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Shape morphing mechanical metamaterials through reversible plasticity


Abstract and Figures

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.
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Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
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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.
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
(14). 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 (58). 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 (2022). 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,2934). 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:
†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
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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.
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
55 °C
Embedded heating layer
(Liquid metal & PET)
Rigidity tuning
(Field’s metal)
Elastomeric kirigami
i. Relaxed (s) ii. Deformed (s
ii. Shape-fixed (s)
iv. Relaxed (l)
v. Deformed (l)
vi. Shape-fixed (s)
30°C 80°C
Undeformed state
Kirigami incisions
Deformed state
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.
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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
0.00 0.02 0.04 0.06 0.08 0.10
eff (N/m)
Experiment Theory FEA
=1.0 0.2mm
=0.6 0.2mm
=0.3 0.1mm
(i) εappl = 0% (ii) εappl = 10% (iii) εappl = 100%
Plastic strain (%)
P (N)
Solid Liquid Elastomer
εappl = 0% εappl = 100%
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.
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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
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 Rf85% 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,
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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 (3841). Creating a reversibly deployable machine with
locomotion and sufficient mechanical stability to perform functions
and practically interact with the environment remains a challenge
(4245). Motivated by this, we use kirigami composites to develop
a deployable underwater machine capable of starting in a flat,
Rigid endoskeletonCompliant endoskeleton Rigid endoskeleton Compliant endoskeleton No endoskeleton
Loaded in liquid
Positive Gaussian Mixed GaussianZero Gaussian
2D kirigami sheet
Rf ≈ 100%
Deforms in ~70 ms
Metal ball (130g)
Free standing
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.
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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
1. Battery
2. Drone microcontroller
3. R/C microcontroller
4. Drone antenna
5. R/C antenna
Drone motor
R/C motor
State 1
State 2
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.
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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
State 1
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
late bottom membran
, unmorp
Morphing composite
Morphing membrane
Propulsion layer
Water jet
Morphing membrane
Morphing composite
In Out
Morphing membraneMorphing composite
70°C20 45
(ii) Deployed
(iii) Obtain cargo
(iv) Retreived
(i) Propelled by
buoyancy & water-jet
Reversed with
integrated heater Cargo
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.
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Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
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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.
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
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Hwang et al., Sci. Robot. 7, eabg2171 (2022) 9 February 2022
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 =
C j0 [
I 1 3] j + 1
D j [J 1] 2j
where J = det (F),
I 1 = J
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.
Figs. S1 to S8
Movies S1 to S4
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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
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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
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... Subsequently, a permanent magnet was attached to it, which could control the shape using an external magnetic field, obtaining an actuator with significant application value in the medical field [22,24]. In addition, researchers have integrated driving components into two-dimensional variable-stiffness structures, using the infinite curvature of the two-dimensional plane to produce complex variable-stiffness actuators [10,23]. These two-dimensional variable-stiffness actuators have potential applications in multimodal vehicles, morphing drones, amphibious robots, reconfigurable exoskeletons, and wearable devices [6,12,25]. ...
... For example, combined driver units expand and deploy structures that can be applied in space exploration and in the medical field [8,9]. Variable-stiffness structures have good shape adaptability in the softened state and good load-bearing capacity in the hardened state, which makes them valuable in robotics, as mechanical grippers, and in rehabilitation medicine [7,[10][11][12][13]. In addition, while soft actuators based on electromagnetic drives and dielectric elastomer drives must continuously provide driving energy when clamping objects, variable-stiffness actuators can clamp objects in a hardened state, which effectively reduces the energy consumption [1,14,15]. ...
... In recent years, research has been extensively conducted on complex actuators with variable stiffness [6,10,[22][23][24]. For example, a low-temperature liquid metal was injected Shenzhen Zhandong Industrial Co., Ltd. ...
