the impact-mitigating properties comprising an impact- ~

mitigating shear modulus and an impact-mitigating
bulk modulus that provide an impact-mitigating tor-
sional rigidity and an impact-mitigating compression
rigidity for the manufactured article being made by the
manufacturing machine, such that the impact-mitigat-
ing properties provide the manufactured article with
greater structural impact mitigation than the primary
properties;

receiving the primary structure from a primary designer;

initiating a point-by-point analysis on the primary struc-
ture in the inverse design machine;

determining the primary properties of the primary struc-
ture with a primary structure analyzer of the inverse
design machine;

receiving, by a structure adjuster of the inverse design
machine, the primary properties from the primary
structure analyzer and the impact-mitigating properties
from a structural property manager of the inverse
design machine;

adjusting, by the structure adjuster, the structural mem-
bers in the primary structure until the structural mem-
bers collectively conform to the impact-mitigating
properties such that the primary structure is structurally
modified into a designer impact-mitigating architec-
tured isotropic structure that comprises the impact-
mitigating properties;

controlling the operation manufacturing machine in
accordance with the designer impact-mitigating archi-

tectured isotropic structure by the inverse design ;

machine;
initiating formation of the manufactured article by con-
trolling a position of a print head of the manufacturing

4

28

machine under control of the inverse design machine in
accord with the designer impact-mitigating architec-
tured isotropic structure

constantly determining the position of the print head of
the manufacturing machine during formation of the
manufactured article;

constantly providing the inverse design machine with the
position of the print head;
repetitively performing in the inverse design machine, at
frequent intervals during formation of the manufac-
tured article, corrections to the position of the printer
head based on designer impact-mitigating architectured
isotropic structure and to monitor completion of for-
mation of the manufactured article by the manufactur-
ing machine
communicating corrections to the position of the printer
head from the inverse design machine to the manufac-
turing machin

correcting the position of the printer head by the manu-
facturing machine based on the corrections received
from the inverse design machine; and

completing formation, by the manufacturing machine

under control of the designer impact-mitigating archi-
tectured isotropic structure from the inverse design
machine, the manufactured article that comprises the
designer impact-mitigating architectured isotropic
structure instead of the primary structure.

9. The method of claim 8, wherein the manufactured
article comprises a disordered-network mechanical material
that comprises bonds and nodes, and the primary structure
provides a three-dimensional reticulated structure of nodes
interconnected by bonds with interstitial spaces separating
proximate nodes interconnected with bonds in the disor-
dered-network mechanical material.

10. The method of claim 9, wherein adjusting the struc-
tural members in the primary structure comprises structural
pruning of the disordered-network mechanical material.

11. The method of claim 10, wherein adjusting the struc-
tural members in the primary structure further comprises
global node position optimization of the disordered-network
mechanical material to produce the designer impact-miti-
gating architectured isotropic structure.

12. The method of claim 8, wherein forming the manu-
factured article comprises three-dimensional printing the
manufactured article from the designer impact-mitigating
architectured isotropic structure provided by the inverse
design machine.

13. The method of claim 12, wherein the manufactured
article comprises a polymer that is printed by the manufac-
turing machine.

14, The method of claim 13, wherein the manuf
machine comprises a three-dimensional printer.

*

cturing

ee ee


U.S. Patent Oct. 18, 2022 Sheet 19 of 19 US 11,475,185 B2

FIG. 19


US 11,475,185 B2

11

should be changed to drive the achieve the targeted impact-
mitigating properties. Based on this analysis, the structure
adjuster 221 decides which element should be changed.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, adjusting, by structure adjuster 221, structural
members in primary structure 207 until structural members
collectively conform to impact-mitigating properties 222
such that primary structure 207 is structurally modified into
designer impact-mitigating architectured isotropic structure
200 that includes impact-mitigating properties 222 can be
performed by repeating the point-by-point analysis based on
engineering mechanics, presumable using finite element
methods, to compare the new impact mitigation properties
of the modified structure produced by the structural property
manager 223 to the targeted impact mitigating properties
222.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, controlling operation manufacturing machine
224 in accordance with designer impact-mitigating archi-
tectured isotropic structure 200 by inverse design machine
214 can occur by outputting the optimized modified struc-
ture created by the structure adjuster 221 as an industry

standard CAD, STL or solids model that is compatible with 2

the manufacturing machine 224.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, initiating formation of manufactured article
208 by controlling position of print head of manufacturing
machine 224 under control of inverse design machine 214 in
accord with designer impact-mitigating architectured isotro-
pic structure 200 can occur by sending the CAD, STL, or
solids model as an output to the manufacturing machine.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, constantly determining a position of print head
of manufacturing machine 224 during formation of manu-
factured article 208 can occur through process control and
feedback loops of manufacturing machine 224. These
machine control and feedback loops can be integrated into
the given manufacturing machine. Elements herein can
conform to industry standard CAD, STL or other solids
models used in manufacturing.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, constantly providing inverse design machine
214 with position of the print head can occur through the
process control and feedback loops of the manufacturing

machine 224. These machine control and feedback loops can 5

be integrated into the manufacturing machine. Elements

herein can interface with and conform to industry standard

CAD, STL or other solids models used in manufacturing.
In the method for operating manufacturing machine 224

for manufactured article 208 with the aid of inverse design 5

machine 214, repetitively performing in inverse design
machine 214, at frequent intervals during formation of
manufactured article 208, corrections to position of printer
head based on designer impact-mitigating architectured iso-
tropic structure 200 and to monitor completion of formation
of manufactured article 208 by manufacturing machine 224
can occur through the process control and feedback loops of
the manufacturing machine 224. These machine control and
feedback loops can be integrated into the manufacturing
machine. Elements herein can interface with and conform to
industry standard CAD, STL or other solids models used in
manufacturing.

20

&

&

12

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, communicating corrections to position of
printer head from inverse design machine 214 to manufac-
turing machine 224 can occur through the process control
and feedback loops of the manufacturing machine 224.
These machine control and feedback loops can be integrated
into the manufacturing machine. Elements herein can inter-
face with and conform to industry standard CAD, STL or
other solids models used in manufacturing.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, correcting position of printer head by manu-
facturing machine 224 based on corrections received from
inverse design machine 214 can occur through the process
control and feedback loops of the manufacturing machine
224. These machine control and feedback loops can be
integrated into the manufacturing machine. Elements herein
can interface with and conform to industry standard CAD,
STL or other solids models used in manufacturing.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, completing formation, by manufacturing
machine 224 under control of designer impact-mitigating
architectured isotropic structure 200 from inverse design
machine 214 can occur through the process control and
feedback loops of the manufacturing machine 224. These
machine control and feedback loops can be integrated into
the manufacturing machine. Elements herein can interface
with and conform to industry standard CAD, STL or other
solids models used in manufacturing.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, structural pruning of disordered-network
mechanical material 236 can occur by having structure
adjustor 221 use results of point-by-point analysis from the
engineering mechanics to analyze the contribution of each
structural bond 202 to the shear and bulk modulus. Based on
this analysis, the structure adjuster 221 decides which bonds
202 should be removed to drive the achieve the targeted
impact-mitigating properties. Based on this analysis, the
structure adjuster 221 decides which bond should be pruned.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, global node position optimization of disor-
dered-network mechanical material to produce designer
impact-mitigating architectured isotropic structure 200 by
having the structure adjustor using the results of the point-
by-point analysis from the engineering mechanics to analyze
the contribution of each nodes 201 to the shear and bulk
modulus. Based on this analysis, the structure adjuster 221
calculates which node can be spatially shifted to drive the
achieve the targeted impact-mitigating properties. Based on
this analysis, the structure adjuster 221 decides which node
should be shifted.

Designer impact-mitigating architectured isotropic struc-
ture 200, and processes disclosed het have numerous
uses and can be used in various manufactured
articles, including shoe soles to absorb impact customized
for an individual gate, stride and weight characteristics,
helmet liners for sporting equipment and transportation that
can decouple rotational and translation impact loading to
reduce mild brain trauma, the customized design of impact
mitigating components in structures for vehicles or protec-
tive equipment to redirect they loading upon impact, pro-
tective foams or packing materials for shipping and trans-
portation of delicate articles, or any other type of mechanical



US 11,475,185 B2

3

design machine comprises: an input unit that receives a
primary structure; a primary structure analyzer in commu-
nication with the input unit and that receives the primary
structure from the input unit and determines primary prop-
erties of the primary structure from the primary structure; a
structure adjuster in communication with the primary struc-
ture analyzer and that receives the primary properties from
the primary structure analyzer, receives impact-mitigating
properties from a structural property manager, and produces
the designer impact-mitigating architectured isotropic struc-
ture for the manufactured article from the primary properties
and the impact-mitigating properties; and the structural
property manager in communication with the structure
adjuster and that provides the impact-mitigating properties
to the structure adjuster.

BRIEF DESCRIPTION OF THE DRAWINGS

‘The following description cannot be considered limiting

in any way. With reference to the accompanying drawings,

like elements are numbered alike.

