Shape morphing mechanical metamaterials through reversible plasticity

Abstract

Biological organisms such as the octopus can reconfigure their shape and properties to perform diverse tasks. However, soft machines struggle to achieve complex configurations, morph into shape to support loads, and go between multiple states reversibly. Here, we introduce a multifunctional shape-morphing material with reversible and rapid polymorphic reconfigurability. We couple elastomeric kirigami with an unconventional reversible plasticity mechanism in metal alloys to rapidly (<0.1 seconds) morph flat sheets into complex, load-bearing shapes, with reversibility and self-healing through phase change. This kirigami composite overcomes trade-offs in deformability and load-bearing capacity and eliminates power requirements to sustain reconfigured shapes. We demonstrate this material through integration with onboard control, motors, and power to create a soft robotic morphing drone, which autonomously transforms from a ground to air vehicle and an underwater morphing machine, which can be reversibly deployed to collect cargo.

Full text

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
1 of 10
SOFT ROBOTS
Shape morphing mechanical metamaterials through
reversible plasticity
Dohgyu Hwang1,2†, Edward J. Barron III1,2†, A. B. M. Tahidul Haque2, Michael D. Bartlett1,2*
Biological organisms such as the octopus can reconfigure their shape and properties to perform diverse tasks.
However, soft machines struggle to achieve complex configurations, morph into shape to support loads, and go
between multiple states reversibly. Here, we introduce a multifunctional shape-morphing material with reversible
and rapid polymorphic reconfigurability. We couple elastomeric kirigami with an unconventional reversible plasticity
mechanism in metal alloys to rapidly (<0.1 seconds) morph flat sheets into complex, load-bearing shapes, with
reversibility and self-healing through phase change. This kirigami composite overcomes trade-offs in deformability
and load-bearing capacity and eliminates power requirements to sustain reconfigured shapes. We demonstrate
this material through integration with onboard control, motors, and power to create a soft robotic morphing drone,
which autonomously transforms from a ground to air vehicle and an underwater morphing machine, which can
be reversibly deployed to collect cargo.
INTRODUCTION
Shape-morphing materials with tunable rigidity are key components
for emerging technologies, ranging from stretchable electronics and
soft robotics to reconfigurable structures and multimodal vehicles
(1–4). Key to these systems is the ability to occupy complex configu-
rations, to maintain shape without consuming power, and to go
between multiple states reversibly. However, such attributes are un-
common in a single material system. One promising approach to create
morphing systems is to use initially flat sheets that contain designed
geometric features. For example, by incorporating cuts (kirigami)
or folds (origami) into materials, prescribed three- dimensional (3D)
output shapes can be obtained under deformation (5–8). This class
of materials, often referred to as mechanical metamaterials, allows
for a high degree of freedom and high extensibility (9,10). These
systems are particularly appealing for shape morphing because of
the energetically favorable bending modes driven by the slender
structures in kirigami networks, compared with continuous mem-
branes whose deformation is dominated by stretching modes that
can cause structural collapse (11). However, the reconfigurability
and reversibility of such systems can be limited, because the struc-
tures are often bistable (12,13), require applied loads to maintain
configurations due to elastic restoring forces (14), or use permanent
deformation to change shapes (15,16). Bistable metamaterials can
successfully go between different stable states, but achievable shapes
are often dictated prefabrication by prescribed designs and specific
loading conditions, which can limit field reconfigurability or multi-
functionality during use (17,18). Furthermore, the intrinsic trade-off
between load-bearing capacity and high deformability in homoge-
neous sheets is limiting for soft matter engineering applications that
require notable shape change and structural strength (19).
Another approach to creating morphing systems is to control
material properties across a sheet. This is often achieved by tuning
deformations through heterogeneous material stiffness or placing
responsive materials at prescribed locations (20–22). For example,
stiffness gradients or swelling regions can allow for expansion at
different locations for prescribed, reversible shapes. This can be driven
through stimuli such as differential growth or swelling (23,24),
pneumatics (22,25), heat (26), electric fields (27), and magnetic fields
(28). However, morphing with these mechanisms cannot be obtained
without constantly applied stimuli or energy inputs (e.g., pressure,
specific solvent/temperatures, and magnetic field), because the re-
configured shape is maintained by a specific condition or applied
field. One way to overcome limited shape reconfigurability is to
leverage variable stiffness materials, such as those driven through
phase change, or shape memory materials (4,29–34). However,
continuous membrane geometries can limit shape fixity, and re-
configuration through melting and subsequent cooling to maintain
different configurations is intrinsically slow because of thermal dif-
fusion (35).
Here, we introduce shape- and rigidity-morphing materials with
reversible and rapid polymorphic 3D reconfigurability and pro-
grammable stiffness (Fig.1). The material rapidly morphs (<0.1 s)
into load-bearing configurations yet reconfigures and self-heals
through a phase transition for shape and stiffness reconfigurability.
To achieve this, we created a kirigami composite metamaterial sheet
that synergistically combines shape morphing by nonlinear defor-
mations of elastomeric kirigami architectures, shape fixing by non-
linear material response through plasticity and phase change of an
embedded low–melting point alloy (LMPA), and reversibility with
an integrated heater to trigger a phase change in the LMPA to elas-
tically recover plastic deformation.
The elastomeric kirigami architecture undergoes extreme defor-
mations, achieves complex shapes, and displays nonlinear force-
extension characteristics, which allows for minimal restoring forces at
high extensibility, enabling high shape retention during shape fixing
in different configurations. The LMPA (Field’s metal) displays mate-
rial nonlinearities for shape morphing, which we introduce through
an unconventional reversible plasticity mechanism. Although plas-
ticity (a nonreversible change of shape in response to applied force)
is typically associated with material failure, we now use this mecha-
nism to introduce advanced functionality: the rapid reconfiguration
of shapes in soft materials that become instantly load bearing. The
1Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA 24061, USA.
2Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia
Tech, Blacksburg, VA 24061, USA.
*Corresponding author. Email: mbartlett@vt.edu
†These authors contributed equally to this work.
Copyright © 2022
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim
to original U.S.
Government Works
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
2 of 10
LMPA intrinsically deforms plastically at low strains, which we
leverage to immediately morph the material into load-bearing shapes
(<0.1 s). Mechanical deformation induces plasticity that sustains
the shape without any electrical energy consumption or time limita-
tions due to mass or thermal transport. Yet, the shape is reversible
by using the embedded heaters to melt the LMPA, which then
allows the elastomeric kirigami to elastically reverse the plasticity
and enable reconfigurability and self-healing over numerous cycles.
By patterning the elastomer and embedded LMPA with kirigami
patterns, complex shapes are achievable and can display combi-
nations of negative, zero, and positive Gaussian curvature. Thus, by
combining kirigami structures, LMPA, and embedded heaters, our
multimaterial system displays extreme deformations and reversible
plasticity. This approach achieves rapid shape fixing into complex
configurations and maintains reversibility and load-bearing capaci-
ty. This approach overcomes limitations in morphing material sys-
tems and trade-offs between extensibility and load-bearing capacity
in reconfigurable soft systems. These materials are integrated with
onboard power, control, motors, and embedded heaters to create a
functional morphing drone with multiple remotely controlled loco-
motion modes enabled by an autonomous morphing from a ground
to air vehicle configuration. We further show a morphing underwa-
ter machine that can be reversibly deployed to collect cargo through
integrated water propulsion and buoyancy control.
