Roboticizing fabric by integrating functional fibers
Trevor L. Bucknera, R. Adam Bilodeaua, Sang Yup Kima, and Rebecca Kramer-Bottiglioa,1aSchool of Engineering & Applied Science, Yale University, New Haven, CT 06520

Edited by John A. Rogers, Northwestern University, Evanston, IL, and approved August 12, 2020 (received for review April 7, 2020)

robotic fabric| functional fibers | active fibers | e-textiles | smart textiles

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F

rom natural plant fibers and animal wool to modern glass filaments and synthetic polymer thread, fabrics are among themost ubiquitous and adaptable materials in history. By nature of
their interlaced fiber structure, fabrics are breathable, conformable, and highly compactible. Further, their general resiliency to
crushing, tearing, and bending positions fabrics as the perfect classof material for wearables and other conformable applications,
including specialized products such as extreme-weather-protective
garments, rugged ripstop nylon in parachutes, and bullet-resistantvests. Given these versatile characteristics and unique application
design space, the possibility of roboticizing fabrics could lead tosmart adaptive clothing, self-deploying shelters, and lightweight,
stowable, shape-changing machines.
Preliminary related works introduced the terms “smart textiles” and “e-textiles” (1–3) to designate fabrics enhanced withelectrical circuitry via the development of flexible (4–6) or
miniaturized (7, 8) versions of traditional electrical components.
In particular, flexible sensors (1, 9–12), electrically conductive
threads (3, 9), and energy collection devices (13–15) have come
forth as potential building blocks for robotic fabrics. There haveeven been rare demonstrations of wearable fabric devices thatuse responsive materials for embedded actuation, including selfrolling temperature-sensitive sleeves (16), an orthotic limb support (17), and dynamic compression stockings (18). While thevast majority of these works showcase the success of individual
robotic components, they are generally passive or uncontrolled,
and the actuators rely on external actors to “reset” them after asingle use or actuation cycle. As many of these concepts rely
upon the presence of a host structure, such as the user of awearable device, the notion of independently functioning fabricmachines has also been little explored (19).
We demonstrate an expanded scope of fabric functionalization
that, through controlled closed-loop behavior and autonomous
task execution, becomes a complete stand-alone robotic platform(Fig. 1A). Our work addresses several gaps in the literature byintroducing a set of functional fibers that unify actuation,
structural control, and sensing functions into a cohesive robotic
fabric unit (Fig. 1 B and C). By using fiber-like components as
the active elements (Fig. 1D), we retain the desirable qualities offabric, which opens the way for machines that are not only thin,lightweight, and breathable but which harness complex curvatureand limitless surface configurations as key functions.
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Below, we detail the design and optimization of functional fibers
as actuators, variable-stiffness (VS) components, and sensors. We
then describe the integration of these functional fibers into robotic
fabrics that enable new capabilities, such as reactive wearables anddeployable fabric structures.
Results
Actuation. As of this writing, motion-generating fabrics have madeonly rare appearances in end-user products (20). However, as efforts are made to mimic the stranded muscular tissue in living animals, several different fiber-like actuators of varying utility havecome to light (19, 21). Some of the more promising examples include shape-memory polymers (22), shape-memory alloys (SMAs)(23), conductive polymers (24), electromechanical twisted carbon
nanotube yarns (25, 26), and supercoiled nylon strands (27).
We selected Nitinol SMA wire as our actuating fiber. SMA iselectrically conductive and, when programmed to remember ashape, activates with heat. These two traits make electrical control via joule heating a simple process. SMA wire is usually shaped
into a coil or mesh to allow for high-strain linear contraction (23,28, 29). We instead utilize SMA wire to generate bending motion(Fig. 2A and SI Appendix, Fig. S1), which has typically only been
demonstrated using large SMA panels bent into “hinges” (30, 31).
Bending allows the SMA wire to actuate “in-plane” with the fabricsubstrate (Fig. 2B) and facilitates reversible antagonistic motion
when paired with an actuator on the opposite side of the fabric.
Bending wire actuators can also be easily anchored to fabric bycouching (Fig. 2C)—a well-established sewing technique.
One challenge when integrating antagonistic wire bending
actuators into a highly flexible fabric is that any off-center forcesencourage the wire to twist the fabric rather than purely bend.
This contortion can introduce chaotic actuation or even bending
opposite the intended direction if the wire turns over within its
SignificanceFabrics are key materials for a variety of applications that require
flexibility, breathability, small storage footprint, and low weight.
While fabrics are conventionally passive materials with static
properties, emerging technologies have provided many flexible
materials that can respond to external stimuli for actuation, structural control, and sensing. Here, we improve upon and processthese responsive materials into functional fibers that we integrate
into everyday fabrics and demonstrate as fabric-based robots thatmove, support loads, and allow closed-loop controls, all while
retaining the desirable qualities of fabric. Robotic fabrics present ameans to create smart adaptable clothing, self-deployable shelters,
and lightweight shape-changing machinery.
Author contributions: T.L.B., R.A.B., S.Y.K., and R.K.-B. designed research; T.L.B., R.A.B.,
and S.Y.K. performed research; T.L.B., R.A.B., and S.Y.K. analyzed data; and T.L.B. and
R.K.-B. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Published under the PNAS license.
1

To whom correspondence may be addressed. Email: rebecca.kramer@yale.edu.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/
doi:10.1073/pnas.2006211117/-/DCSupplemental.

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Fabrics are ubiquitous materials that have conventionally been passive
assemblies of interlacing, inactive fibers. However, the recent emergence of active fibers with actuation, sensing, and structural capabilities provides the opportunity to impart robotic function into fabricsubstrates. Here we present an implementation of robotic fabrics byintegrating functional fibers into conventional fabrics using typical
textile manufacturing techniques. We introduce a set of actuating andvariable-stiffness fibers, as well as printable in-fabric sensors, whichallows for robotic closed-loop control of everyday fabrics whileremaining lightweight and maintaining breathability. Finally, we demonstrate the utility of robotic fabrics through their application to an
active wearable tourniquet, a transforming and load-bearing deployable structure, and an untethered, self-stowing airfoil.