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Variable-stiffness actuators can flexibly adjust the overall or local stiffness of a structure, thus enabling reconstruction, adaptation, and locking capabilities that can meet a wide range of task requirements. However, the programmable design and manufacture of three-dimensional (3D) variable-stiffness actuators has become a challenge. In this paper, we present a method to develop the 3D structure of variable-stiffness actuators that combines variable-stiffness joints with 3D printing technology. The variable-stiffness joints were obtained by arranging steel needles wrapped with enameled copper wire inside the grooves of a polylactic acid (PLA) structure and bonding the three components with silicone glue. First, a variable-stiffness joint was used as a variable-stiffness node and subjected to 3D printing to realize multiple 3D variable-stiffness designs and manufacture a programmable structure. Then, using the repulsive force between paired magnets, we developed a driving actuator for the 3D variable-stiffness structure, enabling the expansion and deployment functions of the structure. In addition, an electromagnetically driven mechanical gripper was designed based on variable-stiffness joints to effectively decrease the driving energy in applications where objects are held for extended periods using variable-stiffness control. Our study provides practical solutions and guidance for the development of 3D variable-stiffness actuators, contributing to the achievement of more innovative and practical actuators.
... The ability to control repeatable transitions between soft and rigid geometries is of use in a range of mechanical, electronic and biomedical engineering applications [9][10][11][12][13][14] . Such capabilities can be used, for example, in origami electronics and foldable displays to create high packing ratios [15][16][17][18] . ...
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Crumpling is potentially a quick and efficient way to pack sheet-like electronic devices at a high compression ratio. However, crumpling is not applicable to conventional electronic devices because disordered and irreversible plastic deformation can occur, which affects electronic function. Here we report crumple-recoverable electronics based on heterogenous integration of silver nanowires, a shape memory polymer and an elastomer. Our approach is inspired by the emergence process of butterfly wings, which have variable stiffnesses as they unfold, and allows the mechanical properties of sheet-like devices to transform via thermal modulation from an elastic (2 MPa) state suitable for smoothing out wrinkles formed during crumpling to a plastic (1,315 MPa) state suitable for free-standing operation. We use the approach to create touch panels (7 cm by 7 cm) that can be crumpled and packed into capsules (1 ml volume), and then used as a flat and smooth surface for reliable touch sensing after unpacking.
... Shape morphing has been leveraged for robots to change their morphology for adaptive manipulation or locomotion 4 . For instance, a robot can adapt its morphology to enable different locomotion modes in different environments 5,6 or overcome obstacles 7 , adjust its leg length to maximize its speed when traversing different terrain 8 , or reconfigure its limb shape and motion for amphibious locomotion 9 . ...
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Shape-morphing robots can change their morphology to fulfill different tasks in varying environments, but existing shape-morphing capability is not embedded in a robot’s body, requiring bulky supporting equipment. Here, we report an embedded shape-morphing scheme with the shape actuation, sensing, and locking, all embedded in a robot’s body. We showcase this embedded scheme using three morphing robotic systems: 1) self-sensing shape-morphing grippers that can adapt to objects for adaptive grasping; 2) a quadrupedal robot that can morph its body shape for different terrestrial locomotion modes (walk, crawl, or horizontal climb); 3) an untethered robot that can morph its limbs’ shape for amphibious locomotion. We also create a library of embedded morphing modules to demonstrate the versatile programmable shapes (e.g., torsion, 3D bending, surface morphing, etc.). Our embedded morphing scheme offers a promising avenue for robots to reconfigure their morphology in an embedded manner that can adapt to different environments on demand.
... In recent years, although significant progress has been made in unmanned systems, particularly in unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs), across a range of industries including search and rescue, exploration, transportation, monitoring, and more, [1] [2] [3] [4] [5] the pursuit of excellence in design and complex applications is still ongoing. ...