FIG. 1 shows a designer Impact-mitigating architectured
isotropic structure after pruning the primary structure shown.
in FIG. 2;

FIG. 2 shows a primary structure;

FIG. 3 shows a manufactured article;

FIG. 4 shows a manufacturing system that includes an
inverse design machine;

FIG. 5 shows an inverse design machine;

FIG. 6 shows a process for making a designer impact-
mitigating architectured isotropic structure;

FIG. 7 shows a process for making a manufactured article
that includes a designer Impact-mitigating architectured
isotropic structure;

FIG. 8 shows changes in A) Poisson’s ratio, B) bulk
modulus, B, and C) shear modulus, G, during bond pruning
and node position optimization. Left panels show bond
pruning; right panels show node position optimization fol-
lowing the pruning except the blue curves. The black curves
are corresponding to pruning protocol I, namely, bonds
leading to min AG are permanently removed; the lightest
curves are corresponding to pruning protocol II, namely,
bonds leading to min Av are permanently removed; the grey
curves denote node position optimization directly from a
network from packing;

FIG. 9 shows effects of angle bending resistance on node
position optimization. The changes in Poisson’s ratio A), B)
and C) and moduli D), E) and F) during node position
optimization. The solid curves are for

ke
7, 70.001:

The dashed curves are for

k
ZF =001;

The dotted curves are for

3

&

&

5

s

at

6:

4

The black curves in B) show bulk modulus, and the red
curves in B) show shear modulus. resistance, the higher is
the plateaued value of the bulk modulus after optimization,
which may originate from the nonaifine nature of the shear
deformation in disordered networks:

FIG. 10 shows decomposition of bulk modulus (A), B)
and C)) and shear modulus (D), E) and F)) into bond
stretching and angle bending resistance at

fe 0,001 (A) and D)), § =0.01 (B) and E)) ana *
H = 0.001 (A) and D)), & =001 (B) anf) and

Out (©) and Fk

FIG. 11 shows bond length distribution of non-optimized
(blue curve) and optimized (red curve) networks;

FIG. 12 shows experimental networks with tracked points
A) without global node position optimization and B) after
global node position optimization under uniaxial compres-
sion up to a strain of €.=0.1. in the compression tests in the
current simulation model:

FIG. 13 shows trajectories of tracked points for networks
A) without global node position optimization and B) after
global node position optimization obtained from simulation

5 (red) and experimental (blue) measurements of uniaxial

compression up to a 17% compressive strain;

FIG. 14 shows Poisson’s ratio as a function of vertical
strain obtained from uniaxial compression in simulations
(red curve) and experiments (blue curve);

FIG. 15 shows impact behavior of representative
unpruned versus pruned networks for a) Free-body diagram
of target (m,,k,)-impact mitigator (m,,,k,,) system. b) Images
of the unpruned and pruned 3D-printed disordered networks.
c) Representative deformation behavior of the unpruned and
pruned networks during linear impact experiments. The
dashed lines are guides to help visualize the lateral expan-
sion (x-axis) of networks due to the uniaxial compression in
the y-direction;

FIG. 16 shows mechanical response to impact of repre-
sentative of a 3D printed elastomeric resin with a Shore-A
30 hardness, a) Poisson’s ratio (v) as a function of true
compressive strain (¢,,) of the unpruned-DNMM (top plot)
and pruned-DNMM (bottom plot). b) True stress (,,) vs.
true compressive strain (e,,) curves of the unpruned-DNMM
(top plot) and pruned-DNMM (bottom plot) as a function of
impact velocity (v), c) The elastic modulus E of unpruned-
DNMM (top plot) and pruned-DNMM as a function of
impact velocity, v. d) Elastic modulus (E) of pruned and
unpruned DNMMs for the range of impact velocities tested.
Increasing marker size indicates increasing velocity;

FIG. 17 shows tuning mechanical impedance of different
constituent materials (Shore-A 30, Shore-A 50 and Shore-A.
70) via pruning. a) Comparison of the elastic modulus (F) as
a function of density of network (p) of the unpruned and
pruned DNMMs for different constituent materials. b) Spe-
cific acoustic impedance (z) versus density of network (p) at
€,,-0 of the unpruned and pruned DNMMs. Marker size
indicates impact velocity ranging from v=0.1 m/s (smallest)
to v=1.5 m/s (largest); and

FIG. 18 shows drop mass experiments of the unpruned
and pruned networks. Transmitted force (Pt), measured by
the force transducer beneath the DNMM, as a function of
time (t) of the unpruned and pruned networks 3D printed
with Shore-A 30, 50 and 70. The inset figure illustrates the
drop mass experiment; and

FIG. 19 shows a graph of force versus compressive true
strain.



U.S. Patent Oct. 18, 2022 Sheet 16 of 19 US 11,475,185 B2

a
“8
£
baa
=
4 aS

g

OQ Gas) g ‘sompeyy

FIG. 16

AYRE SMORIO


U.S. Patent Oct. 18, 2022 Sheet 8 of 19 US 11,475,185 B2

wee Direct optimization

Pruning : Optimization
‘
(A) ——- Protocol | Fe Opt after protocol |
Protocol ff Opt after protocal fl
I

€
B
w
uw
=)

Paisson's ratio, v
i t

Fr Oo Oo ©
Oo Mw Oo

pot
Ww Oo
Oo 2

Bulk modulus,

Q

ics)

be
oQ

Shear modulus, G
Ped
oO

kan

0 100 200 0103036
Removed bonds Opt steps

FIG. 8


US 11,475,185 B2

23

Mitigating the transmitted pressure waves due to impact
can be achieved via reduction in the specific acoustic
impedance of the materials, which is a function of p and E
(Eq. 3). The pruning process reduces both the density (p),
and elastic constants (E, K, 2) since bonds and nodes are
intentionally removed from the network, which also leads to
an associated change in v due to its relationship to K and jt.
To quantify F of the unpruned and pruned DNMMs, we fit
the small-strain region of the stress-strain curves (FIG. 165)
with a linear elastic model. Impact tests were also conducted
along the three principal axes for the DNMMs. We observed
no significant differences in the stress-strain curves along the
principal axes for each network thus indicating that both the
unpruned and pruned DNMMs can be assumed to be
mechanically isotropic.

FIG. 16d summarizes how E and p change as a function
upon pruning for all impact velocities, and we find that the
E~p” with n~3.3. This is a remarkable result when compar-
ing it to the scaling of stochastic open cell foams, where n>2.

We find a decade reduction in K when comparing the pruned 2

versus the unpruned DNMMs. This result demonstrates that
pruning is a rational approach for tuning the extrinsic
materials properties of this class of mechanical metamate-
rials.

Next, we printed the same unpruned and pruned DNMMs 2

using other constituent materials and conducted identical
impact tests on them. FIG. 17a shows the results from the
impact tests of these networks summarizing the change in E
as a function of p, impact velocity and different constituent
materials (with Shore-A hardness=30, 50 and 70). The
effective E increases with increasing impact velocity, and
this change is independent of the constituent material or
pruning. These results suggest that pruning enables a similar
degree of tunability of the elastic constants of the DNMM
irrespective of the constituent material. Specifically, we find
that switching the print material (from Shore-A hardness 30
to 70) increased the effective E of unpruned-DNMMs from
~10° kPa to ~10° kPa. Upon pruning, we observe a decade
reduction in E for each impact velocity and constituent
material. The scaling exponent of elastic modulus with
density is again significantly higher (~3) compared to sto-
chastic open-cell foams. These results show that incorpo-
rating disordered architectures into a material via pruning
enables control over its elastic properties that is independent
of the starting material, which is a characteristic that cannot
be achieved in traditional polymeric foam design.

This significant reduction in the effective el constants
also translates to changes in z. We use Eq. 3 and p at €,,=0
to estimate z of the DNMMs (FIG. 175) to show that the

predicted reduction in z for the pruned DNMMs is indepen- 5

dent of the intrinsic materials properties of the constituent
material. To experimentally demonstrate that pruning
changes z of the network, we performed drop mass experi-
ments on the unpruned-DNMM and pruned DNMM samples

printed using the Shore-A 30, 50 and 70 materials. For the

experiment, a 2 kg mass was dropped from a height of 50
mm and the transmitted force (P,) was measured using a
force transducer mounted directly underneath the DNMM.
FIG. 18 compares the transmitted force (P,) as a function of
the duration of the impact (t) of the unpruned and pruned
networks for each of the constituent materials. A comparison
of the first impact peaks shows that the pruned-DNMM
reduces P, by approximately 33% to 48% relative to that of
the unpruned-DNMM. In addition to effectively reducing
the magnitude of the impact, the duration of the impact event
is extended, which is consistent with the notion that pruning
effectively reduces the elastic constants of the network. This

&

24

simple experiment demonstrates that pruning is a promising
strategy for designing the next generation of materials for
impact mitigation, with facile tailoring of the important
materials properties

There is a growing need for new materials for impact
mitigation. Reaching new levels of high-performing and
effective impact mitigating materials require novel design
concepts that enable development of materials that are
scalable with easily tailorable material properties amenable
to a wide variety of applications. The design herein for
metamaterials based on disordered networks, combined with
additive fabrication, provides materials-by-design approach
for achieving this goal. This Example provides the mechani-
cal response of three-dimensional disordered-network meta-
materials under dynamic impact loading conditions. Exp.
mental results demonstrate computational pruning of three-
dimensional disordered networks provides a rational and
flexible route to designing mechanical metamaterials with
highly tunable elastic modulus and ultimate mass density.
Pruning controls specific acoustic impedance of the disor-
dered network, which is a material property in the design of
material for protective structures relevant to optimal blast or
impact mitigation.

Disordered Networks Computational Details. The pruning
procedure selectively removes bonds that result in the small-
est reduction in the shear modulus, jt. Moreover, in jammed
networks, the change in p,, resulting from the removal of a
bond, 4, is largely independent from the change in K
resulting from removing the same bond, K,. At each step in
the pruning process, 11, is calculated for each bond in the
network, and the bond with the smallest value is pruned.
12.6% of nodes are removed during the pruning process, and
the coordination number is reduced from 9.1 to 3.9.