RESULTS
Morphing composite design
The composite consists of a rigidity tuning endoskeleton made of
an LMPA, an embedded heating layer, and elastomeric kirigami en-
capsulation (Fig.1A). The LMPA is Field’s metal—which is a eutec-
tic alloy of bismuth, indium, and tin—and transitions from a high
elastic modulus (>3 GPa) solid to a flowable liquid at relatively low
melting temperatures (melting point of 62°C) (29). The sample was
fabricated by first creating the endoskeleton through a vacuum-
assisted replica molding process that enabled arbitrary continuous
geometries. This design flexibility can create common kirigami de-
signs such as uniaxial, biaxial, and triaxial cut patterns (see fig. S1).
The endoskeleton and heating layers were then embedded in elasto-
mer, and kirigami incisions were laser-cut throughout the sample to
define the kirigami geometry (Fig.1B). To demonstrate the rapid
shape-morphing capability and reversibility, a relaxed triaxial kiri-
gami composite in the solid state was deformed through an inflated
pneumatic membrane (Fig.1C). This film rapidly morphed into a
doubly curved surface with complex curvature, as demonstrated by
a curvature map showing the positive and negative Gaussian curva-
tures (Fig.1D). Upon deflating the underlying membrane, the
free-standing kirigami film was reconfigured into the programmed
shape through plasticity. Because of the rigidity of the solid endo-
skeleton, the structure immediately achieved load-bearing capacity
80°C
30°C
55 °C
C
D
55°C
Embedded heating layer
(Liquid metal & PET)
Rigidity tuning
endoskeleton
(Field’s metal)
Elastomeric kirigami
encapsulation
i. Relaxed (s) ii. Deformed (s
)i
ii. Shape-fixed (s)
iv. Relaxed (l)
v. Deformed (l)
vi. Shape-fixed (s)
Phase
transition
Phase
transition
Phase
transition
240g
240g
30°C 80°C
BA
Undeformed state
Kirigami incisions
Endoskeleton
Elastomer
Deformed state
+0.06
-0.06
cm-2
0
Fig. 1. Multimaterial kirigami composite with instantaneous complex shape fixing and reversibility. (A) Schematic showing the layers of a kirigami-inspired multi-
layered composite. (B) A top-down schematic showing the kirigami incisions, endoskeleton, and elastomer in an undeformed state with the deformed state in the inset.
(C) Image sequence showing the composite morphing into the programmed shape of an inflating elastomeric membrane underneath and supporting 240 g in the recon-
figured state after the membrane is deflated. By activating embedded heaters [inset shows infrared (IR) images], the morphed composite undergoes a phase change and
returns to the flat initial state and can then be actuated repeatedly. Scale bar, 50 mm. (D) Gaussian curvature map of the deployed kirigami composite showing the
complex shape.
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
3 of 10
and supported a disk-shaped weight (240 g). However, by electrical-
ly activating the embedded heater through Joule heating, the endo-
skeleton underwent a phase transition to a liquid phase, and the
elasticity of the elastomer returned the structure into a relaxed, liquid
state. This phase change, coupled with the elasticity of the elasto-
mer, enables reversible plasticity. The structure can be morphed in
the liquid state to become highly compliant. By holding the de-
formed state and undergoing a phase transition back to a solid state,
the kirigami film becomes rigid to regain a load-bearing configura-
tion. This process can be repeated by activating the heater to return
the film to a relaxed, solid state.
Morphing composite mechanical analysis
The kirigami composite was mechanically analyzed under uniaxial
loading for different endoskeleton states and geometries of the
LMPA endoskeletons (Fig.2A). Figure2B shows representative
load P versus applied strain appl curves for kirigami composites in
either a solid state, a liquid state, or elastomer without an LMPA
endoskeleton. Each specimen was cyclically loaded three times to
100% strain and then returned to zero strain, with the unloading
step performed in the liquid endoskeleton state. The solid-state
composite is shown to be rigid (effective stiffness, Keff=8480±
770 N/m) in the initial loading (appl≤10%); however, once localized
plastic deformation was observed, the load-displacement response
became nonlinear. At this point, substantial softening and a slight
negative stiffness were observed, where the structure extended with
minimal additional strain energy. This load plateau after initial
loading is critical because this allows for high degrees of shape re-
configurability as discussed below. In contrast, the liquid-state
composite exhibited a soft response with a negligible effective stiff-
ness (Keff=65±10 N/m), which is ∼130 times softer than the solid
state (Fig.2D) and softer than the elastomeric kirigami alone.
We determined the underlying elastoplastic morphing mecha-
nism of the endoskeleton in the solid state using finite element anal-
ysis (FEA). We followed the multilayered kirigami composite of
Fig.2A to develop the layered composite section for the FE model.
The LMPA was simulated with elastoplastic material behavior, and
the elastomeric layers were modeled by a hyperelastic formulation.
The Materials and Methods section for FEA describes materials and
elements in more detail. The FEA accurately captures the experi-
mental load-strain characteristics for the solid-phase kirigami com-
posite in Fig.2B. Furthermore, the FEA gives insight into the plastic
deformation process at a material level. In Fig.2C, FEA results illus-
trate the plastic hinge formation at the joints of kirigami beams at
different stages of global strain appl=0, 10, and 100%. The kirigami
joints remained primarily elastic until reaching appl=10%, where
most of the plastic hinges were formed. Thereafter, the plastic zone
intensified around kirigami joints, and the kirigami structure de-
formed without any marked resistance to the applied strain appl.
Stress concentrations are common in kirigami structures near the
Field’s metal
Embedded heater
Elastomer
246810
0.0
0.2
0.4
0.6
0.8
1.0
Cycle(N)
Keff/Keff,0
tLMPA lLMPA
wLMPA
0.00 0.02 0.04 0.06 0.08 0.10
2000
4000
6000
8000
10000
K
eff (N/m)
w
LMPA
/l
LMPA
(Unitless)
Experiment Theory FEA
t
LMPA
=1.0 0.2mm
t
LMPA
=0.6 0.2mm
t
LMPA
=0.3 0.1mm
±
±
±
~130x
0
1000
8000
9000
10000
Elastomer
Liquid
K
eff(N/m)
Solid
500
(i) εappl = 0% (ii) εappl = 10% (iii) εappl = 100%
1.01501050
Plastic strain (%)
020406080100
0
6
12
18
24
30
P (N)
appl
(%)
Solid
Experiment
FEA
Solid Liquid Elastomer
F
E
D
BCA
εappl = 0% εappl = 100%
l0
Fig. 2. Mechanical performance of kirigami composites with uniaxial endoskeleton structures. (A) Kirigami composite at 0 and 100% strain. Scale bar, 20 mm.
(B) Load versus applied tensile strain for different kirigami composites (lLMPA = 20 mm, width wLMPA = 1.9 mm, and thickness tLMPA = 1000 m). (C) FEA results showing the
development of plastic hinges at different applied strains. (D) Kirigami composite stiffness for different endoskeleton states. Error bars represent the SD for n = 10. (E) Effective
stiffness versus kirigami beam geometry wLMPA/lLMPA for kirigami composites with 12 different endoskeleton geometries. Inset: Composite schematic showing geometric
parameters. Error bars represent the SD for n = 3. (F) Normalized stiffness as a function of the number of cycles for an LMPA-embedded kirigami composite. Inset: a cross
section of the composite. Scale bar, 1 mm.