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Fig. 1. Robotic fabrics. (A) Rendering of a potential robotic fabric capableof locomotion. (B) Actualized robotic fabric demonstration. (C) Current robotic fabric vs. rendering of potential fully woven robot. (D) Fiber-form robotic components (from the left: sensors, actuators, and structural supports)
can be combined in a variety of ways to create thin fabric-based machines.

couching. We overcame this challenge by flattening the round
SMA wires (Fig. 2D) into ribbons (Fig. 2E), modifying the area
moment of inertia such that bending is favored over twisting.
Additionally, the couching is able to hold a flattened ribbon
tighter to a fabric base, preventing the actuator from overturning.
To elucidate the cause of twisting we studied bidirectional
actuation of fabric, where SMA ribbons are used in antagonistic
pairs. When its opposing actuator is active, an SMA ribbon isforced to bend backward against its programmed actuation trajectory, building up a spring response within the ribbon. Threepoint bending tests revealed that the flexural modulus of our
SMA ribbons is consistent regardless of bending direction (E ≈66 GPa); however, plastic deformation occurs at different
stresses depending on the bending direction (Fig. 2F). We surmise that it is this difference in maximum stress that often encourages a wire to twist such that it is again bending “forward,”
avoiding excessive buildup of elastic energy.
We characterized the effectiveness of the flattening treatment
by measuring the tendency for SMA wires and ribbons of various
aspect ratios to remain in the desired bending plane in responseto an external force. We clamped the SMA specimens in a
prebuckled configuration and applied a force to the center point
at different incoming angles (Fig. 2G). At an applied force angleof 0°, the wire is expected to experience a snap-through,remaining fully in-plane as it deflects. Conversely, at an angle of90°, the wire should twist out of plane about the fixed-fixed axis.
After recording the dominant behavior (in-plane or out-of-planemotion) for intermediate force angles, the results confirm that byincreasing the wire aspect ratio (flattening the wires) they become more resistant to out-of-plane forces and favor in-plane
deflection (Fig. 2H).
“Activated” (heated) SMA generates force by building up internal material stresses as its crystalline structure transitions
from martensite to austenite (23). Given that stresses in bending
are greatest on the outer surface, we would expect that regions
farthest from the neutral axis contribute most to the bending
force. That is, thicker wires generally provide larger output
forces than thin ribbons of similar cross-sectional area (Fig. 2I).
Indeed, we see that for flattened wires the output force is linearly
proportional to the area moment of inertia (SI Appendix, Fig.
S2). However, round wires underperform in this regard, reachinga force-output plateau due to actuation forces being directed outof plane.
As mentioned, when bending in the direction of programmed
actuation, plastic deformation occurs at a relatively low stress,
which is mostly a result of reversible detwinning of the martensitic
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crystal lattice (23). In the reverse direction, it is possible to introduce permanent dislocations and microcracks into the ribbonthat interfere with the austenite–martensite transition and adversely affect the programmed actuation (32, 33). The point at
which this damage occurs is determined by the material flexuralstrength (SI Appendix, Fig. S3A), although measured strength
seems to be influenced by the processing steps and was not constant across SMA aspect ratios (SI Appendix, Fig. S3B). We maximize the lifetime of our actuators by avoiding this overstrained
regime except for the initial unwrapping and straightening of
the ribbon in preparation for the sewing step. By also avoiding
excessive temperatures, we have continuously used our antagonistic actuators for upwards of 1,000 cycles with no noticeable
degradation.
Given this characterization, we selected an SMA ribbon aspectratio of 2.5 for all further demonstrations, as it provided a reasonable balance of output bending force, system stiffness, andstable in-plane motion. At 100 °C, the blocked force of our selected SMA ribbon reaches ∼33.3 N/m, about 1/14 the average
blocked bending force of a human index finger, ∼480 N/m (34).
VS Support Structure. Although a fabric might be equipped withlocally reliable actuators, its inherent lack of a supportive
structure limits control of the overall robot configuration. By
actively softening and stiffening our VS fibers, we can regulate
the direction and degree of actuation with higher repeatability
and fewer total actuators. In addition, an on-demand support
structure allows a robotic fabric to perform move-and-hold operations to sustain loads which would otherwise collapse a typicalfabric. VS is possible using many different techniques (35, 36),
but expressions of this concept in fiber-like morphologies arelimited. The most successful examples include silicone tubes
filled with a low-melting-point material (37, 38), strands of glasstransition polymer (39, 40), segment jamming via tension in anaxial wire (41, 42), and the use of antagonistic actuator pairings(43).
Our VS fibers (Fig. 3 A–C) are based upon a thermally responsive epoxy that softens significantly as it undergoes a glasstransition over the range of 45 °C to ∼60 °C (44) (Fig. 3 D and
E). We also incorporate a low-melting-point metallic alloy particulate filler (Field’s metal; FM) (45) at a volume ratio of∼85:100 (46 vol % FM), which increases the rigidity of the VS
fibers when cold yet melts at 62 °C to further soften the material
when heated (Fig. 3 F and G). The fibers are joule-heated via aninternal conductive stainless-steel thread (Fig. 3 E and F).
We measured the flexural moduli of fibers made from both theneat epoxy matrix and the FM composite over a range of temperatures (Fig. 3H). The addition of FM raises the maximum
rigid modulus while lowering the heated (i.e., soft) modulus (45).
Even with the addition of the flexible stainless-steel core in thefiber, the lower stiffness bound remains below 25 MPa, which isslightly less flexible than latex rubber and, when in fiber form, iswell matched to the output force capabilities of our SMA actuators. While the addition of FM enables an increased modulus
range, the FM composite has a lower ultimate flexural strengththan neat epoxy, which may be due to poor bonding at the interfaces between epoxy and FM particles (Fig. 3I and SI Appendix, Fig. S4).
Because the response of a thermally responsive fiber is timedependent, characterizing the time to completely transition between rigid and soft states is crucial for effective control sequencing in robotic fabrics. We measured the thermal conductivityof the VS composite fiber, and as expected when compared toanalytical models the increased volume fractions of FM lead toincreased thermal conductivity (Fig. 3J). We then developed anumeric heating and cooling simulation of the VS fibers under awide range of material conditions and compared it to experimental data (SI Appendix, Figs. S5–S9). Fully cooling to room
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Fig. 2. SMA actuators. (A) SMA ribbon programmed to exhibit bending motion. (B) Sewn SMA ribbon used to actuate fabric body. (C) Couching method toaffix SMA ribbon to a fabric substrate. (D) Initial round SMA wire. (E) Flattened SMA ribbon. (F) Bending an SMA against its programmed direction induceshigher flexural stress and encourages the wire to twist instead. Error cloud is 95% confidence interval. (G) Round and flattened wires were subjected to forcesat increasing out-of-plane angles to determine bending response. (H) A flattened ribbon will tend to bend and buckle in plane (green) and a round wire willtend to twist and bend out of plane (red). (I) Round SMA actuators tend to generate higher bending force than flattened actuators of comparable crosssection. Error bars are one SD.