Bond compressive modulus is described with a harmonic
spring. The system is relaxed at zero temperature before
measurements. The elastic constants are measured similarly
to techniques used in previous work. To measure compo-
nents of the shear modulus, the simulation box is deformed.
in such a way as to result in zero volume change to linear
order. Once deformed, the system is relaxed via the Fire
algorithm, and the potential energy is measured. Examples
of deformations that satisfy this criterion include straining in
the x dimension by some positive Ax and straining the y
dimension by the negative.

Disordered Networks Printing. In order to create a 3D
printable model of the network, we use a python script that
creates one bond at a time and merges them together to form
the network. Each bond of the network is a cylinder with its
diameter ~0.4 times the average length of the bonds. The
unpruned network has ~2500 bonds and the pruned network
has ~900 bonds. We convert this structure to an .STL file
format that can then be 3D printed.

Disordered-network metamaterial samples were printed
using a 3D printer using build materials to obtain the
Shore-A 30, 50 and 70 harnesses utilized as constitutive
materials.

Constant-velocity, displacement-controlled impact tests
were performed using a linear impactor. A piston driven by
a computer-controlled linear actuator was instrumented with
a dynamic force transducer to measure the applied force on
the sample during impact. A flat acrylic plate was attached
to the end of piston to evenly distribute the compressive load
across (lateral dimension ~(100 mm)?) the surface of the
sample. Sample deformation was captured using a high-
speed camera. The impactor plate started from rest at a
height of 10 cm above the sample surface to allow the linear
actuator to accelerate to the pre-set constant velocity before



US 11,475,185 B2

17

the shear modulus is even increased after optimization.
However, for

ke
hy

the bulk modulus is only reduced by half and plateaus, and
the shear modulus is also reduced by 14 and plateaus.

We decompose the bulk and shear moduli into contribu-
tions from bond stretching resistance and angle bending
resistance. FIG. 9 show that the angle bending resistance
does not directly contribute to the bulk modulus. This is
consistent with the definition of bulk modulus and the fact
that the angle bending resistance does not contribute to the
trace of the stress tensor since it is always tangential to the
bond it acts on. However, the angle bending resistance
indirectly influences the bulk modulus.

‘Combining the left panels and right panels of FIG. 9, we
find that the change in G is always within an order of
magnitude during global node position optimization. B is
only reduced by half when

ky
he =0.1,
while B is reduced by two orders of magnitude when

& <0
ae

‘Therefore, the limited reduction in B is the major reason for
the difliculties in reducing v by node position optimization
for

Directly enforcing a wider bond length distribution is not
always successful in designing arbitrary auxetic 3D net-
works. FIG. 11 shows that, after global node position
optimization, the bond length distribution of the 3D net-
works is indeed wider than that of non-optimized networks.
Moreover, by global node position optimization, we can

decrease Poisson’s ratio of 3D disordered networks below 5

zero, without prior assumption about the final geometry,
such as the bond length distribution,

We cross-validate the computational design by experi-
mental networks prepared by composite materials 3D print-

ing. We choose plastics as the material for the middle portion 5

of the bonds, and rubber as the material for the end portion
of the bonds attached to the nodes. The strength of angle
bending resistance, k@, is tuned by adjusting the proportion
of the two materials, and the shape of the end portion of the
bonds. We choose the material composition and bond shape
that are best represented by

ky
F200

5 of optimization on tuning the auxetic property

18

FIG. 12 shows the comparison of two compressed experi-
mental networks at a strain of 10%. The network in FIG.
12A is without global node optimization and the network in
FIG. 12B is with global node optimization. The colored dots
highlight the tracked nodes at a strain of 10%. The colored
lines show the trajectories of the tracked nodes during
compression. The trajectories show that, while the former
network expands in the lateral direction, the latter network
contracts in the lateral direction. In addition, FIG. 13 shows
the trajectories of tracked nodes for the two networks during
compression from both simulations (red curves) and experi-
ments (blue curves). The simulation trajectories overlap
with the experimental trajectories at small strains, but the
two sets of trajectories split at higher strains, likely due to
bond overlapping that happens to experimental networks,
but not fully considered

FIG. 14 shows the Poisson’s ratio as a function of strain
from the measurements of both experimental and simulation
networks. For the network without global node optimiza-
tion, in both lation and experimental measurements, the
Poisson’s ratio is close to 0.4. For the network with global
node optimization, in both simulation and experimental
measurements, the Poisson’s ratio is below -0.2 at small
strains. In experiments, the Poisson’s ratio increases with the
strain, but remains below -0.1 at a strain of 10%. The effect
n be further
confirmed by the videos of the drop tower tests on non-
optimized and optimized networks presented in supplemen-
tal video V1 and V2.

For three-dimensional isotropic auxetic materials from
disordered networks, global node position optimization is
effective to achieve auxetic properties because it expands the
design space from a discrete localized space to a continuum.
global space. The computationally designed networks are
cross-validated by experimentally 3D-printed and measured
networks and have quantitative agreement. In addition,
global node position optimization is not only effective in
reducing the Poisson's ratio to negative values but also
effective in recovering the Poisson’s ratio of pruned network
to positive values close to 0.5. This confirms that the
Poisson’s ratio can be tuned in a wide range without
affecting the coordination number.

In bond-pruning, every pruning step proceeds as follows.
A bond i is tentatively removed from the network, where i
is the bond index. Then the decrease in B, G and v, namely
ABi, AGi and Avi are calculated for the network. The
tentatively removed bond is then put back to the network.
We repeat this procedure for every bond in the network. We
then select a bond to be permanently removed based on the
pruning protocol. Two pruning protocols are studied: In
protocol I, the bond leading to min AG is permanently
removed; in protocol II, the bond leading to max Av is
permanently removed.

To account for the redistribution of bond-level contribu-
tion to B and G after bond removal, only one bond is
permanently removed at each step

The node position optimization is realized by a con-
strained gradient descent algorithm:

bop, 0th +12) e)
nr

x

where ric. is the @ component of the coordinate of node i, n
is the iteration number, 2. is the learning rate, and L1 and L2
are two constraints implemented to avoid bond overlapping,
where

L1=Ix{H(@ min-0j)(@j-6 min)] @)


U.S. Patent Oct. 18, 2022 Sheet 5 of 19 US 11,475,185 B2

primary |
designer :

~~ 207 | structural

223 ~~ property
L manager

ho 222

L
v

rimar
P y structure
structure

adjuster
i analyzer
207 C 220

input unit

|

216 219 20 ong

manufacturin manufacture
g machine darticle

) yy
224 208 200

FIG. 5


U.S. Patent Oct. 18, 2022 Sheet 4 of 19 US 11,475,185 B2

_ 208 , 208
( dosien __f manufacturing manufactured
\ ach ( machine article
( 207 C \.
217 214 224 208 900

FIG. 4


U.S. Patent Oct. 18, 2022 Sheet 17 of 19 US 11,475,185 B2

“® 10°;
hore-A 30
tn i hore A TG
£ 10" A&A Shore-A 70
om
2 10
=
210)
ci

360° 360-0 Bo

Density of Nebwork, p (kg/m)

>>

)

© Bis

Ac. Impedance, 2 (kPa

Spee.

10 . —
100 560 300 TN Bho

Density of Network, o (ke/ m)

FIG. 17


U.S. Patent Oct. 18, 2022 Sheet 7 of 19 US 11,475,185 B2

communicate secondary structural design
to manufacturing machine

control manufacturing machine by
secondary structural design

produce custom article from secondary
structural design by manufacturing
machine

FIG. 7


US 11,475,185 B2

7

sports gear (e.g., helmets, helmet padding, athletic shoes,
and the like. Moreover, these structures provide redirection
of mechanical loads experienced under impact in directions
that are less detrimental to function of the object that they
protect by controlling the material’s response under shear
and compressive loading, which provide Poisson’s ratio for
how the material responds under bad. Materials can be
engineered to have a positive Poisson’s ration for expansion
under compression, a Poisson’s ratio of zero for zero expan-
sion under compression, or a negative Poisson’s ratio for
contraction under compression. Accordingly, processes and
devices herein provided engineering of mechanical meta-
materials. In an embodiment, with reference to FIG. 3,
manufactured article 208 is shoe insole 209 that includes
heel portion 211, sole portion 213, and toe portion 212,
wherein a designer for shoe insole 209 specifies an initial
material construction for manufactured article 208 as pri-
mary structure 207. Structural cell 210 is a representative
portion of insole 209 that includes primary structure 207 that

is subjected to structural adjustment to produce designer 2

impact-mitigating architectured isotropic structure 200 with
impact-mitigating properties 222 form which manufactured
article 208 is ultimately produced instead of primary struc-
ture 207. FIG. 1 and FIG. 2 respectively show designer
impact-mitigating architectured isotropic structure 200 and
primary structure 207 in structural cell 210