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
4 of 10
vicinity of the cut, which enhances the generation of plasticity in these
regions (36). This local plastic deformation contributes to the soft
structural response of the solid-state kirigami between appl=10 and
100% in Fig.2B and allows for the composite to be morphed into
different stable configurations.
The effective stiffness of the structure (Keff) can also be tuned by
controlling the kirigami geometry, where the stiffness Keff can be
calculated as
K eff = 
E w 3 t
─
l 3
(1)
where  depends on boundary conditions and system size, and t, w,
and l are beam thickness, width, and length, respectively (10). We
investigated various compositions of LMPA beams—such as length
(lLMPA=20 and 30 mm), width (wLMPA=1.1, 1.5, and 1.9 mm), and
thickness (tLMPA ranging from 300 to 1000m)—with constant en-
capsulating layer geometry. In Fig.2E, the upper line predicts stiff-
ness of kirigami structures that include ∼1-mm-thick endoskeletons
with varying slenderness, and the lower line predicts that with
∼0.3-mm-thick endoskeletons, with the shaded region indicating
intermediate thickness and showing the large tunability through ki-
rigami structure. The experimental data are well captured by the
analytical solution and numerical analyses. The composite is also
robust under cyclic loading (Fig.2F). Here, the kirigami composite
was deformed in the solid state to 100% strain, where after the first
cycle the rigidity was stable for the remaining cycles (10 cycles were
run). During this process, no fracture in the endoskeleton was ob-
served. Robustness was further investigated by intentionally break-
ing the endoskeleton at multiple points, melting the composite
endoskeleton, and then resolidifying at room temperature to heal
the structure. The self-healing efficiency was then quantified by
measuring the stiffness for 10 fracture/healing cycles. The stiffness
of the healed sample was consistent with the pristine sample and
showed no degradation over the 10 cycles, demonstrating excellent
healing efficiency (fig. S2). Critical to this behavior is the over-
pressurization of the LMPA during fabrication (see figs. S3 to S5).
This enables the material to flow back in contact and resolidify into
a monolithic structure.
We quantify the shape-fixing capability of the kirigami compos-
ite through uniaxial cyclic experiments (Fig.3A). Here, we apply
strains of appl=10 to 50% and then unload under quasi-static con-
ditions, until the load drops to zero (loading and unloading rate of
1 mm/s and 0.01 mm/s, respectively). The strain at zero load is the
plastic strain (p) and represents the amount of deformation that
remains after morphing. We define the shape-fixity ratio Rf as
R f =  p
─
 appl (2)
We evaluate Rf as a function of appl for two kirigami films with
endoskeletons in the solid state (the stiffest and least stiff from
Fig.2E), an endoskeleton loaded in the liquid state and solidified at
appl, and a kirigami elastomer control without an endoskeleton
(Fig.3B). When the elastomer control (endoskeleton-free material)
is deformed, nearly no shape retention occurs regardless of appl be-
cause of the elastomer elasticity that restores the structure to the
undeformed state. For the smallest stiffness solid endoskeleton, we
observe 10%<Rf<30%, where the low values of Rf are attributed
to the restoring force of the elastomeric layers, which dominates
over the endoskeleton. In contrast, the sample with the largest stiff-
ness shows Rf∼30% for small appl (2.5%) and reaches Rf∼85% for
larger appl (50%). Recall from Fig.2B that the development of full
plasticity in the kirigami endoskeleton requires appl>10%. There-
fore, modest Rf for low appl is attributed to a low degree of plastic
deformation in the kirigami endoskeleton. A high shape-fixity ratio
(≈100%) can be obtained by loading the sample at T>Tm and hold-
ing it until the LMPA solidifies (see data points for Loaded in liquid
in Fig.3B). However, in this case, heating and cooling are required,
and the morphing process can take minutes (35). In contrast, when
loaded in the solid state, the material is instantaneously load bear-
ing and does not require electrical energy input to maintain its re-
configured shape. We also varied the unloading rate to determine
the time dependence of shape fixity for appl=50% and found that
when varying the unloading rate by over two orders of magnitude
(from 0.005to 1 mm/s), Rf varies by less than 7% (see figs. S6 and
S7) and is always higher than 83%.
Shape fixing
Kirigami architectures and material plasticity enable very rapid, large
dynamic reconfigurability and stable shape fixity without a continu-
ous input of energy. To demonstrate the rapid shape-fixing behavior,
we created a kirigami composite with a spiral cut pattern and then
impacted a metal ball (130 g) into the center of the composite (Fig.3C).
Upon impact of the metal ball, extreme deformation occurred in ∼70 ms
by dissipating the kinetic energy through large plastic deforma-
tion of the kirigami composite (movie S1). After removal of the
metal ball and inversion of the structure, the deformed shape was
maintained with an excellent shape fixity (Rf∼100%). The embed-
ded heater was then activated to melt the LMPA endoskeleton, which
allowed the elastomer to elastically reverse the plasticity and transformed
the structure back to its initial configuration. This demonstrated the
ability to achieve substantial deformation and shape fixing at rapid
time scales through plasticity coupled with the ability to restore the
initial configuration through heating and elastic recovery. To further
demonstrate the shape-morphing capability of the kirigami composite,
a single kirigami composite sheet with triangular cut patterns was
morphed into various objects that exhibited positive (a spherical
orange), zero (a cylindrical cucumber), and mixed Gaussian curvature
(bottom of a bell pepper) shapes (Fig.3D). The same sheet was re-
configured through heating to conform to the three different objects,
demonstrating reversibility. The triaxial pattern enables planar ex-
pansions due to negative Poisson’s ratio, ensuring good replication of
the different complex shapes in three dimensions. This is character-
istic of the nonlinear structural response of the system, where local-
ized rotations or bending enables a minimal rise in force with
increasing deformation. This low restoring force allows for shape-
fixing capabilities in different complex configurations.
Morphing drone
Morphing materials that can support load and reconfigure shape
without continuous energy input can enable highly adaptable and
mobile machines. To demonstrate these enabling characteristics,
the kirigami composite was used as a reconfigurable body to create
a multifunctional, bimodal morphing soft robotic drone (Fig.4,
Aand B). The kirigami-drone body consists of LMPA endoskele-
tons embedded in an elastomer to provide shape morphing and an
embedded heating layer to enable phase transition of the endoskel-
eton. By integrating onboard power, control, antennas, and motors,
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
5 of 10
the drone can be remotely driven in state 1 on the ground, autono-
mously morphed from a ground to air vehicle configuration, and
then be flown in state 2 (Fig. 4C and movie S2). The embedded
heater was localized at specific morphing points to enable the au-
tonomous transformation from an upright driving state to the flat
flying state (Fig.4D). The shape transformation was initiated upon
contact between copper wires on the drone and liquid metal layers
deposited on a power transfer station (see Materials and Methods),
which enabled transformation to occur with no external intervention.
To measure the power for Joule heating, we normalized the power
input by the interfacial area between the liquid metal channels and
LMPA regions, and the value was measured to be 9.3 mW/mm2. By
going beyond manual reconfiguration or morphing demonstrations
that lack integration of functional components, our morphing material–
based drone achieves locomotion in multiple distinct configurations.