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Mechanical metamaterials are known for their prominent mechanical characteristics such as programmable deformation that are due to periodic microstructures. Recent research trends have shifted to utilizing mechanical metamaterials as structural substrates to integrate with functional materials for advanced functionalities beyond mechanical, such as active sensing. This study reports on the ultra‐stretchable kirigami piezo‐metamaterials (KPM) for sensing coupled large deformations caused by in‐ and out‐of‐plane displacements using the lead zirconate titanate (PZT) and barium titanate (BaTiO 3 ) composite films. The KPM are fabricated by uniformly compounding and polarizing piezoelectric particles (i.e., PZT and BaTiO 3 ) in silicon rubber and structured by cutting the piezoelectric rubbery films into ligaments. Characterizes the electrical properties of the KPM and investigates the bistable mechanical response under the coupled large deformations with the stretching ratio up to 200% strains. Finally, the PZT KPM sensors are integrated into wireless sensing systems for the detection of vehicle tire bulge, and the non‐toxic BaTiO 3 KPM are applied for human posture monitoring. The reported kirigami piezo‐metamaterials open an exciting venue for the control and manipulation of mechanically functional metamaterials for active sensing under complex deformation scenarios in many applications.
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Some bi/multi‐stable mechanical meta‐structures are implemented as mechanical memory devices, which are with limits such as complex structural forms, low information storage capability and/or fragile structural stability to maintain the stored information bits robustly under external interferences. To address these issues, the structural intelligence is addressed by constructing a simple 3D‐printable multi‐layered cylindrical kirigami module with gradient structural parameters and a high‐efficiency mechanical memory device that can robustly store information bits exponentially larger than previous designs is proposed. The promising enhancement of information storage capability is demonstrated for the proposed mechanical memory device and relies on two mechanisms: 1) the deformation sequences of the kirigami module enabled by the gradient structural parameter, which brings the extra dimensional degree of freedom to break the traditional mechanical memory unit with only planar form and merits information bits with spatially combinatorial programmability, and 2) the combinatorics of the deformation independences among the cylindrical kirigami unit arrays in the constructed mechanical memory device. Particularly, both the structural stabilities and the desired structural robustness are achieved in the mechanical memory devices by additively introducing magnetic “N–S” poles in units, which can protect the stored information from interferences like mechanical crushing, impact, and/or vibration.
Liquid metal‐elastomer composites have immense potential for emerging electronic applications due to their exceptional mechanical and functional properties. Underwater exploration is one area of interest for these composites, where divers or robots could benefit from wearable sensing, health monitoring, and energy harvesting. However, the influence of water submersion on liquid metal composites is not well understood. Here, the effect of underwater environments on the mechanical, thermal, and electrical properties of liquid metal composites exposed to month‐long aging is quantified. Under most conditions, liquid metal composites maintain their initial properties over the course of aging. However, for composites with high volume loadings of liquid metal ( = 80%) exposed to saltwater conditions, a decrease up to 70% in tensile modulus and up to 44% in thermal conductivity can occur. The aging environments were not shown to have an effect on the electrical conductivity of the composites. Liquid metal composites are then shown to outperform traditional copper electrodes after saltwater aging, demonstrating these soft, multifunctional composites as strong candidates for wearable, water‐resistant devices and machines.