Designer impact-mitigating architectured isotropic struc-
ture 200 can be determined in various ways. In an embodi-
ment, with reference to FIG. 6 and FIG. 7, a method of
operating manufacturing machine 224 for manufactured
article 208 with aid of inverse design machine 214 includes:
providing inverse design machine 214 with primary struc-
ture 207 for manufactured article 208 and with impact-
mitigating properties 222 for manufacturing machine 224,
the primary structure 207 including a plurality of structural
members arranged in primary structure 207 that collectively
provide primary properties 220 to manufactured article 208
and that include primary shear modulus and primary bulk
modulus that provide primary torsional rigidity and primary
compression rigidity of manufactured article 208 being
made by manufactured article 208; and the impact-mitigat-
ing properties 222 including impact-mitigating shear modu-
lus and impact-mitigating bulk modulus that provide
impact-mitigating torsional rigidity and impact-mitigating
compression rigidity for manufactured article 208 being
made by manufacturing machine 224, such that impact-
mitigating properties 222 provide manufactured article 208
with greater structural impact mitigation than primary prop-
erties 220; receiving primary structure 207 from primary

designer 217; initiating a point-by-point analysis on primary 5

structure 207 in inverse design machine 214; determining
primary properties 220 of primary structure 207 with pri-
mary structure analyzer 219 of inverse design machine 214;
receiving, by structure adjuster 221 of inverse design

machine 214, primary properties 220 from primary structure

analyzer 219 and impact-mitigating properties 222 from
structural property manager 223 of inverse design machine
214; adjusting, by structure adjuster 221, structural members
in primary structure 207 until structural members collec-
tively conform to impact-mitigating properties 222 such that
primary structure 207 is structurally modified into designer
impact-mitigating architectured isotropic structure 200 that
includes impact-mitigating properties 222; controlling
operation manufacturing machine 224 in accordance with
designer impact-mitigating architectured isotropic structure
200 by inverse design machine 214; and forming, by manu-
facturing machine 224 under control of designer impact-

&

&

8

mitigating architectured isotropic structure 200 from inverse
design machine 214, manufactured article 208 that includes
designer impact-mitigating architectured isotropic structure
200 instead of primary structure 207

In an embodiment, adjusting structural members in pri-
mary structure 207 includes structural pruning of disor-
dered-network mechanical material. According to an
embodiment, adjusting structural members in primary struc-
ture 207 further includes global node position optimization
of disordered-network mechanical material to produce
designer impact-mitigating architectured isotropic structure
200.

In an embodiment, forming manufactured article 208
includes three-dimensional printing manufactured article
208 from designer impact-mitigating architectured isotropic
structure 200 provided by inverse design machine 214. It is
contemplated that manufactured article 208 includes a poly-
mer that is printed by manufacturing machine 224. Further,
manufacturing machine 224 can be a three-dimensional
printer.

In an embodiment, a method of operating manufacturing
machine 224 for manufactured article 208 with aid of an
inverse design machine 214 includes: providing inverse
design machine 214 with primary structure 207 for manu-

5 factured article 208 and with impact-mitigating properties

222 for manufacturing machine 224, the primary structure
207 including a plurality of structural members 235 arranged
in primary structure 207 that collectively provide primary
properties 220 to manufactured article 208 and that include
primary shear modulus and primary bulk modulus that
provide primary torsional rigidity and primary compression
rigidity of manufactured article 208 being made by manu-
factured article 208: and impact-mitigating properties 222
including impact-mitigating shear modulus and impact-miti-
gating bulk modulus that provide impact-mitigating tor-
sional rigidity and impact-mitigating compression rigidity
for manufactured article 208 being made by manufacturing
machine 224, such that impact-mitigating properties 222
provide manufactured article 208 with greater structural
impact mitigation than primary properties 220; receiving
primary structure 207 from primary designer 217; initiating
point-by-point analysis on primary structure 207 in inverse
design machine 214; determining primary properties 220 of
primary structure 207 with primary structure analyzer 219 of
inverse design machine 214; receiving, by structure adjuster
221 of inverse design machine 214, primary properties 220
from primary structure analyzer 219 and impact-mitigating
properties 222 from structural property manager 223 of
inverse design machine 214; adjusting, by structure adjuster
221, structural members 235 in primary structure 207 until
structural members 235 collectively conform to impact-
mitigating properties 222 such that primary structure 207 is
structurally modified into designer impact-mitigating archi

tectured isotropic structure 200 that includes impact-miti-
gating properties 222; controlling operation manufacturing,
machine 224 in accordance with designer impact-mitigating
architectured isotropic structure 200 by inverse design
machine 214; initiating formation of manufactured article
208 by controlling position of print head of manufacturing
machine 224 under control of inverse design machine 214 in
accord with designer impact-mitigating architectured isotro-
pic structure 200; constantly determining position of print
head of manufacturing machine 224 during formation of
manufactured article 208; constantly providing inverse
design machine 214 with position of the print head; repeti-
tively performing in inverse design machine 214, at frequent
intervals during formation of manufactured article 208,



a2) United States Patent

Soles et al.

US

US 11,475,185 B2
Oct. 18, 2022

(10) Patent No.:
(45) Date of Patent:

(54) INVERSE DESIGN MACHINE AND MAKING
A DESIGNER IMPACT-MITIGATING
ARCHITECTURED ISOTROPIC STRUCTURE

(71) Applicant: Government of the United States of
America, as represented by the
Secretary of Commerce, Gaithersburg,
MD (US)

(72) Inventors: Christopher L. Soles, Boyds, MD
(US); Edwin Pak-Nin Chan, Rockville,
MD (US); Irmgard Bischofberger,
Chicago, IL (US); Sidney Robert
Nagel, Chicago, IL (US); Heinrich
Martin Jaeger, Chicago, IL (US); Juan
Jose de Pablo, Chicago, IL (US); Nidhi
Pashine, Chicago, IL (US); Daniel
Robert Reid, Chicago, IL (US); Carl
Goodrich, Chicago, IL (US); Andrea
Jo-Wei Liu, Chicago, IL (US); Daniel
Hexner, Chicago, IL (US); Mareos A.
Reyes-Martinez, Washington, DC (US);
Meng Shen, Los Angeles, CA (US)

(73) Assignee: GOVERNMENT OF THE UNITED
STATES OF AMERICA, AS
REPRESENTED BY THE
SECRETARY OF COMMERCE,
Gaithersburg, MD (US)

(*) Notice: Subject to any disclaimer, the term of this
patent is extended or adjusted under 35
USC. 154(b) by 266 days.

(21) Appl. No.: 16/837,504

(22) Filed: Apr. 1, 2020

(65) Prior Publication Data
US 2020/0320235 Al Oct. 8, 2020
Related U.S. Application Data

(60) Provisional application No. 62/827,987, filed on Apr.
2, 2019.

(51) Int. Cl.
GO6F 30/23

(2020.01)
(2020.01)
(Continued)

(52) US. Cl.

. GO6F 30/23 (2020.01); GO6F 30/17
(2020.01); GO6F 2101/02 (2013.01); GO6F
2113/10 (2020.01); GO6F 2119/14 (2020.01)

(58) Field of Classification Search
CPC .......... GO6F 30/00; GO6F 30/23; GO6F 30/17;
GO6F 30/10; GO6F 30/20; GO6F 2101/02;

(Continued)

(56) References Cited

PUBLICATIONS

Raza, Irfan Mohammad Hussain, “Addictive Manufacturing of
Locally Resonant Metamaterials”, Apr. 2017, Department of Aero-
nauties, Imperial College London. (Year: 2017).*

(Continued)

Primary Examiner — Cedric Johnson
(74) Attorney, Agent, or Firm — Office of Chief Counsel
for National Institute of Standards and Technology

(57) ABSTRACT

An inverse design machine for making a manufactured
article that includes a designer Impact-mitigating architec-
tured isotropic structure includes: an input unit that receives
a primary structure; a primary structure analyzer that
receives the primary structure from the input unit and
determines primary properties of the primary structure; a
structure adjuster that receives the primary properties from
the primary structure analyzer, receives impact-mitigating
properties from a structural property manager, and produces
the designer Impact-mitigating architectured isotropic struc-
ture from the impact-mitigating properties; and the structural
property manager that provides the impact-mitigating prop-
erties to the structure adjuster.

14 Claims, 19 Drawing Sheets



U.S. Patent

=

B
an
uw
i)

Bulk modulus,
i
oO

Bulk modulus, B &

Bulk modulus, B ©

| see
100}

Oct. 18, 2022 Sheet 10 of 19 US 11,475,185 B2
Kalkp = 9.001 {D) semen Kelkp = 0.001
Stretching uO maw Stretching
Bending 3 80} See Bending

3 60F

& 40F

@ 20+

ai HEH
wy

()
isa)
Kelkp= 0.01  $ 80F —— kosky = 0.01

i

Mii
10

20
Opt steps

30

FIG. 10

~ 30
Opt steps

~10—


US 11,475,185 B2

Sheet 9 of 19

Oct. 18, 2022

U.S. Patent

©) ‘SnINPOW IBBUS

sda3s 3do
Of 0¢ Ot

Lo= Gy /Oy veepenee?

T0'0 = 24/8 ----
100°0 = 99/°¥ ——

ce

6D

gq ‘sninpow xing

(a)

sdajs 1d0

To= 9/8 seeneee
TOO = 9/84 ----
T1000 = 9/89 ——

O€ OZ OT O4_

G0

A ‘Oye S,UOSSIOd


US 11,475,185 B2

21

Q

Therefore, Eq. (2) suggests that m,,>>m, to effectively
reduce the transmitted impulse.

To mitigate the pressure wave, the transmitted force (P,)
needs to be minimized relative to the incident force (P;). The
figure of merit for minimizing P/P, is the specific acoustic
impedance (z), which is a measure of the resistance to
mechanical deformation when subjected to a dynamic force.
This parameter is a function of the Young’s modulus (E) and
the mass density of the material (p) for an isotropic material,

2PEp. @)

If we consider employing an impact mitigating material
system consisting of material A layered on top of material B,
the ratio of transmitted to incident force can be written as a
function of z of the respective materials,

P,_ 2a
Pi ta tie

4

Eq. (4) indicates that z,<<z,, A in order to reduce the
transmitted pressure wave. It is evident from Eq. (3) that
polymeric foams are excellent materials for impact mitiga-
tion. Their low densities and relatively low elastic constants
minimize the transmission of the pressure wave amplitude
when coupled to a second material with a higher z. Thus,
polymeric foams are widely used for impact mitigation
applications ranging from the aerospace industry to foot-
wear, personal protection and product packaging. Although
the mechanical and structural diversity of polymeric mate-
rials allows for a theoretically wide parameter space for the
design of polymeric foams, actual control over these physi-
cal properties often requires radical changes in the polym-
erization and crosslinking chemistries, which are limited by
traditional manufacturing techniques.