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temperature from a uniform 65 °C in free convection takes ∼70 s
regardless of FM content (Fig. 3K), although after only 20 s thefiber reaches below 45 °C and the glass transition is safely complete. Attaching the fibers to fabric interferes with this coolingprocess, and VS fibers used in the demonstrations below wereconsequently allowed an additional 20 s to ensure complete glasstransition (SI Appendix, Fig. S10). On the other hand, heatingtimes varied slightly depending on the material composition andwhether the steel heating yarn was properly centered in the fiber(Fig. 3L). Notably, the increased thermal conductivity from the
FM inclusions smooths the thermal gradient in the fiber, reducing
hot spots which could result in premature material degradationand cold spots with incomplete phase transitions (Fig. 3 K and L).
With these results, we selectively use both the neat and composite VS fiber formulations depending on the use case, favoringhigher rigidity and reduced deflections with the FM composite or
higher strength and robustness with the neat epoxy.
Sensing. An important part of any robot is the ability to sense internal or environmental changes and respond appropriately. To
create sensors, we used a self-coagulating, paintable conductive ink,
which allows a region of fabric to become highly sensitive to smallchanges in strain while adding negligible stiffness to the fabric (46).
Composed of a polydimethyl-siloxane (PDMS) precursor emulsified
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in a carbon black nanoparticle/ethanol suspension, this ink caneasily permeate and bond to individual filaments of a fabric(Fig. 4 A and B). Penetration into the fiber weave itself maintains
much of the porosity of the fabric (Fig. 4 C and D) and creates anelectrically conductive pathway that changes in resistance as the
fabric weave is stretched and the gaps present between fibers areenlarged (Fig. 4E).
By printing this ink on opposite faces of a fabric, sensors canbe used to detect structural bending. Despite some permeation
through the cloth, the printed face will have a higher density of
conductive material, and this small offset from the neutral axis isenough to bias the sensor toward a compression response in one
bending direction and extension in the other. The sensor signal ismost consistent in extension, so querying the corresponding
sensor depending on bend direction leads to repeatable sensor
values.
In Fig. 4F we show a section of fabric with these printed
sensors and two antagonistic bending SMA ribbon actuators attached via couching. The sensor feedback made it possible tocontrol the fabric actuation and hold different curvatures (represented as target sensor signals; Fig. 4G and Movie S1). Without VS elements, the device naturally relaxes into a neutral
center position when neither actuator is active due to a balancein opposing spring forces in the SMA ribbons.
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Fig. 3. VS fibers. (A) A shaped VS fiber supports a 20-g load. (B) VS fiber sewn onto a fabric substrate. (C) A VS fiber tethered by fabric is prevented frombuckling outward, increasing support up to 50 g before legs begin slipping. (D) Neat epoxy VS fiber. (E) Neat epoxy cross-section. (F) FM composite crosssection. (G) FM composite VS fiber. (H) Hot and cold flexural modulus for both the neat epoxy and FM composite (46 vol % FM), with and without stainlesssteel yarn core used for joule heating. Error bars are SD. (I) Ultimate flexural strength of the VS fibers. (J) Measured thermal conductivity of the composite vs.
volume percent of FM, compared with Bruggeman effective medium theory. Error bars are 95% confidence interval. (K) Free convection cooling of VS fibers.
Experimental data are for neat epoxy specimens. Numerical simulations for both neat epoxy and FM composite had negligible difference (error cloud
represents 95% CI). (Inset) Computed cross-sectional thermal gradient for both 0 and 50 vol % FM fibers after 7 s of cooling from 65 °C. (L) Numericalsimulation results for a “worst-case” heating scenario, with the heating core center offset to two-thirds of the VS fiber diameter. (Inset) Computed crosssectional thermal gradient after 6 s of heating at 13 W/m.

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Applications. We present a series of demonstrations that utilize