The load-bearing capacity coupled with the ability to markedly
transform configurations is critical to the locomotion modes and
highlights the potential of our morphing kirigami composites to
enable future applications in multifunctional systems for reconfigu-
rable robotics and electronics.
Morphing and deployable underwater machine
The morphing kirigami composites presented here rapidly and
reversibly morph into complex, load-bearing geometries without
the need for continuous energy input. This combination of proper-
ties is enabling for deployable robots, which must exist in a slim,
easily transportable form factor before being deployed to perform
tasks. Morphing mechanisms can allow underwater machines to
achieve advanced functions and deploy from a packed state (37,38).
Different approaches to create underwater morphing robots have
been shown; however, morphing has been predominantly used for
locomotion (38–41). Creating a reversibly deployable machine with
locomotion and sufficient mechanical stability to perform functions
and practically interact with the environment remains a challenge
(42–45). Motivated by this, we use kirigami composites to develop
a deployable underwater machine capable of starting in a flat,
P
Unloading
εappl
εp
AB
Rigid endoskeletonCompliant endoskeleton Rigid endoskeleton Compliant endoskeleton No endoskeleton
Loaded in liquid
Positive Gaussian Mixed GaussianZero Gaussian
-K
+K
0
2D kirigami sheet
Rf ≈ 100%
Lead
Reverse
Deforms in ~70 ms
Metal ball (130g)
Free standing
C
D
Loaded in solid
Fig. 3. Shape fixing at rapid time scales with complex shapes. (A) Load versus strain shape-fixing curves for two specimens with different kirigami stiffness and a
sample without an endoskeleton. The inset presents a schematic of the measurement of a shape-fixity ratio (Rf). (B) Shape-fixity ratio Rf as a function of appl from (A). Error
bars represent the SD for n = 3. (C) A kirigami composite undergoes substantial out-of-plane deformation through the impact of a metal ball (movie S1), which causes
rapid reconfiguration and shape fixing into the deformed shape in ~70 ms. The second to last image shows the structure inverted against gravity where it maintains the
reconfigured shape, and the last image shows reversibility of the shape through activation of the embedded heater. Scale bar, 50 mm. (D) Photographs of a triaxial kirigami
composite that morphs onto objects with complex curvatures reversibly. Insets show the representative Gaussian curvature of the objects. Scale bar, 50 mm.
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
6 of 10
transportable geometry (state 1), which is then sequentially morphed
into a swimming state with features that interact with the environ-
ment to collect cargo (state 2), and then morph back to the retracted
configuration (state 1) (Fig.5A). The underwater machine consists
of multiple stacked layers, including morphing kirigami composites
with embedded liquid metal heaters, inflatable pneumatic mem-
branes, and water propulsion channels. The pneumatic membranes
on each side of the machine are individually controllable, which
allows for independent morphing of the top and bottom layers and
offers buoyancy control. Figure5B illustrates the different states of
the underwater machine. The machine was deployed by actuating the
pneumatic membranes, which expanded to morph the composite layers.
The morphed kirigami composites instantaneously became fixed
into the deformed shapes and maintained their desired structure after
the pneumatic membranes were deflated without consuming power.
Upon completion of its task, the machine can be reversed to its original
retracted shape using the embedded liquid metal heaters. This under-
water morphing machine was capable of reversible deployment by
morphing between the retracted state and deployed state, moving by
water jet propulsion with buoyancy control, and interacting with the
environment with rigid functional structures to collect cargo (Fig.5C).
The morphing layers are multifunctional, providing structural
shape, buoyancy control, and protection of the soft pneumatic
membrane and allowing for environmental interaction. The bottom
layer is designed to morph to collect cargo, enabling the machine to
collect materials during deployment, and the top layer morphs and
controls buoyancy for locomotion. The functionality of the under-
water machine is demonstrated in Fig.5D and movie S3. The un-
derwater machine was dropped into the water in Fig. 5D(i) and
immediately morphed and deployed to simultaneously achieve flo-
tation and its functional form factor in Fig. 5D(ii). The bottom
membrane was then deflated, producing an empty cargo bay with
size and shape controlled by the bottom morphing composite layer.
Next, air was removed from the top membrane to reduce the buoy-
ancy of the underwater machine, causing it to descend. The water
jets propelled the machine quickly toward the desired cargo at a
speed greater than 210mm s−1 (1.3 body lengths per second; movie
S4). The machine then collected spherical, hydrogel beads as cargo.
The top membrane was inflated, and the machine resurfaced by
propelling forward in Fig. 5D(iii). The underwater machine was
then retrieved in Fig.5D(iv), and its cargo was emptied (Fig. 5E).
Last, the machine was connected to an electrical power source, sup-
plying power of 1.9and 2.5 mW/mm2 to the top and bottom heaters,
respectively, where it reversed to its original, easily transportable shape.
This implementation highlights the reversible deployability of mor-
phing kirigami sheets, providing a platform for underwater robots
that can morph into different functional shapes while moving through
water to perform tasks such as sampling and transporting cargo.
70°C20 45
t = 0 st = 76 st = 89 st = 106 s
Morphed
1. Battery
2. Drone microcontroller
3. R/C microcontroller
4. Drone antenna
5. R/C antenna
Drone motor
R/C motor
Heater
Endoskeleton
Lead
1
23
5
4
State 1
State 2
D
B
AC
Fig. 4. Multifunctional autonomously morphing drone. (A and B) Photographs of the two distinct functional states of the soft robotic morphing drone and its integrated
rigid electronics. State 1 is a land transport machine. State 2 is a fully functional quadrotor air vehicle. Scale bar, 60 mm. (C) Video frame sequence showing the morphing
drone driving in state 1, transforming into the flying state, then taking flight in state 2 (movie S2). Scale bar, 100 mm. (D) Image sequence showing the transformation
from states 1 to 2; the top row shows images, and the bottom row shows IR images. Scale bar, 60 mm.
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
7 of 10
DISCUSSION
We have introduced a composite material system that can morph
into diverse 3D shapes through kirigami-inspired structures, be-
come instantaneously load-bearing through plastic deformation of
the LMPA endoskeleton, and recover the initial shape through an
unconventional reversible plasticity mechanism driven by the ther-
mally induced phase transition of the LMPA. The combination of
material plasticity and structural deformation provides a platform
to simultaneously achieve reversible morphing and shape-fixing
mechanisms at rapid time scales. Although plasticity is typically
associated with permanent, irrecoverable deformation, by using
LMPA we can induce plasticity and then “elastically” recover the
deformation to reverse the plasticity. This recovery is achieved by
activating the heaters, which causes the LMPA endoskeleton to
melt, allowing the kirigami elastomer to both encapsulate the liquid
and also elastically recover and guide the system back to the unde-
formed state. When the endoskeleton resolidifies, morphing can be
performed again and a different shape can be achieved, where this
reconfiguration process can be repeated over multiple cycles.