There has been a drive towards the design of periodic
metamaterials for impact mitigation applications. Unfortu-
nately, their structural symmetry limits the extent of strain or
stress localization and range of tunability in extrinsic mate-
rials properties. Additionally, most of the studies on
mechanical metamaterials focus on maximizing the energy
absorption capacity of an impact but they have not been
designed for transmitted force reduction.

On the other hand, an aperiodic mechanical metamaterial

shows significantly different mechanical behavior. The 5

response of each material point to a global deformation can
vary drastically relative to a neighboring one. This facilitates
strain localization since bonds experiencing larger stresses
are more likely to fail first. When a bond buckles or breaks,

the changes in the global elastic constants depend on the ;

details of the broken bond. This bond-to-bond variation in
Disordered-Network Mechanical Metamaterials (ODNMM)
can be exploited to manipulate their mechanical properties
by removal of specific bonds. The computational process
that selectively removes bonds from disordered networks is
known as pruning. Compared with random bond removal,
pruning allows the removal of bonds that contribute the most
to E for a given p. This control is critical in impact
mitigation since the materials requirements for reducing
impulse and transmitted stress wave are different thus requir-
ing independent control over the density and the Young’s
modulus of a given material. In this work, we make advan-

20

4

&

22

tageous use of the mechanical tunability of these computa-
tionally generated DNMMs by fabricating these materials
using 3D printing and then experimentally studying their
mechanical response with dynamic impact experiments

We selected a model three-dimensional disordered net-
work and subjected it to the computational pruning process
to generate a new network with a different set of effective
elastic moduli. The structures for both unpruned and pruned
networks generated computationally were then converted to
a stereolithographic file format that enables them to be
realized into actual materials for impact testing. All the
DNMM samples were printed using UV-curable 3D printing
elastomeric resins (FIG. 156), which offers access to a wide
range of constituent materials. For this study, we focused on
fabricating DNMMs using resins with Shore-A scale hard-
ness that vary from approximately 30 (soft) to 70 (stiff). We
printed all the DNMM samples with approximate dimen-
sions of (50 mm)>.

To study the mechanical response of DNMMs under
dynamic loading conditions, we performed instrumented
linear impact experiments with impact velocities ranging
from 0.1 m/s to 1.5 m/s on unpruned and pruned DNMMs
(FIG. 1c). High-speed videos were captured during the
entire impact test and specific video frames of the tests (FIG.
15c) illustrate the differences in the deformation in the
transverse direction between the unpruned-DNMM and the
pruned-DNMM. Specifically, the unpruned-DNMM
expands laterally more than the pruned-DNMM when com-
pressed thus indicating that the Poisson’s ratio (v=e,/e,),
defined as the incremental change in the transversal (¢,)
versus the axial (e,) strain, of the two DNMMs are different

FIG. 16a shows that v for the unpruned-DNMMs ranges
approximately from 0.2 to 0.35 whereas v of the pruned-
DNMMs is systematically lower ranging approximately
from 0.1 to 0.2. v is not only strain dependent in both
samples, but it also shows that the pruned-DNMM displays
a higher rate dependence than the unpruned-DNMM. At
higher impact velocities, the pruned-DNMM displays a
general decrease in the magnitude of v that becomes more
pronounced at higher compressive strains. A similar rate-
dependent v has been observed in open-cell auxetic poly-
urethane foams, with the behavior attributed to a combina-
tion of buckling of the struts that make up the foam and
inertial effects of the mechanical test. We speculate that
similar effects can explain the increased rate-dependence of
v in pruned-DNMM. Specifically, pruning can increase the
effective length of the remaining bonds in the network and,
therefore, change the critical conditions when buckling
instabilities occur.

The true-stress (o,,) versus true-strain (e,,) curves for
unpruned-DNMM and pruned DNMM printed with the
Shore-A 30 material are shown in FIG. 165. At a given
impact velocity, there is a significant drop in the stiffness of
the network after pruning. This is to be expected due to the
reduction in the overall load bearing ability of the network
after pruning because bonds and nodes are removed in the
pruning process. We also observe an apparent stiffening of
the DNMMs with increasing impact velocity. However, this
velocity dependent stiffness (FIG. 16c) does not change after
the pruning process thus suggesting that this change is a
property of the constituent material (ce. an intrinsic prop-
erty), and not a result of the change in the macroscopic
structure of the network (i.e. an extrinsic property). Based on
these results, we attribute the strain stiffening behavior to a
combination of the viscoelastic properties of the constituent
materials used to 3D print the DNMMs and the inertia of the
system, not the structure of the network.



US 11,475,185 B2

19

where 11=0.01 is a constant, @ is the angle between con-
nected bonds, j is the angle index, @ min=15° is the mini-
mum angle allowed, and H(@ min=6j) is the Heaviside step
function.

12=1x{H(r min-rij\(rij-r min)] 4

where 12=1000.0 is a constant, istance between
node i and node j, r min=0.3 is the minimum distance
allowed in length units, and H(r min-rij) is the Heaviside
step function.

At every step, the coordinate of a node i, ri, is displaced
infinitesimally in the @ direction, the force field parameters
for the equilibrium angle and bond length are updated
accordingly, and then B, G and v are measured for the
virtually displaced network. After a scan of all the nodes in
all three directions by this procedure, we calculate the
gradient of (v+L14L2) with respect to the node coordinate
components. Then we update the node positions according
to eq. (2).

Elastic constants cijkl are calculated by taking the deriva-

tive of the stress tensor with respect to the strain tensor
components. Energy minimization is performed at various
strain to allow nonaffine relaxation. G and B are calculated
as

CVs eye ee year ang

and

BWCxexitCp93*#Ccrt 2 ect 2c 25)

‘The Poisson’s ratio is calculated by eq. (1) during bond
pruning and optimization and measured by the displacement
of edge nodes during validation. In the athermal limit, the
Hamiltonian for the simulations is written as:

1 6)

Kayi(Om ~ Pom)”

where U is the potential energy, kb and k@0 are the bond
stretching resistance and angle bending resistance, respec-
tively.

where kO is the total angle bending resistance per bond per
node, and Ne is the coordination number. The factor of 2
accounts for 2 rotational degrees of freedom for angle
bending of each bond in 3D, as opposed to only 1 rotational

degree of freedom in 2D. Ibi and @m are the bond length of

bond i and the bending angle of angle m, respectively. Ib0
and 60 are the equilibrium bond length and the bending
angle, respectively. The bending angle is defined between
two connected bonds, similar to the respective definitions in
widely used classical molecular dynamics force fields. IbO
and 60 are the equilibrium bond length and bending angle,
respectively. kb and k@ have the same units and can be
directly compared with each other.

Regarding dual-material 3D printing, to create a 3D
printable model of the disordered networks studied, we use
a python script that creates one bond at a time and merges
them together to form the network. Each bond of the

3

4

4

5

20

network is a cylinder with its diameter ~0.4 times the
average length of the bonds. We convert this structure to an
.STL file format that can then be 3D printed.

All the disordered-network metamaterial samples were
3D printed using UV-curable printing resins on a 3D printer.
‘To minimize kO in the samples, the nodes were printed using
materials that was significantly softer than the bond mate-
rial. Stiff material was used as the material for the bonds. and
an elastomeric material was for the nodes. Quasi-static,
uniaxial compression experiments were performed no 3D
disordered network samples using a texture analyzer

Experiments were displacement-controlled at a rate of 0.1
mm s-] for both loading and unloading. Force and displace-
ment were recorded. A digital camera captured images of the
sample deformation during the experiments at a rate of 10
frames per second.

Example 2. Intelligent Tuning of the Mechanical
Impedance of Three-Dimensional Disordered
Networks

Disordered-Network Mechanical Materials (DNMM),
comprised of random arrangements of bonds and nodes,

have emerged as mechanical metamaterials with the poten-

tial for achieving fine control over the elastic properties of
open-cell materials. Recent computational studies have
demonstrated this control whereby an extremely high degree
of mechanical tunability can be achieved in disordered
networks via a selective bond removal process called prun-
ing. In this study, we experimentally demonstrate how
pruning of a disordered network alters its macroscopic
dynamic mechanical response and its capacity to mitigate
impact. Linear impact studies with velocities ranging from
0.1 m/s to 1.5 m/s were performed on 3D printed pruned and
unpruned networks comprised of materials spanning a range
of stiffness. High-speed videography was used to quantify
the changes in elastic constants and energy absorbed as a
function of the network structure and the intrinsic material
properties. Our results demonstrate that pruning signifi-
cantly enhances the medium rate (10! s~'-10° s~') mechani-
cal response of disordered network metamaterials and pro-
vides an alternative route for designing materials with
tailored impact mitigating properties.

‘An impact mitigation system can be considered as a
protective structure (e.g., armor or helmet) coupled to a
delicate target (e.g. brain). It can be simplified to a one-
dimensional spring-mass system (FIG. 15) with m,,,k,,
corresponding to the combined mass and stiffness of the
impact mitigator and supporting structure (i.e. skull, neck).
The parameters m, and k, correspond to the mass and
stiffness of the delicate target. When a time-dependent force
(P(t) is applied to m,,, it propagates to m, at a rate deter-
mined by k,, and k, To mitigate this impact, both the
acceleration of m, and the magnitude of the transferred
pressure wave need to be minimized.