the SMA ribbon actuators, VS fibers, and in-fabric strain sensors,
suggesting a range of possible applications for robotic fabric.
First, we showcase a robotic fabric tourniquet (Fig. 5A andMovie S2). This device comprises a breathable fabric sleeve withembedded rows of parallel ribbon actuators, VS fibers, andconductive carbon ink traces. When the fabric is severed along
one of the conductive carbon ink traces, the damage is detected
as a broken circuit and an emergency response is triggered at thedamage site. The fabric will compress and then hold that position
without further power expenditure (Fig. 5 B–D). The bending
motion of the SMA ribbons is suited to compressive actuation bysqueezing from a circle to a pinched, “clover-like” configuration(Fig. 5 B, Inset), rather than circumferential contraction. Each
SMA ribbon was measured to contribute ∼1.6 ± 0.1 kPa, whichapproaches the recommended arm cuff pressure of ∼2 kPa to
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combat orthostatic hypotension (47). We expect that further
developments and an increased actuator count may achieve thehigher pressure of ∼26.6 kPa that is recommended to properly
cut off blood flow (48). The current implementation is able tosoften, constrict, and stiffen at one damage site over a course of
100 s, consuming ∼415 J in the process. This type of responsive
sleeve could potentially be used as a smart garment in military or
exploratory environments, where automatic emergency measures
could counteract life-threatening situations if medical aid is not
immediately available. By altering the arrangement of actuators,
sensors, and VS fibers, it is conceivable that other types ofassistive wear could also be created, such as clothing that augments muscular motion, provides dynamic orthostatic pressure,or even simply changes shape to fit different climate conditions.
Second, we demonstrate a shape-changing robotic fabric sheetthat functions independently from any host body (Fig. 5 E and F
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Fig. 4. Conductive ink sensors. (A) The carbon black/PDMS/ethanol emulsion is printed directly onto the fabric. The surface conductivity is sufficient such thatprinted sensor blocks can be electrically connected by sewing over them with conductive thread. (B) A microscope image of ink-coated knitted spandex fabric.
(C) Porosity measurement of neat, unstrained fabric. (D) Porosity of inked fabric. (E) Porosity of inked fabric after stretching. (F) A simple actuator-sensor
device curls up and down, generating a sensor signal dependent on device curvature. (G) The curling device follows the control signal by modulating thepower output to the SMA actuators. Each sensor is actively used only when the corresponding fabric face is in extension.

and Movie S3). The initial form of this device is a flat, squaresection of cloth (Fig. 5G). Upon activation, the device softens its
VS frame and lifts itself up into a table-like platform structure.
This new shape becomes rigid and load-bearing, supporting a
50-g weight on the platform with little deflection, while the legs
begin to buckle apart somewhat under a 100-g weight. The shapeis then softened and returned to its initial configuration via anantagonistic ribbon actuator, which flattens the device again(Fig. 5F). Each complete shape change (soften, actuate, andstiffen) takes 90 s to complete, consuming ∼830 J. Carrying its
own 50-g battery (11.1 V, 650 mAh), this robotic fabric could
theoretically perform ∼25 such shape changes on a single charge.
By choosing not to soften certain VS fibers, such as the central
VS ring (Fig. 5 H and I), the actuation motion and subsequent
shape is influenced. This signifies that even complex transformations may be possible with reduced component counts byleveraging actuators and VS components in concert. Further, thecontinuous curvature displayed by this machine sets robotic
fabrics apart from origami-inspired machines (49), as the rangeof transformation and conformability is not limited by discretefolds. While this demonstration could be a preliminary version of
a self-deploying shelter or load-bearing furniture, the shapechange ability demonstrated is also an early indication of thepotential for extremely adaptable, independent machines with
on-demand tool generation.
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Last, taking inspiration from the fabric wings of the 1903
Wright Flyer, we demonstrate a self-deploying airplane wing in a
fully untethered system (Movie S4). The robotic fabric wings areseated into small slits in the side of the fuselage, wherein all
additional circuitry, microcontrollers, and batteries are enclosed.
The fabric wings curl to wrap around the fuselage for compact
storage (Fig. 5J) and uncurl into a deployed, rigid state withwings extended (Fig. 5 K–N). Each complete shape change(soften, curl or uncurl both wings, and stiffen) takes 160 s tocomplete, consuming ∼2,550 J. The 11.1-V, 1,200-mAh rechargeable battery used supports up to 47 shape changes withthese energetics on a single charge. This demonstration showsthe ease of integrating robotic fabric with rigid machinery,allowing fabric-based components that can self-stow or move outof the way when not in use. This is a key functionality for use
cases when light weight and low storage volumes are highly desired, as in transportation to and from remote locations or inspace exploration.
System Design Considerations. As a planar structure, the mass of arobotic fabric unit will scale linearly with its length and width,
assuming uniform distribution of functional fiber components.
This is not an issue for the SMA ribbon actuators, as they exhibit
a constant bending force along the length of the actuator,
meaning a long actuator ribbon can curl up just as easily as a
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Fig. 5. Robotic fabric demonstrations. (A) Robotic fabric tourniquet. (B) Tourniquet is buttoned about a foam body. It reacts to a damaged circuit bycontracting and holding a tightened “clover-shape” pose. (C) Thermal image of the tourniquet as VS fibers soften. (D) Thermal image of activated SMA
actuators constricting. (E) Robotic fabric “pop-up” table. (F) From an initial flat state, the table is able to stand up, stiffen into a load-bearing platform, andthen collapse under a load as it softens and actuates back into its initial flat configuration. (G) Fabric “pop-up” table is ∼2 mm thick. (H) Activation andsoftening of table “leg” VS fibers. (I) Activation of SMA actuator wire, causing table to stand up. (J) Robotic fabric wing in self-stowed position. (K) Robotic
fabric wing curls and uncurls from deployed, open state into a compacted, stowed state. (L) Robotic fabric wing in deployed position. (M) Activation andsoftening of wing VS fibers. (N) Activation of curling SMA wires.