Therefore, plasticity or deformation while the endoskeleton is in the
solid state can be thought to switch on the shape shifting, and melt-
ing the endoskeleton with elastic recovery driven by the elastomeric
C
State 1
HeaterEndoskeleton
Pneumatic actuation
Water-driven propulsion
Cargo bay
State 2
Cargo Shape-fix top composite Deflate top membrane
Deflate bottom membraneShape-fix bottom compositeActivate heaters, unmorph
Frame
In/out
D
e
f
late bottom membran
e
, unmorp
h
In
Out
Morphing composite
Morphing membrane
Propulsion layer
ReversePropelDeployRetract
Water jet
Morphing membrane
Morphing composite
Frame
In Out
In/out
Lead
AB
D
Morphing membraneMorphing composite
E
70°C20 45
(ii) Deployed
(iii) Obtain cargo
(iv) Retreived
(i) Propelled by
buoyancy & water-jet
Reversed with
integrated heater Cargo
Lead
Power source
Fig. 5. Morphing and deployable underwater machine. (A) Photographs of the distinct functional states of the underwater morphing machine with a schematic show-
ing the machine cross section. State 1 is a compact, retracted configuration for storage. State 2 is a functional deployed machine for underwater locomotion and cargo
collection. Scale bar, 20 mm. (B) Image sequence showing the independent morphing, shape fixing, and reversibility of the top and bottom sides on the machine.
(C) Images showing multifunctionality of the machine, which can deploy through instantaneous shape morphing and fixing, propel through water jetting, and reverse to
a retracted state through integrated heaters. Scale bar, 20 mm. (D) Demonstration of the multifunctional underwater morphing robot that was deployed, locomoted
through water propulsion and buoyancy control, obtained cargo, and retrieved (tubing is cropped out for clarity beyond the first image). (E) After retrieval, the cargo was
emptied, and the machine was connected to a power source to activate reversibility to return to the original retracted state.
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
8 of 10
kirigami can switch off the shape shifting. If the endoskeleton frac-
tures, the composite can also self-heal by melting the LMPA to re-
pair the broken endoskeleton. Because the LMPA endoskeleton is
embedded in kirigami-inspired architectures, large deformations
can be achieved with high degrees of shape fixity combined with the
ability to conform to complex geometries defined by nonzero
Gaussian curvatures. Although LMPA fibers/sheets and kirigami
approaches have been independently demonstrated, by introducing
an LMPA endoskeleton embedded into kirigami structures, our in-
tegrated composite enables unique possibilities for advanced mor-
phing systems. Our composite introduces a reversible plasticity
mechanism in LMPAs to leverage material nonlinearities (plasticity
and phase change), combined with kirigami structures that leverage
nonlinear mechanical response, which allows for unique force-
displacement relationships for efficient morphing to large deformations.
This allows us to synergistically combine material and structural
nonlinearities to achieve unique functionality, such as rapid shape
morphing into complex shapes, which are immediately load bear-
ing. In addition, we show that our composite morphs reversibly and
does not consume power to hold the reconfigured state. Together,
this represents an enabling combination of properties for integrated
morphing systems.
The reversible plasticity mechanism enables nearly instant load-
bearing capacity and high rigidity even after large deformations.
One of the limitations in our current approach is the necessity to
couple the shape-morphing composites with external actuation
mechanisms. For the case of the multifunctional morphing drone,
we did not use external actuation but relied on gravity to morph the
vehicle in one direction, where further reconfiguration after the ini-
tial morphing step currently requires manual intervention. In the
morphing membrane in Fig.1 and in the morphing and deployable
underwater machine in Fig.5, we coupled the morphing composite
with integrated pneumatic actuators. This allows for controlled
transitions between multiple stable states through the reversible
plasticity mechanism without external intervention. Therefore, the
incorporation of actuation schemes is key to cyclic morphing be-
havior. In addition to the pneumatic actuators that we have used,
other actuation schemes offer intriguing opportunities for integra-
tion into the shape-morphing composites presented here. These
can include using soft active materials like liquid crystal elastomer
(LCE) actuators (27,46), artificial muscles like shape memory alloy
wires or carbon nanotube fibers (47,48), or tendon-driven actua-
tion with electromechanical motors (49). Materials like LCEs could
replace the currently passive elastomer layer where the LCE could
be programmed to deform to different shapes (50). Artificial mus-
cles and pneumatic actuation can also be directly incorporated into
the elastomer layer or as a supporting layer (51). Electromechanical
motors could be deployed into supporting structures, as has been
done in foldable drones (52), or could be leveraged with fiber-driven
actuation throughout the film (53). These different actuation ap-
proaches will require co-design with the shape-morphing com-
posites through geometric and material selections to ensure optimal
shape morphing and performance.
Our kirigami composite sheetallows us to achieve complex cur-
vatures across the entire sheet, without having to preprogram spe-
cific deformations. Instantaneous load bearing is achieved through
plasticity or phase change to reconfigure into different complex
shapes. Although bistable systems can display different load-
bearing configurations, creating multiple stable states often requires
preprogramming or tiling subunits together, which can increase
complexity and result in a restricted set of achievable morphologies.
The kirigami composite sheet does not need preprogramming to
achieve diverse configurations, which can be an advantage for re-
configurable or multifunctional applications. Furthermore, the ma-
terials and processes to make the kirigami composite sheets can be
adapted to other kirigami or origami metamaterial approaches and
geometries, which we anticipate could open further possibilities for
deployable, architectured, or mechanical logic applications.
The materials presented here enable complex reconfigurations,
load-bearing, and incorporation of functional components—
including controllers, motors, and batteries—that can lead to dynam-
ic functionalities in robotic systems. Because the reconfigured state
is maintained without continuous energy supply, mobile and de-
ployable machines can be reconfigured in the field for multiple
tasks that require load-bearing capability. Although complex shapes
have been achieved, optimization of kirigami layouts with embed-
ded reversible plasticity could potentially enhance load-bearing ca-
pabilities. This could allow for additional functionalities such as
field reconfigurable materials to rapidly support injuries or multi-
purpose robotics for gripping, carrying, or delivering supplies.
MATERIALS AND METHODS
Endoskeleton fabrication
We fabricated kirigami endoskeletons made of LMPAs [Field’s
metal, 32.5 weight % (wt %) bismuth, 16.5wt % tin, and 51wt %
indium; RotoMetals] through replica molding and vacuum-assisted
injection of liquid metals. A replica mold of polydimethylsiloxane
elastomer (Sylgard 184 with a 20:1 base-to-curing agent ratio; Dow
Corning) with the kirigami pattern was cleaned with isopropyl alco-
hol to remove all residues and was brought into contact with clean
glass. Liquid Field’s metal was placed on an inlet of the replica mold
and was placed under vacuum for ∼15min (for the fabrication of
LMPA skeleton in the drone demonstration, the vacuum time ex-
tended to 3hours because of its larger scale). When the vacuum was
released, the atmospheric air pressure pushed the liquid metal into
the microchannels. After the channels were completely filled, the
sample was removed from the oven to cool, and the metal skeleton
was removed.
Embedded heating layer fabrication
Polyethylene terephthalate (PET) films (E= 2.6±0.1 GPa, t=75,
125 m, Grainger) were patterned using a laser machine (Epilog
Laser Fusion M2, 75 W), and then copper tapes (3M Inc.) were
attached to both ends of the heater. The prepared sample was
spray-coated across the entire sheet with liquid metal [eutectic
gallium-indium (EGaIn)] and then sealed inside elastomeric sheets
during the composite fabrication process.