Different materials requirements determine the reduction
of these two dynamic effects. Mitigating the changes in
acceleration in a time interval At=t,-t, requires a reduction
in the transmitted impulse (1,) relative to the incident
impulse (1),

Tf,PP(ode a)

The ratio of transmitted to incident impulse can be related
in terms of the ratio of the mass of the delicate object to the
mass of the impact mitigator as


U.S. Patent Oct. 18, 2022 Sheet 6 of 19 US 11,475,185 B2

receive primary structural design

perform point analysis on primary
structural design

determine primary structural properties of
primary structural design

receive secondary structural properties

adjust primary structural design to
conform with secondary structural
properties

produce secondary structural design from
primary structural design

FIG. 6


US 11,475,185 B2

1
INVERSE DESIGN MACHINE AND MAKING
A DESIGNER IMPACT-MITIGATING
ARCHITECTURED ISOTROPIC STRUCTURE

CROSS REFERENCE TO RELATED,
APPLICATIONS

‘The application claims priority to U.S. Provisional Patent
Application Ser. No. 62/827,987 filed Apr. 2, 2019, the
disclosures of which is incorporated herein by reference in
its entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department

of Commerce, and The Government has certain rights in the

invention. Licensing inquiries may be directed to the Tech-
nology Partnerships Office, NIST, Gaithersburg, Md., 99:
voice (301)-975-2573: email tpo@nist.gov.

BRIEF DESCRIPTION

Disclosed is a method of operating a manufacturing
machine for manufactured article with the aid of an inverse
design machine, the method comprising: providing the
inverse design machine with a primary structure for a
manufactured article and with impact-mitigating properties
for the manufacturing machine, the primary structure com-
prising a plurality of structural members arranged in the
primary structure that collectively provide primary proper-
ties to the manufactured article and that comprise a primary
shear modulus and a primary bulk modulus that provide a
primary torsional rigidity and a primary compression rigid-
ity of the manufactured article being made by the manufac-
tured article; and the impact-mitigating properties compris-
ing an impact-mitigating shear modulus and an impact-
mitigating bulk modulus that provide an impact-mitigating
torsional rigidity and an impact-mitigating compression
rigidity for the manufactured article being made by the
manufacturing machine, such that the impact-mitigating
properties provide the manufactured article with greater
structural impact mitigation than the primary properties:
receiving the primary structure from a primary designer;
initiating a point-by-point analysis on the primary structure

in the inverse design machine; determining the primary s

properties of the primary structure with a primary structure
analyzer of the inverse design machine; receiving, by a
structure adjuster of the inverse design machine, the primary
properties from the primary structure analyzer and the

impact-mitigating properties from a structural property man- 5

ager of the inverse design machine; adjusting, by the struc-
ture adjuster, the structural members in the primary structure
until the structural members collectively conform to the
impact-mitigating properties such that the primary structure
is structurally modified into a designer impact-mitigating
architectured isotropic structure that comprises the impact-
mitigating properties; controlling the operation manufactur-
ing machine in accordance with the designer impact-mii
gating architectured isotropic structure by the inverse design
machine; and forming, by the manufacturing machine under
control of the designer impact-mitigating architectured iso-
tropic structure from the inverse design machine, the manu-

&

&

2

factured article that comprises the designer impact-mitigat-
ing architectured isotropic structure instead of the primary
structure.

Disclosed is a method of operating a manufacturing
machine for manufactured article with the aid of an inverse
design machine, the method comprising: providing the
inverse design machine with a primary structure for a
manufactured article and with impact-mitigating properties
for the manufacturing machine, the primary structure com-
prising a plurality of structural members arranged in the
primary structure that collectively provide primary proper-
ties to the manufactured article and that comprise a primary
shear modulus and a primary bulk modulus that provide a
primary torsional rigidity and a primary compression rigid-
ity of the manufactured article being made by the manufac-
tured article; and the impact-mitigating properties compris-
ing an impact-mitigating shear modulus and an impact-
mitigating bulk modulus that provide an impact-mitigating
torsional rigidity and an impact-mitigating compression
rigidity for the manufactured article being made by the
manufacturing machine, such that the impact-mitigating
properties provide the manufactured article with greater
structural impact mitigation than the primary properties;
receiving the primary structure from a primary designer;
initiating a point-by-point analysis on the primary structure
in the inverse design machine; determining the primary
properties of the primary structure with a primary structure
analyzer of the inverse design machine; receiving, by a
structure adjuster of the inverse design machine, the primary
properties from the primary structure analyzer and the
impact-mitigating properties from a structural property man-
ager of the inverse design machine; adjusting, by the struc-
ture adjuster, the structural members in the primary structure
until the structural members collectively conform to the
impact-mitigating properties such that the primary structure
is structurally modified into a designer impact-mitigating
architectured isotropic structure that comprises the impact-
mitigating properties; controlling the operation manufactur-
ing machine in accordance with the designer impact-miti-
gating architectured isotropic structure by the inverse design
machine; initiating formation of the manufactured article by
controlling a position of a print head of the manufacturing
machine under control of the inverse design machine in
accord with the designer impact-mitigating architectured
isotropic structure; constantly determining the position of
the print head of the manufacturing machine during forma-
tion of the manufactured article; constantly providing the
inverse design machine with the position of the print head;
repetitively performing in the inverse design machine, at
frequent intervals during formation of the manufactured
article, corrections to the position of the printer head based
on designer impact-mitigating architectured isotropic struc-
ture and to monitor completion of formation of the manu-
factured article by the manufacturing machine communicat-
ing corrections to the position of the printer head from the
inverse design machine to the manufacturing machine; cor-
recting the position of the printer head by the manufacturing
machine based on the corrections received from the inverse
design machine; and completing formation, by the manu-
facturing machine under control of the designer impact-
mitigating architectured isotropic structure from the inverse
design machine, the manufactured article that comprises the
designer impact-mitigating architectured isotropic structure
instead of the primary structure.

Disclosed is an inverse design machine for making an
manufactured article that comprises a designer impact-
mitigating architectured isotropic structure, the inverse



US 11,475,185 B2

13

metamaterial for impact mitigation where the goal is to
redirect mechanical loads in non-traditional routes not
achievable by traditional materials. Advantageously,
designer impact-mitigating architectured isotropic structure
200 overcomes limitations of technical deficiencies of con-
ventional compositions with tailored mechanical responses
that can be engineered to structural design, creating
mechanical responses that are not achieved with traditional
materials. Such can be mechanical metamaterials. Further,
embodiments herein provide customized mechanical
response for individual applications, on an individual case
basis, by integrating inverse design machine 224 with on-
demand or digital manufacturing methods.

Designer impact-mitigating architectured isotropic struc-
ture 200, inverse design machine 214, and processes herein
independent controls a structural response in shear and
compressive loading using inverse design described herein.
‘A user specifies properties for mechanical response. The
inverse design machine determines optimum design and
communicates such to the digital manufacturing platform.
This simplifies development of applications for impact miti-
gation and provides user-specified customization. For
orthotic insoles customized to dimensions of a user's foot,
embodiments herein provide impact mitigation properties
for such insoles to be customized for the user. Designer
impact-mitigating architectured isotropic structure 200,
inverse design machine 214, and processes herein provide
the creation of designer mechanical responses, responses
that conventional unstructured materials do not provide.
Inverse design machine 214 creates disordered but struc-
tured materials as designer impact-mitigating architectured
isotropic structure 200 that have unique or non-traditional
mechanical responses and having size-scales that can span
from meters to nanometers. Conventional finite element
designing of materials use trial and error discovery with
human intuition. Inverse design machine 214 provides
designer impact-mitigating architectured isotropic structure
200 that is non-intuitive and different than conventional
architectured materials, e.g., primary structure 207, such as
mechanical metamaterials that have a periodic structure with
anisotropic mechanical properties as primary properties 220.
Designer impact-mitigating architectured isotropic structure
200 beneficially has isotropic mechanical properties as
impact-mitigating properties 222 that are selected for a
specific impact mitigation application.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting.

EXAMPLES,

Example 1. Rational Design of Three-Dimensional
Auxetic Metamaterials from Disordered Networks

Tuning a local response of disordered networks can lead

to anomalous mechanical properties such as a negative ;

Poisson’s ratio, namely, auxetic behaviors. Although prun-
ing local bonds has been proven successful in obtaining 2D
auxetic metamaterials from disordered networks, it is chal-
lenging to design 3D auxetic materials from disordered
networks that agree with experiments. The design of disor-
dered isotropic auxetic materials requires independent con-
trol of bulk and shear moduli. In 3D, it requires the shear
modulus, G, to be 1.5 times larger than the bulk modulus, B.
which is much stricter than G>B in 2D. Here we investigate
the design strategy, namely, global node position optimiza-
tion, for disordered 3D auxetic networks. We show that
global node position optimization is effective in designing

0

20

&

0

4

14

3D isotropic auxetic networks, and faithfully allows for
independent control of shear and bulk moduli, when the
angle bending resistance, k0, is much lower than the bond
stretching resistance, kb. After global node position optimi-
zation, without changing the coordination number or reduc-
ing the material density, the bulk modulus is reduced by
almost two decades, while the shear modulus remain
unchanged and can be even slightly increased at a low ratio
of

ke
ie

The computationally designed networks are fabricated by
composite-materials 3D printing, and the Poisson’s ratio is
measured. The experimental measurements are quantita-
tively consistent with computational calculations. The
research demonstrates the power of top-down design for
disordered auxetic materials with independent control of
moduli and can be generalized to the design of other
mechanical metamaterials.