short ribbon. However, the support structure provided by VSfibers will be limited in this regard. Following Euler–Bernoulli
beam theory, a cantilevered section of fabric of length L andweight w will induce high bending moments at the fixed end
proportional to L2 following M = wL2 =2, while deflection at the
tip will increase proportional to L4. With a weight of 2.16 g/m, asingle rigid epoxy fiber could only sustain its self-weight up to
2.29 m before surpassing its ultimate flexural strength. For reference, the self-deploying airplane wings above have a winglength (cantilever length) of 130 mm, which exhibits minimal
deflection in the extended position. An FM–epoxy composite
fiber with its higher weight of 8.01 g/m would only support itself
for 1.55 m. It is more likely, however, that an unsupported
cantilever structure would become unbalanced before that occurred. For these reasons, it is encouraged that robotic fabricstructures have a firm support on both ends of large extended
regions, which will increase the viable length by a factor of
6 (M = wL2 =12). Of course, the weight of all other components
must be included when considering this step (2.51 g/m for SMA
ribbons and 0.073 g/m for 10-mm-wide strips of cotton fabric).
Increased fiber lengths also require more power for full activation. Both the SMA ribbons and VS fibers are driven by joule
heating, which requires power that scales linearly with length. In
our case, our selected SMA actuators were powered at a rate of
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25 W/m, and VS fibers were powered at 8.2 W/m. In addition to
consuming more power, the higher voltages needed to maintainthe appropriate current might be difficult to reach without alarger power supply. For this reason, it may be useful to split longfibers into multiple shorter fibers that can act in parallel and are
only as long as necessary to affect their local region before
powering down.
As both the SMA actuators and VS fibers are thermally responsive, it is important to avoid any thermal cross-talk to prevent unwanted activations. Observation of powered SMA
ribbons up to 120 °C reveals that the adjacent fabric region drops
to below the glass transition threshold of VS fibers at a distanceof ∼3 mm on either side (SI Appendix, Fig. S11). Maintaining this
3-mm separation between functional fibers prevents the VS fibers from prematurely softening, as shown in the parallel fiber
arrangement of the tourniquet demonstration. When components must cross, as in the shape-changing table demonstration,
we have found that placing them on opposing faces of the fabric,or inserting a small snip of painter’s tape at the junction, isenough to thermally isolate the fibers. Our selected sensor material is also susceptible to temperature effects, exhibiting an
increase in resistance approaching 5% at 125 °C (SI Appendix,
Fig. S12A), although in practice, as in the controlled bending
fabric example (Fig. 4F), if the sensor is placed at least 3 mm
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Discussion
By treating fabric as the foundation of a robot, it can be enhanced from a passive material to smart adaptive clothing, selfdeploying structures, or lightweight shape-changing machinery.
We expect that with time scientific advances will unveil improved
actuation, VS, and sensory technologies that are ideal for future
robotic fabric developments. By leveraging well-established textile manufacturing process, we envision that the future will bringmass-produced rolls of robotic fabric, available for purchase, andprogrammable as-required to fit varied tasks. Self-reconfiguringmachinery made from this material could bend and twist into newand complex shapes as needed and then collapse for compact
storage.
Of course, there are still many hurdles to overcome before
robotic fabrics reach their full potential. For wearables, washability and heat dissipation will be important. The added rigidityand bulk of specialized fibers could also make wearable robotic
fabrics uncomfortable or difficult to don and doff. Additionally,
thermally controlled materials typically have slow cycle times andare power-inefficient, which leads to increased battery size. Future work will also require advancements in other areas, such as
the development of practical simulation and design tools for fiber placement optimization, robust thin-body controls, and evenlightweight embedded power supplies. With this in mind, we
hope that our early step toward robotic fabrics can inspire many
more future advances in a field with so much potential.
Materials

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Antagonistic Actuating Fiber Manufacture.
Flattening shape memory wire. After annealing Nitinol wire (McMaster-Carr) at∼500 °C and allowing it to air-cool it becomes ductile enough to allow incremental flattening via a simple manual rolling mill machine. The wire
undergoes significant stress hardening during this step, so the annealing andpressing process is repeated as often as necessary until a wire of the desired
thinness is obtained. A final annealing and pressing step is performed at
the same thickness to firmly lock in the new cross-section by counteracting
any shape loss that may occur due to residual shape-memory effect. The
wire will experience some amount of elongation as it is flattened, andconsequently the total wire cross section area is reduced slightly. All plotted data involving the Nitinol wires is normalized to account for thischange in cross-section area.
Programming shape memory wire. SMA wire is first annealed at 500 °C for
15 min and allowed to air-cool, making the wire malleable and easy to form
into the desired shape. The wire is then tightly wrapped about a 3.175-mm(1/4 in)-diameter 316 stainless steel rod, with the ends clamped using split
shaft collars (McMaster-Carr). The entire fixture is then heated to 390 °C for
15 min (50) and then quenched in room-temperature water. The heating
and quenching process is repeated three times. At this stage, the wire is
unclamped and unwrapped from its coiled shape and straightened. Application of heat to this wire will cause it to return to its tightly coiled programmed shape (SI Appendix, Fig. S1).
VS Fiber Manufacture.
FM particle preparation. FM particles are created by melting the metal in warm
water and agitating vigorously. A block of FM (Roto144F; RotoMetals) is
weighed out to 60 g; 150 mL of deionized water is added to a 500-mL beaker
and the FM is placed inside. A silicone oil bath is heated on a hot plate with amagnetic stirring rod up to 90 °C, and the 500-mL beaker is supported inside
the silicone oil bath such that the water level is below the surface of the oil.
The water is allowed to warm for ∼15 min until it settles at ∼70 °C and themetal is fully melted. At this stage, a mechanical homogenizer (VDI25; VWR)
with a 20-mm-diameter attachment and a vortex generator (RW16; IKAwerke) with a 42-mm-diameter turbine attachment are placed into thewater on opposite sides of the beaker. The beaker is tilted slightly such thatthe heavy metal will flow downward toward the homogenizer rather than