Composite fabrication
Kirigami composites were composed of LMPA endoskeletons, em-
bedded heating layers, and encapsulating elastomers. For all com-
posites presented here, stacks of single-sided adhesive layers (t of
single layer=160m, Blazer Orange Laser Mask, IKONICS Imag-
ing) were used to pattern bulk materials and control the thickness
of each layer. First, a thin Dragon Skin layer (Dragon Skin 00-30,
Smooth-on) was formed on a substrate within a stack of mask layers
(t=320m) using a thin-film applicator (ZUA 2000, Zehntner) and
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
9 of 10
then cured at 80°C for 5min. The liquid metal–coated side of the
prepared heating layer was placed onto the cured Dragon Skin lay-
er. Another stack of mask layers (t=480m) was attached, and a
batch of Dragon Skin was formed within the frame (cured at 80°C
for 5 min). The substrate was then cooled, and an LMPA endoskel-
eton was placed on the substrate in alignment with the heating layer
underneath (cured at 80°C for 10 min). A last stack of mask layers
(t = 960 m) was attached, and the top Dragon Skin layer was
formed (cured at 80°C for 10 min). The fabricated composite was
then laser-machined to create kirigami films. To pressurize the
LMPA endoskeleton channels, we placed the patterned composite
on a hot plate (80°C) and injected excess liquid-state LMPA into the
channels. The inlet was sealed back with glue (Sil-Poxy, Smooth-
On). Embedded heaters were pressurized with liquid metal EGaIn
with a syringe and needle. After filling, the injected hole was sealed
with Sil-Poxy and cured for 12hours.
Mechanical testing
Tests were conducted under uniaxial loading on an Instron 5944
mechanical testing machine with a 50-kN load cell at a loading rate
of 1 mm/s and at various unloading rates. All mechanical data were
analyzed with custom MATLAB code to measure stiffness and plas-
tic strain at each step of each cycle. Copper leads were connected to
a DC power supply to provide current when melting LMPA skeleton.
Morphing drone
The soft robot body was a kirigami composite composed of a single
LMPA endoskeleton located between two embedded heaters con-
nected in series and encapsulated in an elastomer. Drone compo-
nents were harvested from a quadrotor drone (Drocon Bugs 3). The
body was outfitted with a fiberglass and acrylic frame for integra-
tion of rigid electronics and machinery. We placed 6-mm-thick
acrylic wheels at the four inner protrusions of the frame. The
4.5-cm-diameter rear wheels were adhered to 200rpm brushed mo-
tors (Greartisan DC 6V), and the 4-cm-diameter front wheels were
attached to screws and allowed to freely rotate. The soft robot was
powered by a lithium polymer battery (7.4 V 1000 mAh, Tenergy)
connected in parallel to the drone and remote-controlled car
(Jeypod 2.4GHz Racing Car) microcontrollers. Two 17-cm-long 20
AWG copper wires were connected to either end of the embedded
heaters to allow for contact with the power transfer station. At
the supplied power input of 9.3 mW/mm2, the morphing drone
changed shape from states 1 to 2in ∼1min and 30s with an active
transformation time of ∼2s. Power was then turned off, and the
morphing drone was cooled at room temperature for ∼7min before
the drone took flight.
Underwater machine fabrication
The kirigami composite for both upper and bottom layer was com-
posed of an LMPA endoskeleton and a liquid metal heater, which
was encapsulated by the elastomeric layer. A 1/16″ solid acrylic layer
was adhered between the top and bottom pneumatic systems with
Sil-Poxy adhesive (Smooth-On) to allow for independent control of
the membranes. The top system was composed of a 7/64″-thick
acrylic sheet with cut channels to allow for insertion of a 3/32″-outer-
diameter pneumatic tube for inflation of the membrane. The 7/64″
acrylic sheet was adhered with Sil-Poxy to a 700-m-thick Dragon
Skin membrane. The bottom system was composed of a 3/16″ acrylic
layer with cut channels to allow for a 3/32″ outer diameter pneumatic
tube and two 5/32″ outer diameter water propulsion tubes. A
700-m-thick Dragon Skin membrane was adhered to the acrylic
layer. Thick PET sheets (125 m) were added to both the top and
bottom Dragon Skin membranes to control the inflated shape.
Stainless steel frames (1/32″) were placed on the outside of the kirigami
composites. The layers were bolted together with #6-32 stainless
steel binding barrels and screws. Water propulsion was controlled
by a diaphragm pump (Hooshing 12V 60W diaphragm water pump).
Mechanical and finite element analysis
The analytical calculations were performed by considering only the
geometry and material properties of LMPA endoskeleton, because
its modulus and thickness were substantially higher than the elasto-
meric encapsulation and embedded heating layer. The kirigami
structure was simulated using nonlinear finite element program
ABAQUS (SIMULIA, Providence, RI) in the framework of 3D co-
ordinate system. The 3D deformable shell objects were modeled
using four-node reduced integration shell element with enhanced
hourglass control. The composite layout feature of ABAQUS was
used to develop the five-layered rigidity tuning endoskeleton, where
the solid LMPA and heating layer were defined using elastoplastic
behavior of Field’s metal and PET, respectively. The elastomeric ki-
rigami encapsulation of this endoskeleton was modeled by a hyper-
elastic model. We used an elastic modulus of E=4.0 GPa and yield
stress of E= 30.0MPa to capture the LMPA behavior. The stress-
strain relation of the elastomer was calibrated using nonlinear Yeoh
hyperelastic model (54) by fitting to a strain energy function
U = ∑
j=1
3
[
C j0 [
_
I 1 − 3] j + 1
─
D j [J − 1] 2j
]
(3)
where J = det (F),
_
I 1 = J −
2
_
3 tr( F Τ F) , and F represent volumetric de-
formation, first invariant, and deformation gradient, respectively.
The material coefficients C10=0.16 MPa, C20=0.002 MPa, C30=0,
and D1=D2=D3=0 were used to incorporate the elastomers in the
FE model. The material calibration parameters of elastomer (Dragon
Skin) were curve-fitted to simulate the experimental stress-strain
relation (see fig. S8). All these materials and section definitions were
incorporated into the FEA simulation to validate the experimental
elastoplastic character shown in Fig.2B. Furthermore, the study on
geometric configuration of LMPA beam composition was also simu-
lated for various combinations of lengths (lLMPA) and widths (wLMPA).
Statistical tests
The meaning of all error bars and how they were calculated is de-
scribed within the captions of the figures in which they occur.
SUPPLEMENTARY MATERIALS
www.science.org/doi/10.1126/scirobotics.abg2171
Figs. S1 to S8
Movies S1 to S4
REFERENCES AND NOTES
1. D.-H. Kim, J. Song, W. M. Choi, H.-S. Kim, R.-H. Kim, Z. Liu, Y. Y. Huang, K.-C. Hwang,
Y.-w. Zhang, J. A. Rogers, Materials and noncoplanar mesh designs for integrated circuits
with linear elastic responses to extreme mechanical deformations. Proc. Natl. Acad. Sci.
U.S.A. 105, 18675–18680 (2008).
2. N. W. Bartlett, M. T. Tolley, J. T. B. Overvelde, J. C. Weaver, B. Mosadegh, K. Bertoldi,
G. M. Whitesides, R. J. Wood, A 3D-printed, functionally graded soft robot powered by
combustion. Science 349, 161–165 (2015).