Materials of a negative Poisson’s ratio (NPR) are referred
to as auxetic materials. Due to both the anomalous defor-
mation modes and the shear/bulk moduli ratio, auxetic
materials have applications such as biocompatibility, impact
absorption, and acoustic attenuation. Disordered networks
can be designed to have auxetic behaviors with an arbitrary
anisotropy. Disordered 3D auxetic networks have broader
applications, such as indentation resistance and impact miti-
gation, than their 2D counterparts. However, there are few
works reported on the top-down computational design of
disordered 3D networks that is quantitatively reproduced in
experiments.

Poisson’s ratio, v, is a function of bulk modulus, B, and
shear modulus, G [1]:

w

d(d-1)

where d is the dimension. The higher the ratio of

G

el

the more negative is v. This implicates that the design of
auxetic materials is correlated with the independent control
of shear and bulk moduli. In fact, a high shear modulus and
a low bulk modulus is desirable for applications such as
nuclear reactors. Bond-pruning can be based on local con-
tributions to shear and bulk moduli for design of auxetic
materials from disordered central-force spring networks. G
is not reduced, and B is sharply decreased after pruning, and
40% of bonds can be pruned to obtain auxetic behavior in
2D networks, and the decrease of bulk modulus is accom-
panied by a reduction of shear modulus by 50%. This
inhibits the design of auxetic materials with independent
control of bulk and shear moduli. The design of 3D auxetic
networks is even more difficult than 2D networks since the
minimum requirement for auxetic behaviors in 3D is G>1.5
B, as opposed to the minimum requirement of G>B in 2D.
The mechanics is also more complicated in 3D due to



U.S. Patent Oct. 18, 2022 Sheet 2 of 19

FIG. 2


US 11,475,185 B2

Sheet 13 of 19

Oct. 18, 2022

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U.S. Patent Oct. 18, 2022 Sheet 15 of 19 US 11,475,185 B2

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US 11,475,185 B2

9

corrections to position of printer head based on designer
impact-mitigating architectured isotropic structure 200 and
to monitor completion of formation of manufactured article
208 by manufacturing machine 224 communicating correc-
tions to position of printer head from inverse design machine
214 to manufacturing machine 224; correcting position of
printer head by manufacturing machine 224 based on cor-
rections received from inverse design machine 214; and
completing formation, by manufacturing machine 224 under
control of designer impact-mitigating architectured isotropic
structure 200 from inverse design machine 214, manufac-
tured article 208 that includes designer impact-mitigating
architectured isotropic structure 200 instead of primary
structure 207. In an embodiment, manufactured article 208
includes disordered-network mechanical material 236 that
includes bonds 237 and nodes 238, and primary structure
207 provides three-dimensional reticulated structure of
nodes 201 interconnected by bonds 202 with interstitial
spaces 203 separating proximate nodes 201 interconnected

with bonds 202 in disordered-network mechanical material 2

236. In. an embodiment, adjusting structural members 235 in
primary structure 207 includes structural pruning of disor-
dered-network mechanical material 236. In an embodiment,
adjusting structural members 235 in primary structure 207
further includes global node position optimization of disor-
dered-network mechanical material 236 to produce designer
impact-mitigating architectured isotropic structure 200. In
an embodiment, forming manufactured article 208 includes
three-dimensional printing manufactured article 208 from
designer impact-mitigating architectured isotropic structure
200 provided by inverse design machine 214. In an embodi-
ment, manufactured article 208 includes a polymer printed
by manufacturing machine 224. In an embodiment, manu-
facturing machine 224 includes a three-dimensional printer.

The process for operating manufacturing machine 224 for
manufactured article 208 with the aid of inverse design
machine 214 can include different inverse design strategies
to drive primary structure analyzer 219 in its determination
of how structural changes provided by structure adjustor 221
is implemented. Here, a user starts with primary design 217
for manufacturing article 208 that meets the impact mitiga-
tion property requirements for an intended application with
primary properties 220. These balance properties for a wide
range of uses for multiple units made by manufacturing unit
208 for mass production. At this point inverse design
machine 214 intercedes. The user specifies impact mitigat-
ing properties 222, point-by-point across manufacturing
article 208, wherein impact-mitigating properties 222 are
customized for a specific use or user. Inverse design machine

214 produces a prospective change to the primary design: s

structure adjustor 221 implements the design change; and
structural property manager 223 determines whether the
proposed design change improves or degrades impact miti-
gation relative to impact mitigating properties 222. If the

design change degraded impact mitigation, the proposed ;

change is discarded. If the design change improved impact
mitigation, the design change is accepted. The inverse
design machine loops back and proposes a second design
change and evaluates the resulting properties. Inverse design
machine 214 iterates this process until impact mitigating
properties 222 meet selected values.

Proposed structural changes by inverse design machine
214 can include removing single bond 202 from the struc-
ture (referred to as pruning) or shifting a spatial location of
anode 201 in the structure, referred to as node optimization.
These are different inverse design methods that can be
implemented with efficacy in providing the target require-

&

10

ments that depend on rigidity bond bending to stretching.
The decision of structural modification is based on a targeted.
ratio of shear-to-bulk modulus that is selected at each
location in manufactured article 208 based on targeted
impact mitigation properties 222, analyzing how much each
node 201 bond 202 contributes to the shear and bulk
modulus, identifying bonds and nodes contributing to cur-
rent properties, and eliminating the bond or shifting the node
that modify properties toward targeted impact mitigation
properties 222. Pruning and node optimization can be imple-
mented independently or in combination.

In the method of operating manufacturing machine 224
for manufactured article 208 with aid of an inverse design
machine 214, providing inverse design machine 214 with
primary structure 207 for manufactured article 208 and with
impact-mitigating properties 222 for manufacturing
machine 224 can occur after the inverse design machine
optimized the initial structure to meet desired mechanical
response. The optimized model is output as a standard CAD
or STL format that is compatible with digital manufacturing
platforms, such as 3D printers.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, receiving primary structure 207 from primary

5 designer 217. The primary structure can target generic,

approximate impact properties that are optimized for use of
manufacturing article 208 under selected operating condi-
tions. The primary structure can be used as a starting point
for a class of bonds and nodes architectures for manufac-
tured unit 208. The approximate properties can be targeted
for mass production of identical copies of manufacturing
unit 208. The properties are not optimized for a specific
situation but represent a trade-off for acceptable perfor-
mance under certain conditions.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, point-by-point analysis on primary structure
207 in inverse design machine 214 is performed by deter-
mining mechanical properties material (bulk modulus, shear
modulus) for manufacture and constitutive equations that
describe material deformation and analyzing with engineer-
ing mechanics software to model how the primary structure
will perform when subjected to an impact. The analysis can
be performed with finite clement analysis

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, determining primary properties 220 of pri-
mary structure 207 with primary structure analyzer 219 of
inverse design machine occurs by determining mechanical
properties for the material (bulk modulus, shear modulus)
that is being manufactured, using constitutive equations for
material deformation to analyze with engineering mechanics
software how the primary structure will perform under
impact. Analysis can be performed with finite element
analysis methods.

In the method for operating manufacturing machine 224
for manufactured article 208 with the aid of inverse design
machine 214, receiving, by structure adjuster 221 of inverse
design machine 214, primary properties 220 from primary
structure analyzer 219 and impact-mitigating properties 222
from structural property manager 223 of inverse design
machine 214 can occur by the structure adjustor using the
results of the point-by-point analysis from the engineering
mechanics to analyze the contribution of each structural
element (nodes 201 and bonds 202) to the shear and bulk
modulus. Based on this analysis, structure adjuster 221
decides which structural element (nodes 201 or bonds 202)



US 11,475,185 B2

Page 2
(51) Int. Cl.
GOOF 113/10 (2020.01)
GOOF 119/14 (2020.01)
(58) Field of Classification Search
crc GOGF 2113/10; GOGF 2119/14; GO6F
2111/10
USPC . ... 7103/2

See application file for complete search history.

(56) References Cited

PUBLICATIONS,

Correa, Dixon Malcolm, “Design and Evaluation of Negative
Stiffness Honeycombs for Recoverable Shock Isolation”, May 2015,
Master of Science in Engineering, University of Texas at Austin.
(Year: 2015).*

Reid, Daniel R. et al., “Auxetic Metamaterials from Disordered
Networks”, Jan. 2018, PNAS. (Year: 2018).*

Rocks, J.W,,etal., “Designing allostery-inspired response in mechani-
cal networks”, PN 2017, p. 2520-2525, vol. 114 No. 10.

Reid, D.R., et al., “Auxetic metamaterials from disordered net-
works”, PNAS, 2018, p. E1384-E1390, DOI: www-pnas.org/cgi!
doi/10.1073/pnas.17 17442115.

Reid, D.R,, et al., “Ideal isotropic auxetic networks from random
networks”, Soft Matter, 2019, p. 8084-8091, vol. 15

Hexner, D.,et al., “Role of local response in manipulating the elastic
properties of disordered solids by bond removal”, Soft Matter, 2018,
p. 312-318, vol. 14.

* cited by examiner


US 11,475,185 B2

25

impact. The impactor moved with a constant velocity during
impact until the pre-set displacement was reached, at which
point it stopped.

Edge-detection software was used to measure the changes
in height (¢,,;4)) and average Width (€jpansversa’) of DNMM
samples during the linear impact experiments. The true
strain was then calculated following the definition ¢,=In(1+
€aniai)» Impact force (P,) was measured by a dynamic force
transducer during impact. True stress, 6,,, was estimated
using the average width, w, at each strain to estimate the
sample cross-sectional area in o,,=P,/w?.