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Inspired by the adaptive features exhibited by biological organisms like the octopus, soft machines that can tune their shape and mechanical properties have shown great potential in applications involving unstructured and continuously changing environments. However, current soft machines are far from achieving the same level of adaptability as their biological counterparts, hampered by limited real‐time tunability and severely deficient reprogrammable space of properties and functionalities. As a steppingstone toward fully adaptive soft robots and smart interactive machines, this work introduces an encodable multifunctional material that uses graphical stiffness patterns to in situ program versatile mechanical capabilities without requiring additional infrastructure. Through independently switching the digital binary stiffness states (soft or rigid) of individual constituent units of a simple auxetic structure with elliptical voids, this work demonstrates in situ and gradational tunability in various mechanical qualities such as shape‐shifting and ‐memory, stress‐strain response, and Poisson's ratio under compressive load, as well as application‐oriented functionalities such as tunable and reusable energy absorption and pressure delivery. This digitally programmable material is expected to pave the way toward multi‐environment soft robots and interactive machines. This article is protected by copyright. All rights reserved
Biomimetic soft robots are typically made of soft materials with bioinspired configurations. However, their locomotion is activated and manipulated by externally controlled soft actuators. In this study, piezo-wormbots were developed by automatically triggering the mechanical metamaterial-inspired soft actuator to mimic the continuous crawling of inchworms without manipulation, where crawling was controlled by the deformation of the piezo-wormbots themselves. We designed the flexible piezo-wormbots with an actuator to generate bending deformation under continuous inflation, piezoelectric rubber to automatically create internal excitation voltage to trigger deflation, as well as true legs and prolegs to convert the bending-recovering sequence into continuous crawling. We tailored the actuator to enhance the crawling performance and found that the response was critically affected by the leg pattern, inflation-to-deflation time duration ratio, air pressure, and ground environment. We observed satisfactory locomotion performance for the following tasks (pushing boxes and approaching a predefined target) through accurate self-actuated crawling under up to 51 continuous bending cycles. The maximum crawling velocity of the piezo-wormbots was found to be 16.6 mm/s, resulting in a maximum body length per second (BL/s) of 0.13, which is comparable to those of most natural inchworms (0.1-0.3 BL/s). This study offers new insight into bioinspired soft robotics and expands its biomimetic performance to continuously autonomous locomotion.
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Magnetorheological elastomers (MREs), which adapt their mechanical properties in response to a magnetic field, can enable changes in stiffness and shape for applications ranging from vibration isolators to shape morphing robots and soft adaptive grippers. Here, a unified design approach is introduced to create MRE materials for extreme stiffness tuning, up to 70×, with rapid (∼20 ms) and reversible shape change. This guides the creation of a hybrid MRE composite architecture that incorporates a combination of magnetic particles and magnetic fluids into elastomers. The role of both solid and fluid inclusions on magnetorheological response is systematically investigated and a predictive model is developed that captures the stiffness tuning response of MREs across diverse material microstructures and compositions. This general understanding enables MRE materials with programmable response and greatly enhanced stiffness tuning and rapid response times compared to many MRE, granular jamming, and phase change approaches. This insight is utilized to optimize composites for a soft adaptive gripper which grasps and releases objects of diverse geometries.
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Fibers capable of generating axial contraction are commonly seen in nature and engineering applications. Despite the broad applications of fiber actuators, it is still very challenging to fabricate fiber actuators with combined large actuation strain, fast response speed, and high power density. Here, we report the fabrication of a liquid crystal elastomer (LCE) microfiber actuators using a facile electrospinning technique. Owing to the extremely small size of the LCE microfibers, they can generate large actuation strain (~60 percent) with a fast response speed (<0.2 second) and a high power density (400 watts per kilogram), resulting from the nematic-isotropic phase transition of liquid crystal mesogens. Moreover, no performance degradation is detected in the LCE microfibers after 10 ⁶ cycles of loading and unloading with the maximum strain of 20 percent at high temperature (90 degree Celsius). The small diameter of the LCE microfiber also results in a self-oscillatory behavior in a steady temperature field. In addition, with a polydopamine coating layer, the actuation of the electrospun LCE microfiber can be precisely and remotely controlled by a near-infrared laser through photothermal effect. Using the electrospun LCE microfiber actuator, we have successfully constructed a microtweezer, a microrobot, and a light-powered microfluidic pump.
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The deep sea remains the largest unknown territory on Earth because it is so difficult to explore1–4. Owing to the extremely high pressure in the deep sea, rigid vessels5–7 and pressure-compensation systems8–10 are typically required to protect mechatronic systems. However, deep-sea creatures that lack bulky or heavy pressure-tolerant systems can thrive at extreme depths11–17. Here, inspired by the structure of a deep-sea snailfish¹⁵, we develop an untethered soft robot for deep-sea exploration, with onboard power, control and actuation protected from pressure by integrating electronics in a silicone matrix. This self-powered robot eliminates the requirement for any rigid vessel. To reduce shear stress at the interfaces between electronic components, we decentralize the electronics by increasing the distance between components or separating them from the printed circuit board. Careful design of the dielectric elastomer material used for the robot’s flapping fins allowed the robot to be actuated successfully in a field test in the Mariana Trench down to a depth of 10,900 metres and to swim freely in the South China Sea at a depth of 3,224 metres. We validate the pressure resilience of the electronic components and soft actuators through systematic experiments and theoretical analyses. Our work highlights the potential of designing soft, lightweight devices for use in extreme conditions.