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
SCIENCE ROBOTICS | RESEARCH ARTICLE
10 of 10
3. B. Mosadegh, P. Polygerinos, C. Keplinger, S. Wennstedt, R. F. Shepherd, U. Gupta, J. Shim,
K. Bertoldi, C. J. Walsh, G. M. Whitesides, Pneumatic networks for soft robotics that
actuate rapidly. Adv. Funct. Mater. 24, 2163–2170 (2014).
4. A. Tonazzini, S. Mintchev, B. Schubert, B. Mazzolai, J. Shintake, D. Floreano, Variable
stiffness fiber with self-healing capability. Adv. Mater. 28, 10142–10148 (2016).
5. T. C. Shyu, P. F. Damasceno, P. M. Dodd, A. Lamoureux, L. Xu, M. Shlian, M. Shtein,
S. C. Glotzer, N. A. Kotov, A kirigami approach to engineering elasticity
in nanocomposites through patterned defects. Nat. Mater. 14, 785–789 (2015).
6. E. Hawkes, B. An, N. M. Benbernou, H. Tanaka, S. Kim, E. D. Demaine, D. Rus, R. J. Wood,
Programmable matter by folding. Proc. Natl. Acad. Sci. U.S.A. 107, 12441–12445 (2010).
7. Z. Zhakypov, K. Mori, K. Hosoda, J. Paik, Designing minimal and scalable insect-inspired
multi-locomotion millirobots. Nature 571, 381–386 (2019).
8. E. T. Filipov, T. Tachi, G. H. Paulino, D. A. Weitz, Origami tubes assembled into stiff, yet
reconfigurable structures and metamaterials. Proc. Natl. Acad. Sci. U.S.A. 112,
12321–12326 (2015).
9. M. Konakovic, K. Crane, B. Deng, S. Bouaziz, D. Piker, M. Pauly, Beyond developable:
Computational design and fabrication with auxetic materials. ACM Trans. Graph. 35, 1–11
(2016).
10. D. G. Hwang, M. D. Bartlett, Tunable mechanical metamaterials through hybrid kirigami
structures. Sci. Rep. 8, 3378 (2018).
11. D. P. Holmes, Elasticity and stability of shape changing structures. Curr. Opin. Colloid
Interface Sci. 40, 118–137 (2018).
12. A. Rafsanjani, D. Pasini, Bistable auxetic mechanical metamaterials inspired by ancient
geometric motifs. Extreme Mech. Lett. 9, 291–296 (2016).
13. H. Yasuda, J. Yang, Reentrant origami-based metamaterials with negative poisson’s ratio
and bistability. Phys. Rev. Lett. 114, 185502 (2015).
14. M. A. Dias, M. P. McCarron, D. Rayneau-Kirkhope, P. Z. Hanakata, D. K. Campbell, H. S. Park,
D. P. Holmes, Kirigami actuators. Soft Matter 13, 9087–9092 (2017).
15. A. Rafsanjani, Y. Zhang, B. Liu, S. M. Rubinstein, K. Bertoldi, Kirigami skins make a simple
soft actuator crawl. Sci. Robot. 3, eaar7555 (2018).
16. A. Sedal, A. H. Memar, T. Liu, Y. Menguc, N. Corson, Design of deployable soft robots through
plastic deformation of kirigami structures. IEEE Robot. Autom. Lett. 5, 2272–2279 (2020).
17. G. P. Choi, L. H. Dudte, L. Mahadevan, Programming shape using kirigami tessellations.
Nat. Mater. 18, 999–1004 (2019).
18. Z. Zhai, Y. Wang, H. Jiang, Origami-inspired, on-demand deployable and collapsible
mechanical metamaterials with tunable stiffness. Proc. Natl. Acad. Sci. U.S.A. 115,
2032–2037 (2018).
19. L. Wang, Y. Yang, Y. Chen, C. Majidi, F. Iida, E. Askounis, Q. Pei, Controllable and reversible
tuning of material rigidity for robot applications. Mater. Today 21, 563–576 (2018).
20. Z. S. Davidson, H. Shahsavan, A. Aghakhani, Y. Guo, L. Hines, Y. Xia, S. Yang, M. Sitti,
Monolithic shape-programmable dielectric liquid crystal elastomer actuators. Sci. Adv. 5,
eaay0855 (2019).
21. A. Sydney Gladman, E. A. Matsumoto, R. G. Nuzzo, L. Mahadevan, J. A. Lewis, Biomimetic
4D printing. Nat. Mater. 15, 413–418 (2016).
22. J. H. Pikul, S. Li, H. Bai, R. T. Hanlon, I. Cohen, R. F. Shepherd, Stretchable surfaces
with programmable 3D texture morphing for synthetic camouflaging skins. Science 358,
210–214 (2017).
23. J. Kim, J. A. Hanna, M. Byun, C. D. Santangelo, R. C. Hayward, Designing responsive
buckled surfaces by halftone gel lithography. Science 335, 1201–1205 (2012).
24. D. P. Holmes, M. Roché, T. Sinha, H. A. Stone, Bending and twisting of soft materials by
non-homogenous swelling. Soft Matter 7, 5188–5193 (2011).
25. E. Siéfert, E. Reyssat, J. Bico, B. Roman, Bio-inspired pneumatic shape-morphing
elastomers. Nat. Mater. 18, 24–28 (2019).
26. H. Aharoni, Y. Xia, X. Zhang, R. D. Kamien, S. Yang, Universal inverse design of surfaces
with thin nematic elastomer sheets. Proc. Natl. Acad. Sci. U.S.A. 115, 7206–7211 (2018).
27. Q. He, Z. Wang, Y. Wang, A. Minori, M. T. Tolley, S. Cai, Electrically controlled liquid crystal
elastomer-based soft tubular actuator with multimodal actuation. Sci. Adv. 5, eaax5746 (2019).
28. Y. Kim, H. Yuk, R. Zhao, S. A. Chester, X. Zhao, Printing ferromagnetic domains
for untethered fast-transforming soft materials. Nat. Lett. 558, 274–279 (2018).
29. I. M. Van Meerbeek, B. C. Mac Murray, J. W. Kim, S. S. Robinson, P. X. Zou, M. N. Silberstein,
R. F. Shepherd, Morphing metal and elastomer bicontinuous foams for reversible stiffness,
shape memory, and self-healing soft machines. Adv. Mater. 28, 2801–2806 (2016).
30. K. Yu, Q. Ge, H. J. Qi, Reduced time as a unified parameter determining fixity and free
recovery of shape memory polymers. Nat. Commun. 5, 3066 (2014).
31. T. L. Buckner, M. C. Yuen, S. Y. Kim, R. Kramer-Bottiglio, Enhanced variable stiffness
and variable stretchability enabled by phase-changing particulate additives. Adv. Funct.
Mater. 29, 1903368 (2019).
32. F. Deng, Q. K. Nguyen, P. Zhang, Multifunctional liquid metal lattice materials through
hybrid design and manufacturing. Addit. Manuf. 33, 101117 (2020).
33. D. Zappetti, S. H. Jeong, J. Shintake, D. Floreano, Phase changing materials-based
variable-stiffness tensegrity structures. Soft Robot. 7, 362–369 (2020).
34. Y. Hao, T. Wang, X. Fang, K. Yang, L. Mao, J. Guan, L. Wen, A variable stiffness soft robotic
gripper with low-melting-point alloy. Chinese Control Conf. CCC , 6781–6786 (2017).