‘A 2-kg instrumented drop mass was dropped from a
height of 50 mm onto the DNMM samples. The transmitted
force was measured with force transducer plate located
under the sample. The data was recorded at 1 kHz by the
force transducer and 2 kHz by the instrumented drop mass.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The suflix (s)
as used herein is intended to include both the singular and
the plural of the term that it modifies, thereby including at
least one of that term (e.g., the colorant(s) includes at least
‘one colorants). Optional or optionally means that the sub-
sequently described event or circumstance can or cannot
occur, and that the description includes instances where the
event occurs and instances where it does not. As used herein,
combination is inclusive of blends, mixtures, alloys, reaction
products, and the like.

As used herein, a combination thereof refers to a combi-
nation comprising at least one of the named constituents,
components, compounds, or elements, optionally together
with one or more of the same class of constituents, compo-
nents, compounds, or elements.

All references are incorporated herein by reference.

‘The use of the terms a and an and the and similar referents
in the context of describing the invention (especially in the
context of the following claims) are to be construed to cover
both the singular and the plural, unless otherwise indicated
herein or clearly contradicted by context. Or means and/or.

It can further be noted that the terms first, second, primary, s

secondary, and the like herein do not denote any order,
quantity, or importance, but rather are used to distinguish
one element from another. The modifier about used in
connection with a quantity is inclusive of the stated value
and has the meaning dictated by the context (e.
the degree of error associated with measurement of the
quantity). The conjunction or is used to link objects of a list
or alternatives and is not disjunctive; rather the elements can
be used separately or can be combined under appropriate
circumstances.

What is claimed is:

1. A method of operating a manufacturing machine for
manufactured article with aid of an inverse design machine,
comprising:

providing the inverse design machine with a primary

structure for a manufactured article and with impact-
mitigating properties for the manufacturing machine,

it includes s

20

0

&

at

26

the primary structure comprising a plurality of structural
members arranged in the primary structure that collec-
tively provide primary properties to the manufactured
article and that comprise a primary shear modulus and
a primary bulk modulus that provide a primary tor-
sional rigidity and a primary compression rigidity of
the manufactured article being made by the manufac-
tured article; and

the impact-mitigating properties comprising an impact-

mitigating shear modulus and an impact-mitigating
bulk modulus that provide an impact-mitigating tor-
sional rigidity and an impact-mitigating compression
rigidity for the manufactured article being made by the
manufacturing machine, such that the impact-mitigat-
ing properties provide the manufactured article with
greater structural impact mitigation than the primary
properties;

receiving the primary structure from a primary designer;

initiating a point-by-point analysis on the primary struc-

ture in the inverse design machine;

determining the primary properties of the primary struc-

ture with a primary structure analyzer of the inverse
design machine;

receiving, by a structure adjuster of the inverse design

machine, the primary properties from the primary
structure analyzer and the impact-mitigating properties
from a structural property manager of the inverse
design machine;

adjusting, by the structure adjuster, the structural mem-

bers in the primary structure until the structural mem-
bers collectively conform to the impact-mitigating
properties such that the primary structure is structurally
modified into a designer impact-mitigating architec-
tured isotropic structure that comprises the impact-
mitigating properties;

controlling the operation manufacturing machine in

accordance with the designer impact-mitigating archi-
tectured isotropic structure by the inverse design
machine; and

forming, by the manufacturing machine under control of

the designer impact-mitigating architectured isotropic
structure from the inverse design machine, the manu-
factured article that comprises the designer impact-
mitigating architectured isotropic structure instead of
the primary structure.

2. The method of claim 1, wherein the manufactured
article comprises a disordered-network mechanical material
that comprises bonds and nodes, and the primary structure
provides a three-dimensional reticulated structure of nodes
interconnected by bonds with interstitial spaces separating
proximate nodes interconnected with bonds in the disor-
dered-network mechanical material.

3. The method of claim 2, wherein adjusting the structural
members in the primary structure comprises structural prun-
ing of the disordered-network mechanical material

4. The method of claim 3, wherein adjusting the structural
members in the primary structure further comprises global
node position optimization of the disordered-network
mechanical material to produce the designer impact-miti-
gating architectured isotropic structure.

§. The method of claim 1, wherein forming the manufac-
tured article comprises three-dimensional printing the manu-
factured article from the designer impact-mitigating archi-
tectured isotropic structure provided by the inverse design
machine.



US 11,475,185 B2

15
additional degrees of freedom. 2D auxetic networks can be
obtained from lattice geometries by bond length distortion
based on a pure spring network model but may not achieve
a negative Poisson’s ratio in 3D networks.

In bond-pruning, a bond is removed at a time, which
corresponds to a discrete design space. By contrast, the node
positions provide a continuum design space to program the
network structures. The coordination number of the network
is not reduced with the optimization of node positions,
making it possible to introduce less reduction in the shear
modulus. In addition, it is important to include angle bend-
ing resistance to the pure spring network models, since
networks with even a small angle bending resistance have
much lower critical coordination number for rigidity tran-
ion than central-force spring networks.

Efficiencies of bond-pruning and global node position
optimization in the design of three-dimensional auxetic
disordered networks is described here. Isotropically auxetic
3D mechanical networks are generated from disordered
structures by carefully designed computational algorithms.
We also analyze the effects of angle bending resistances on
the independent tunabilities of G and B by decomposing the
moduli. Computationally designed networks are fabricated
in experiments by composite-materials 3D printing. Quan-
titative consistence between computational calculations and
experimental measurements are established.

Regarding effects of bond pruning and node position
optimization for the design of auxetic networks, to find an
efficient design, we systematically investigated both the
bond pruning and global node position optimization meth-
ods. Two pruning protocols are investigated. In protocol 1,
the bonds leading to min AGi are permanently removed; in
protocol II, the bonds leading to max Avi are permanently
removed. Furthermore, we perform global node position
optimization on the networks pruned based on both pruning
protocols, as well as unpruned networks. Node position
optimization is distinct from bond pruning as the former is
determined by the local bond-level response, while the latter
‘optimizes the Poisson’s ratio by simultaneously updating all
the node positions. Strikingly, node position optimization is
always effective in obtaining auxetic behaviors, regardless
of how the network is pruned, or whether the network is
pruned or not.

Regarding the eflicacy of the pruning protocols, we
choose a network with a coordination number Z7=7.2 gen-
erated from packing. FIG. 8A, left panel shows that protocol
II is more effective in bringing down the Poisson’s ratio,
comparing with protocol I. The reduction of v in protocol I

is negligible, while in protocol II, the Poisson’s ratio is

reduced from 0.35 to -0.21 afier about 16% of the bonds are
removed and Z of the networks are dropped from 7.2 to 6.1.
FIG. 8B, left panel shows that the bulk modulus is reduced
by two orders of magnitude in protocol II, consistent with
the reduction of v. However, protocol II also causes more
reduction in the shear modulus
left panel). The reduction of G restricts the further decrease
of y, since v decreases with

G
B

By comparison, node position optimization successfully
brings v down below -0.5 for the networks pruned by both
protocols (FIG. 8A, right panel), Furthermore, when we
modify the optimization protocol to increase v instead of

. than protocol I (FIG. 8C), ~

at

5 node position optimizatios

16

decreasing v, we find that v is recovered to above 0.43,
slightly higher than the Poisson’s ratio of a network directly
from packing with the same coordination number and with
the same k@ and kb.

Moreover, we directly perform node position optimiza-
tion on unpruned networks of a coordination number of 7.2,
and v is also reduced below -0.5 after only 25 optimization
steps.

This indicates that node position optimization is efficient
in designing auxetic networks, without changing the coor-
dination number. Node position optimization is not only
effective in reducing B for all networks (FIG. 8, middle
panel), but also effective in maintaining the shear modulus,
G (FIG. 8, bottom panel), indicating a more independent
control of B and G than the bond pruning methods.

To challenge the robustness of the optimization in lab-

ized networks, we perform uniaxial stress tests on finite-

sized systems. The Poisson’s ratio is still negative for the
finite sized networks with 500 nodes. (The video of the
quasi-static compression) When we increase the system size
by two times in each dimension, the negative Poisson’s ratio
gets closer to that calculated for periodic systems.

Regarding effect of angle bending resistance on global
10 challenge the effectiveness of
the node position optimization, we test the optimization
method on a network of coordination number Z=6.1 directly
generated from packing. We vary the angle bending resis-
tance by three orders of magnitude and investigate the
tunability in v, B and G. FIG. 10 shows the change of
Poisson’s ratio and moduli during global node position
optimization with various values of angle bending resis-
tances that span three decades, i

ke

ki
= 0.001,  =0; and
hy

hy

FIG. 10A shows that the node position optimization is
effective in reducing the Poisson’s ratio when the angle
bending resistance is in the regime smaller than two orders
of magnitude of the bond stretching resistance. However,
when

although the Poisson’s ratio is smaller in the initial structure
than that of the same network structure with a smaller KO, the
lower limit of the Poisson’s ratio after global node position
optimization is positive.

FIG. 10B shows that when

the bulk modulus is reduced by two orders of magnitude,
while the change in shear modulus is very small. For



U.S. Patent Oct. 18, 2022 Sheet 11 of 19 US 11,475,185 B2

—~~ Non-optimized
~o« Optimized

b

Distribution density
KO

Ds

10 i520
Bond length

OD
Ot
OQ
Wa

FIG. 11


US 11,475,185 B2

Sheet 14 of 19

Oct. 18, 2022

U.S. Patent

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