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gathering at the edges of the beaker. At this point, the homogenizer isturned on to a speed of 24,000 rpm and manually swept through the mixture for several seconds so as to initially break up the mass of metal which isheld together by surface tension, dispersing it into the water. The homogenizer is turned off and then fixed in place. With both instruments in position, the homogenizer is again turned on to a speed of 24,000 rpm tofurther break up the melted particles, and the vortex generator is turned on
to a speed of 1,200 rpm, which keeps the metal in motion and prevents itfrom settling and agglomerating. This agitation is applied for 10 min.
Next, the beaker is quickly raised out of the hot silicone oil bath to cool.
The vortex generator remains on to keep particles in motion until they havecooled solid, but the homogenizer is turned off so as not to shatter thesolidified particles, creating unpredictable particle geometries and sizes. The
mixture is allowed to cool for ∼15 min until its temperature is well below thefreezing point of FM (<∼50 °C), at which point the vortex generator isturned off and the mixture is allowed to settle. After several hours, themajority of the particles will have settled to the bottom of the beaker, andthe supernatant is extracted via syringe (rather than pouring) so as not todisturb the small particles. The remaining particle sediment is then stirredand “fluffed” to minimize any cementing during the drying process. The
particles are dried in a vacuum oven at 60 °C to remove as much of theremaining moisture as possible. The resulting dry material may clump together like sandstone and need to be shaken apart. The resulting material
has a fine, sand-like appearance.
Epoxy preparation. The stiffness-changing epoxy is created by combining an
epoxy curing agent, Jeffamine D400 (Huntsman International, LLC), with astandard epoxy resin, EPON 828 (Momentive Performance Materials Inc.) at
the stoichiometric ratio of 58:100 by weight, which maximizes the rigidity of
the resulting cured epoxy when in the solid state. After stirring lightly byhand, the epoxy mixture is placed in a vacuum chamber for 15 min toremove any trapped air. The epoxy can then be used as is or mixed withparticles of FM for an amplified stiffness-change behavior. The desired
amount of FM is measured out by weight then poured into the epoxy andstirred by hand until thoroughly dispersed.
Fiber preparation. The VS fibers are formed by first threading a strand of
conductive steel yarn (Adafruit Industries) through a section of silicone tubing(McMaster-Carr) cut to the desired fiber length, with an inner diameter of
1.58 mm (1/16 in). This can be eased by first lubricating the tube with isopropyl alcohol and feeding in a long segment of rigid wire such as copper ornickel and then pulling the yarn through behind it. Both ends of the steel yarn
are crimped with 1.5-mm-diameter noninsulated ferrules (McMaster-Carr) insuch a way that the ferrules are recessed slightly inside the silicone tubing,keeping the steel yarn taut and discouraging leaking in the next step. This
also provides a reliable electrical access point, since liquid epoxy will tend to
wick up the steel thread, creating insulating surface that would otherwise
make the steel thread inaccessible.
If no FM is used, the prepared epoxy can be injected directly into one endof the tubing using a syringe with an 18-gauge needle tip until the entire tube
is filled. Otherwise, the epoxy–FM mixture will need to be continuously
heated to melt the metal particles and allow it to flow through the tubing.
This can be done by filling a large glass beaker (500 mL) with boiling water.
A syringe is filled with the epoxy–FM mixture and affixed with an 18-gauge
needle. After holding it under the hot water for several seconds until the
mixture begins to flow inside, any excess air is expelled. The syringe can thenbe removed from the water and the needle is inserted into one end of thetubing. The steel yarn and crimp can be pulled out slightly on that end toallow the needle to fit and gain an airtight seal. The entire tubing and syringe assembly is then placed inside the hot water and allowed several
seconds for the metal to melt again. At that point, the syringe is held with
the nozzle pointing down and the material is injected until the entire tube isfilled. If the syringe is held upright, the metal particles will settle to the backof the syringe and will not be expelled into the tube. The steel yarn andcrimp are then reseated as needed in each end.
The filled tubes are placed into an incubator at 60 °C for 12 h for final
curing. It should be noted that the working time of the epoxy can be up to afull day at room temperature, but only 30 min when submerged in boilingwater. Finally, the silicone tubing can be cut away and the individual
1.59 mm (1/16 inch) diameter VS fibers can be removed. The conductive
crimps can then be soldered to or inserted into a second crimp for electricalconnection to the robotic fabric circuitry.
Conductive Strain-Sensory Ink Manufacture. The conductive ink exploits conductive nanoparticles to stabilize a PDMS/ethanol emulsion. The conductive
ink is made by first adding 0.705 g carbon black (Blackpearl 2000; Cabot) in
100 mL ethanol (15% by weight). The mixture is sonicated at 70% amplitude

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from any heated fibers the sensor temperature will not exceed∼36 °C, which corresponds to a resistance change of only ∼0.9%(SI Appendix, Fig. S12B). Further, full enclosure of thermally
responsive fibers inside the fabric should also be avoided tominimize cooling times.

for 3 min, with a 1-s on/1-s off pulse using a tip sonicator (QSonica Q700) to
break up carbon black aggregates. After sonication, 4 g of PDMS precursor(SEMICOSIL 964; Wacker) is added to the carbon black/ethanol mixture, andan identical sonication pulse is applied to emulsify the resin, creating a
Pickering emulsion with precure PDMS particles stabilized by a carbon black
particle “shell” at the surface. Upon completion, the emulsion is moved intoa syringe where it can be expelled by hand or inserted into an extrusion
printer for sensor fabrication.
This Pickering emulsion-based ink contains ∼2-μm droplets suspended in a
nonviscous carrier solvent that evaporates upon deposition. The small
droplets (which form the conductive composite) penetrate the fabric via thefiber-interstitial spaces, but some are also filtered by the fibers. As a result,the printed ink is thicker on the receiving side, while droplets that penetrated into the fabric enhance sensor-to-fabric adhesion and promotecoating of individual fibers. We repeated the printing process three or fourtimes on the same side of the fabric, further increasing the sensor thickness
on that side and ensuring it is biased toward one bending direction. The
applied ink cures in ∼1 h.