35. J. Shintake, B. Schubert, S. Rosset, H. Shea, D. Floreano, Variable stiffness actuator for soft
robotics using dielectric elastomer and low-melting-point alloy. 2015 IEEE/RSJ Int. Conf.
Intell. Robot. Syst. 1097–1102 (2015).
36. Y. Yang, M. A. Dias, D. P. Holmes, Multistable kirigami for tunable architected materials.
Phys. Rev. Mater. 2, 110601 (2018).
37. Y. Li, T.-c. Su, B. Ouyang, Design and deployment analysis of subsea deployable
structures, 27th Int. Ocean Polar Eng. Conf., ISOPE–I–17–216 (2017).
38. T. Paschal, J. Shintake, S. Mintchev, D. Floreano, Development of bio-inspired underwater
robot with adaptive morphology capable of multiple swimming modes. 2017 IEEE/RSJ Int.
Conf. Intell. Robot. Syst. 4197–4202 (2017).
39. G. Picardi, H. Hauser, C. Laschi, M. Calisti, Morphologically induced stability on an
underwater legged robot with a deformable body. Int. J. Rob. Res. 40, 435–448
(2021).
40. F. Giorgio-Serchi, A. Arienti, C. Laschi, Underwater soft-bodied pulsed-jet thrusters:
Actuator modeling and performance profiling. Int. J. Rob. Res. 35, 1308–1329 (2016).
41. F. Giorgio-Serchi, A. Arienti, F. Corucci, M. Giorelli, C. Laschi, Hybrid parameter
identification of a multi-modal underwater soft robot. Bioinspir. Biomim. 12, 025007
(2017).
42. J. Shintake, H. Shea, D. Floreano, Biomimetic underwater robots based on dielectric
elastomer actuators. IEEE Int. Conf. Intell. Robot. Syst. 4957–4962 (2016).
43. G. Li, X. Chen, F. Zhou, Y. Liang, Y. Xiao, X. Cao, Z. Zhang, M. Zhang, B. Wu, S. Yin, Y. Xu,
H. Fan, Z. Chen, W. Song, W. Yang, B. Pan, J. Hou, W. Zou, S. He, X. Yang, G. Mao, Z. Jia,
H. Zhou, T. Li, S. Qu, Z. Xu, Z. Huang, Y. Luo, T. Xie, J. Gu, S. Zhu, W. Yang, Self-powered
soft robot in the Mariana Trench. Nature 591, 66–71 (2021).
44. W. Wang, N. G. Kim, H. Rodrigue, S. H. Ahn, Modular assembly of soft deployable
structures and robots. Mater. Horizons 4, 367–376 (2017).
45. A. D. Marchese, C. D. Onal, D. Rus, Autonomous soft robotic fish capable of escape
maneuvers using fluidic elastomer actuators. Soft Robot. 1, 75–87 (2014).
46. Q. He, Z. Wang, Y. Wang, Z. Wang, C. Li, R. Annapooranan, J. Zeng, R. Chen, S. Cai,
Electrospun liquid crystal elastomer microfiber actuator. Sci. Robot. 6, eabi9704 (2021).
47. M. D. Bartlett, N. Kazem, M. J. Powell-Palm, X. Huang, W. Sun, J. A. Malen, C. Majidi, High
thermal conductivity in soft elastomers with elongated liquid metal inclusions. Proc. Natl.
Acad. Sci. U.S.A. 114, 2143–2148 (2017).
48. H. Chu, X. Hu, Z. Wang, J. Mu, N. Li, X. Zhou, S. Fang, C. S. Haines, J. W. Park, S. Qin,
N. Yuan, J. Xu, S. Tawfick, H. Kim, P. Conlin, M. Cho, K. Cho, J. Oh, S. Nielsen, K. A. Alberto,
J. M. Razal, J. Foroughi, G. M. Spinks, S. J. Kim, J. Ding, J. Leng, R. H. Baughman, Unipolar
stroke, electroosmotic pump carbon nanotube yarn muscles. Science 371, 494–498
(2021).
49. F. Renda, M. Cianchetti, M. Giorelli, A. Arienti, C. Laschi, A 3D steady-state model
of a tendon-driven continuum soft manipulator inspired by the octopus arm. Bioinspir.
Biomim. 7, 025006 (2012).
50. T. H. Ware, M. E. McConney, J. J. Wie, V. P. Tondiglia, T. J. White, Voxelated liquid crystal
elastomers. Science 347, 982–984 (2015).
51. E. J. Markvicka, M. D. Bartlett, X. Huang, C. Majidi, An autonomously electrically
self-healing liquid metal–elastomer composite for robust soft-matter robotics
and electronics. Nat. Mater. 17, 618–624 (2018).
52. D. Falanga, K. Kleber, S. Mintchev, D. Floreano, D. Scaramuzza, The foldable drone:
A morphing quadrotor that can squeeze and fly. IEEE Robot. Autom. Lett. 4, 209–216 (2019).
53. B. Mazzolai, A. Mondini, F. Tramacere, G. Riccomi, A. Sadeghi, G. Giordano, E. Del Dottore,
M. Scaccia, M. Zampato, S. Carminati, Octopus-inspired soft arm with suction cups
for enhanced grasping tasks in confined environments. Adv. Intell. Syst. 1, 1900041 (2019).
54. O. H. Yeoh, Some forms of the strain energy function for rubber. Rubber Chem. Technol.
66, 754–771 (1993).
55. D. Hwang, E. J. Barron III, A. B. M. Tahidul Haque, M. D. Bartlett, Dataset for a kirigami
composite metamaterial sheet (2022); https://doi.org/10.7294/18306044.
Acknowledgments: We thank S. T. Frey for assistance with sample fabrication. Funding: We
acknowledge support through Defense Advanced Research Projects Agency Young Faculty
Award (DARPA YFA) (D18AP00041). Author contributions: D.H., E.J.B., A.B.M.T.H., and M.D.B.
designed research; D.H., E.J.B., and A.B.M.T.H. performed research; D.H., A.B.M.T.H., and M.D.B.
analyzed data; D.H., E.J.B., A.B.M.T.H., and M.D.B. wrote the paper. Competing interests: The
authors declare that they have no competing interests. Data and materials availability: All
data needed to evaluate the conclusions in the paper are presented in the paper or the
Supplementary Materials and are available at the Virginia Tech Data Repository (55).
Submitted 17 December 2020
Accepted 18 January 2022
Published 9 February 2022
10.1126/scirobotics.abg2171
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022

Use of think article is subject to the Terms of service
Science Robotics (ISSN ) is published by the American Association for the Advancement of Science. 1200 New York Avenue NW,
Washington, DC 20005. The title Science Robotics is a registered trademark of AAAS.
Copyright © 2022 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim
to original U.S. Government Works
Shape morphing mechanical metamaterials through reversible plasticity
Dohgyu HwangEdward J. Barron IIIA. B. M. Tahidul HaqueMichael D. Bartlett
Sci. Robot., 7 (63), eabg2171. • DOI: 10.1126/scirobotics.abg2171
View the article online
https://www.science.org/doi/10.1126/scirobotics.abg2171
Permissions
https://www.science.org/help/reprints-and-permissions
Downloaded from https://www.science.org at Virginia Polytechnic Institute and State University on February 09, 2022