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Soft robots leverage deformable bodies to achieve different types of locomotion, improve transportability, and safely navigate cluttered environments. In this context, variable-stiffness structures provide soft robots with additional properties, such as the ability to increase forces transmitted to the environment, to lock into different body configurations, and to reduce the number of actuators required for morphological change. Tensegrity structures have been recently proposed as a biologically inspired design principle for soft robots. However, the few examples of tensegrity structures with variable stiffness displayed relatively small stiffness change (i.e., by a factor of 3) or resorted to multiple and bulky actuators. In this article, we describe a novel design approach to variable-stiffness tensegrity structures (VSTSs) that relies on the use of variable-stiffness cables (VSCs). As an example, we describe the design and implementation of a three-strut tensegrity structure with VSCs made of low melting point alloys. The resulting VSTS displays unprecedented stiffness changes by a factor of 28 in compression and 13 in bending. We show the capabilities of the proposed VSTS in three validation scenarios with different tensegrity architectures: (1) a beam with tunable load-bearing capability, (2) a structure that can self-deploy and lock its shape in both deployed and undeployed states, and (3) a joint with underactuated shape deformations.
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Soft robotics may enable many new technologies in which humans and robots physically interact, yet the necessary high-performance soft actuators still do not exist. The optimal soft actuators need to be fast and forceful and have programmable shape changes. Furthermore, they should be energy efficient for untethered applications and easy to fabricate. Here, we combine desirable characteristics from two distinct active material systems: fast and highly efficient actuation from dielectric elastomers and directed shape programmability from liquid crystal elastomers. Via a top-down photoalignment method, we program molecular alignment and localized giant elastic anisotropy into the liquid crystal elastomers. The linearly actuated liquid crystal elastomer monoliths achieve strain rates over 120% per second with an energy conversion efficiency of 20% while moving loads over 700 times the elastomer weight. The electric actuation mechanism offers unprecedented opportunities toward miniaturization with shape programmability, efficiency, and more degrees of freedom for applications in soft robotics and beyond.
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Soft tubular actuators can be widely found both in nature and in engineering applications. The benefits of tubular actuators include (i) multiple actuation modes such as contraction, bending, and expansion; (ii) facile fabrication from a planar sheet; and (iii) a large interior space for accommodating additional components or for transporting fluids. Most recently developed soft tubular actuators are driven by pneumatics, hydraulics, or tendons. Each of these actuation modes has limitations including complex fabrication, integration, and nonuniform strain. Here, we design and construct soft tubular actuators using an emerging artificial muscle material that can be easily patterned with programmable strain: liquid crystal elastomer. Controlled by an externally applied electrical potential, the tubular actuator can exhibit multidirectional bending as well as large (~40%) homogenous contraction. Using multiple tubular actuators, we build a multifunctional soft gripper and an untethered soft robot.