Methods

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SMA Twist Vs. Bend Behavior Testing. We characterized the tendency for SMA
wires and ribbons to bend or twist out of plane in the presence of opposing
forces. This is particularly useful data for the case where opposing antagonistic actuators are affixed to the fabric on opposite faces of the same cloth
region. When the wires are round, the actuating wire will tend to force theopposing wire to flip over in its couching and bend in the same direction,
which generally ruins subsequent actuation cycles and can even tangle
nearby fiber components in the resulting chaotic fabric warping. For theremainder of this section, we refer to both round SMA wires and flattened
SMA ribbons as simply “wires” with varying aspect ratio.
In this test, we clamped both ends of the SMA wires in a custom fixture,with clamps spaced 50 mm apart and the wire length at 52 mm. This placed
the wires into a prebuckled configuration, as in Fig. 2G. All wires wereclamped tightly enough that they could not rotate. Next, force was applied
at a constant rate of 0.5 mm/s to the wire center point using a materials
tester (Instron 3345). The bending state of the wires was observed by eye todetermine whether snap-through had occurred by the time the testing tip
had reached the midway point, in line with the fixed wire ends. If so, thespecimen was marked as ultimately bending “in plane,” and if not, the wire
had instead twisted a full 90° and was marked as “out of plane.” The fixture
was designed to be attached to the Instron at different angles, allowing theforce to be applied at differing angles relative to the snap-through directionof the wire. At an angle of 0°, parallel with the bending direction, the wire is
expected to experience a snap-through as the beam is deflected (Fig. 2H,
green region). Conversely, at an applied force angle of 90°, the wire should
only twist about the fixed-fixed axis (Fig. 2H, red region). As the wire buckles
in plane, the moment arm for twisting becomes smaller, while similarly as
the wire twists out of plane the angle of force becomes aligned more directly toward further twist. Eventually, one of these two cases dominates.
With increasing aspect ratio, the maximum angle of applied force where thein-plane snap-through still dominates also becomes larger, while smaller
aspect ratios can occasionally twist even at very low angles of force (Fig. 2H).
Therefore, with higher aspect ratio, an actuating ribbon will be more resistant to out-of-plane forces or slight misalignments, and will more consistently bend in plane with its paired antagonistic actuator rather thantwisting around into a more favorable low-energy configuration.
SMA Bending Stiffness Testing. Specimens of SMA ribbon of varying aspectratio were measured in a 30-mm three-point bending setup on a materials
tester (Instron 3345). The test provided bending stiffnesses of the ribbon
through the equation F = 48dEI=L3 for an applied force F, deflection d,
three-point support spacing L, flexural modulus E, and area moment of inertia I. The bending modulus was measured for ribbons in both the “forward” bending direction (in the direction of programmed curling actuation)and in the “reverse” direction (against the programmed actuation) by orienting each ribbon face up or face down as required. It was found thatregardless of bend direction or ribbon aspect ratio, the flexural modulus wasapproximately equal at ∼66 GPa.
Each test was allowed to continue until plastic deformation was reached,detected by a plateau in the force-displacement curve. The yield stress determines the point of plastic deformation onset, and follows the formulaσ flex = (Fyield L=8)(t=I) for yield force Fyield , three-point support spacing L, wire
thickness t, and area moment of inertia I. Interestingly, while the flexuralstrength is nearly constant in the forward direction across SMA aspect ratios,
the antagonistic flexural strength is not (SI Appendix, Fig. S3A). Additionally,

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since the bending moment of inertia is related to the flexural strength byσ flex = Mt=2I, and the wire radius of curvature R = EI=M, we find the minimum radius of curvature before failure to be R = Et=2σ flex. Notably, whenusing our experimental values for antagonistic flexural strength and wire
thickness in this equation, we find that when forced to bend against theirprogrammed curling direction, SMA actuators of all aspect ratios undergo
plastic deformation at the about same radius of curvature, ∼12 mm (SIAppendix, Fig. S3B). This may indicate some atypical response due to stressinduced austenite–martensite phase transition behavior (51) that is dependent on the programmed shape, as each SMA ribbon was programmed tothe same initial radius of 3.175 mm.
SMA Blocked Bending Force Testing. To characterize the effect of SMA wire/ribbon cross-section on actuation force, we measured the blocked bending
tip forces of several simple actuating fabric specimens on a materials tester(Instron 3345). Each fabric specimen consisted of a long SMA wire/ribbon of
the aspect ratio to be tested, bent into a U-shape and sewn into a section ofmuslin fabric (Fig. 2C). This U-shaped wire was programmed such that thetwo parallel legs of the wire/ribbon bend in the same direction, lending theactuator some stability. The specimens were clamped on the end to provide
an 8cm actuator arm, with the bend of the “U” positioned beneath theInstron probe. Specimens were supplied with increasing steps of electrical
power, and the steady-state blocked force was recorded at each level. SMA
temperature was also recorded after each plateau using a thermal camera(Fluke TiX 580). The data displayed in Fig. 2I and SI Appendix, Fig. S2 werenormalized to account for any reduction in cross-sectional area that arose
due to wire elongation in the flattening process.
Operating within the linear elastic region during antagonistic actuation,
the remaining force Frem available to perform work on the environment willbe the difference between actuating force Fact and the force required tobend the antagonistic wire Fant . Because both actuation force and antagonistic bending stiffness are linearly proportional to the wire’s area momentof inertia (i.e., Fact = αI and Fant = βI for some constant values α, β and moment of inertia I), we find that Frem = Fact − Fant = αI − βI = (α − β)I. Therefore, increasing the area moment of inertia should lead to a higher residual
force to perform work. On the other hand, the bending stiffness of thesystem will depend on the rigidity of individual wires (EI). For a robotic
fabric, it is somewhat desirable to retain a measure of flexibility, meaningthat there is a trade-off that must be made between working force andsystem softness.
VS Flexural Modulus Measurement. The flexural moduli of VS fibers made fromboth neat epoxy and the FM composite were measured using a dynamic
mechanical analyzer (DMA Q800; TA Instruments). Specimens were cut fromlengths of VS fiber to dimensions of 1.5875-mm diameter × 10 mm. Specimens were placed in a single‐cantilever clamp with a clamp separation of 4mm. Assuming the two ends of the specimen are clamped and do not rotate,
the specimen flexural modulus Ef can be calculated from the measured
force: Ef = FL3 =12δI, where L is the length of the beam, I is the area momentof inertia of its cross‐section, and F is the force needed to deflect the beam a
distance δ. All specimens were applied a temperature sweep from 25 °C to
85 °C at a rate of 1.5 °C/min around the glass and melting transitions from 50
to 70 °C, and 3 °C/min everywhere else. Specimens were applied a sinusoidal
force on the end of the cantilever at a rate of 1.0 Hz and a maximum deflection of 150.0 μm. Specimens were clamped with a torque of 1 in-pounds.
VS Ultimate Strength and Failure Strain Measurements. The ultimate flexuralstrength of VS fibers was calculated from the stress-strain curves of both neat
epoxy and the FM composite, as measured in a three-point bending setup ona materials tester (Instron 3345). “Cold” specimens were tested at room
temperature with a span length of 130 mm, while “hot” specimens were
tested after heating with a heat gun to an approximately uniform temperature of 70 °C with a span length of 70 mm. Each test was allowed tocontinue beyond plastic deformation until total material failure, and eachparameter combination was tested at least five times. The average stress andstrain values for each specimen set are plotted in SI Appendix, Fig. S4, andthe average ultimate stress and ultimate strain values are plotted in Fig. 3I.
VS Thermal Conductivity Measurement. The thermal conductivity of the VS
materials was measured using the transient hotwire method as in ref. 52, in
which an embedded wire acts as both a resistive heat source and temperature sensor. Under a brief application of current, the wire measurably increases in resistivity as its temperature rises, with the magnitude of change
dependent on the thermal conductivity of the surrounding material. Because of the high density of FM, the particles tend to settle while the epoxy