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A novel phase‐changing particulate that amplifies a composite's modulus change in response to thermal stimulus is introduced. This particulate additive consists of a low melting point alloy (Field's metal; FM) formed into microparticles using a facile fabrication method, which enables its incorporation into polymer matrices using simple composite manufacturing processes. The effect of the solid–liquid phase change of the FM particles is demonstrated in two host materials: a thermally responsive epoxy and a silicone elastomer. In the epoxy matrix, this thermal response manifests as an amplified change in flexural modulus when heated, which is highly desirable for stiffness‐changing move‐and‐hold applications. In the silicone matrix, the stretchability can be switched depending on the phase of the FM particles. This phenomenon allows the silicone to stretch and hold a strained configuration, and gives rise to mechanically programmable anisotropy through reshaping of the FM inclusions. FM particles present many opportunities where on‐demand tunable modulus is required, and is particularly relevant to soft robotics. Because the melting temperature of FM is near room temperature, triggering the phase change requires low power consumption. The utility of FM particle‐containing composites as variable stiffness and variable stretchability elements for soft robotic applications is demonstrated. Particles of low melting point alloys can be leveraged to create a new class of functional, responsive composite materials. Here, the solid–liquid phase change of Field's metal particles is used to amplify the range of stiffness modulation in an epoxy, and to create on‐demand switchable stretchability and mechanically programmable anisotropy in a silicone elastomer.
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Kirigami tessellations, regular planar patterns formed by partially cutting flat, thin sheets, allow compact shapes to morph into open structures with rich geometries and unusual material properties. However, geometric and topological constraints make the design of such structures challenging. Here we pose and solve the inverse problem of determining the number, size and orientation of cuts that enables the deployment of a closed, compact regular kirigami tessellation to conform approximately to any prescribed target shape in two or three dimensions. We first identify the constraints on the lengths and angles of generalized kirigami tessellations that guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a compact, non-overlapping planar cut pattern. We then encode these conditions into a flexible constrained optimization framework to obtain generalized kirigami patterns derived from various periodic tesselations of the plane that can be deployed into a wide variety of prescribed shapes. A simple mechanical analysis of the resulting structure allows us to determine and control the stability of the deployed state and control the deployment path. Finally, we fabricate physical models that deploy in two and three dimensions to validate this inverse design approach. Altogether, our approach, combining geometry, topology and optimization, highlights the potential for generalized kirigami tessellations as building blocks for shape-morphing mechanical metamaterials.
Pump it up Carbon nanotube yarns can be used as electrochemical actuators because infiltration with ions causes a contraction in length and an expansion in diameter. Either positive or negative ions can cause this effect. Chu et al. constructed an all-solid-state muscle that eliminated the need for an electrolyte bath, which may expand the potential for its use in applications. By infiltrating the yarns with charged polymers, the fibers start partially swollen, so the length can increase through the loss of ions. It is thus possible to increase the overall stroke of the muscle. Further, these composite materials show a surprising increase in stroke with scan rate. Science , this issue p. 494
Multifunctional lattice materials exhibit functionalities beyond conventional load-bearing usage and are usually fabricated by additive manufacturing. This work introduces a new class of functional lattice materials called liquid metal lattice materials. These lattice materials consist of liquid metals and elastomers organized in a core-shell manner. This hybrid design induces a shape memory effect by harnessing the solid-liquid phase transition of liquid metals. Consequently, several remarkable functionalities are achieved such as recoverable energy absorption, tunable rigidity, and reconfigurable behaviors. These liquid metal lattice materials are fabricated by using a hybrid manufacturing approach, which integrates the 3D printing, vacuum casting, and conformal coating techniques. A variety of lattice structures are presented to demonstrate the capability of this hybrid manufacturing method and the functionalities of liquid metal lattice materials. This new class of lattice materials have promising applications in aerospace, robotics, tunable metamaterials, etc.
Kirigami-patterned mechanisms are an emergent class of deployable structure that are easy to fabricate and offer the potential to be integrated into deployable robots. In this paper, we propose a design methodology for robotic kirigami structures that takes into consideration the deformation, loading, and stiffness of the structure under typical use cases. We show how loading-deformation behavior of a kirigami structure can be mechanically programmed by imposing plastic deformation. We develop a model for plasticity in the stretching of a kirigami structure. We show the creation of kirigami structures that have an increased elastic region, and specified stiffness, in their deployed states. We demonstrate the benefits of such a plastically-deformed structure by integrating it into a soft deployable crawling robot: the kirigami structure matches the stiffness of the soft actuator such that the deployed, coupled behavior serves to mechanically program the gait step size.