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VS Heating and Cooling Measurement and Modeling. To validate the numericalsimulation of the heating and cooling of the VS fibers, a physical experiment was
set up with a representative fiber suspended between two clamps. This fiber,composed of neat epoxy and a core stainless-steel yarn was joule-heated, with an
infrared (IR) camera (Fluke TiX 580) recording a video of the external temperature across the suspended fiber. The fiber was heated using a range of powers(4.6 to 32.8 W/m, equivalent to 0.3 to 0.8 A of current from the power supply)and was allowed to cool down to room temperature between each heating test
(SI Appendix, Fig. S5). Each heating rate was run four times to provide error data.
Heating and cooling data were extracted from the captured IR video using anative pixel-to-data exporter built into the IR camera processing software (Fluke
SmartView), for each frame of the video. Data were analyzed only around themidsection of the fiber (see boxed region in SI Appendix, Fig. S5) to reduce theerror introduced by conduction cooling through the clamps on the fiber ends.
From the region of interest, the data for each frame was recorded with atimestamp, maximum temperature, minimum temperature, and average temperature down the center of the fiber across the whole region of interest. It is
important to note that because the steel yarn sometimes did not remain fully
centered within the VS fiber during manufacturing, the whole fiber did not heatevenly, but instead had warmer and cooler sections. However, during cooling,these warm/cold spots rapidly smoothed out until the maximum and minimums
were equivalent to the average temperature on the fiber.
SI Appendix, Fig. S6 shows the average temperature across the region ofinterest of the fiber as it increased over time during the heating of the fiber.
Each of the curves is the average of all tests run at each of the power inputs.
For the most part, the data follow the logical conclusion that higher power
inputs resulted in faster heating times. However, near the highest power
inputs the data begin to run together. Additionally, all curves appear jagged
and irregular, with the error bounds on the higher power inputs being muchhigher. Both of these oddities are artifacts of the IR camera’s limitations: The
camera could only accurately record at a rate of nine frames per second ofdata, and this could occasionally be interrupted as the temperature rose
beyond the current temperature scale and the camera performed an automatic recalibration on the temperature range. This resulted in the higher
power regions sometimes having clipped initial data (they appear to start at
higher temperatures; see SI Appendix, Fig. S6, Inset) and the more jagged
averages. Regardless, the averages of the lower temperatures provided alarge pool of data from which to evaluate the quality of the numeric
simulation.
SI Appendix, Figs. S7–S9 show the time for the fiber to reach a specifictemperature, at different power inputs, compared with the numericallycomputed time. The maximum and minimum temperatures were computed
numerically by assuming the joule heating conduit is offset at two-thirds ofthe total fiber cross diameter to represent the steel thread being manufactured off-center. To compensate for calibration delays in the thermal
camera when starting the heating cycle in the experimental data, the numerical data curves were truncated to start at the same temperature as thefirst recorded temperature of the experimental data. There is typically very
good agreement between the numerical data and the experimental data forthe average, maximum, and minimum values. Notable exceptions to thisagreement occurred at in the observations of the maximum temperature at
the highest power inputs—in which the temperature values changed soquickly that the data from the thermal camera are suspected to be a significant factor in this error. With this strong agreement spanning such a large
range of power inputs and geometric constraints, we then moved on to observing the quality of the numerical model for predicting the cooling time.
As demonstrated in Fig. 3K, the cooling data for all of the different heating
rates averaged out to nearly identical sets of curves, as recorded experimentally, regardless of heating rate or maximum temperature achieved. To compare the experimental data, we truncated the cooling temperature data sets
to start at 70 °C, setting that time to t = 0 s and plotted the time for the fiber
to cool down to 27 °C where the fiber would be fully solidified. This was
sufficient for our purposed of confirming the validity of the numerical model,
as it was close enough to room temperature that additional cooling required
significantly longer times (due to the asymptotic nature of free convection

Buckner et al.

heat transfer). To develop the numerical solution, we used the same material
parameters used in the heating study and altered the geometry only in that
we removed the “heating core” and simply treated the fiber as a single homogenous material. On doing this, the experimental data lined up neatly with
the numerical data, validating the quality of our model (Fig. 3K). We note that
Fig. 3K only showed the graphs starting from 65 °C as this is the temperatureof interest for obtaining complete softening in the VS fibers, but the data
starting at 70 °C still showed the same trend and agreement as is shown.
Further, we further tested the effect on cooling and heating times of integrating the VS fibers into cotton fabric, focusing on the transition from 27 °C
to 70 °C in both directions. The addition of fabric on one side of a VS fiber
hampers the effectiveness of free convection such that the cooling time isnearly doubled (SI Appendix, Fig. S10), but heating time is reduced somewhat
except at low power inputs, where the fabric appears to wick away the heat.
This behavior must be taken into account when determining actuation sequences to ensure the fiber can fully stiffen as needed.
Thermal Cross-Talk. An unprogrammed, U-shaped SMA ribbon was couched
into a section of fabric and suspended in the air at either end, such that the
SMA was not touching any thermally conductive surface. The SMA was thenjoule-heated to 120 °C and held at that temperature for 2 min to reach asteady-state temperature profile in the adjacent fabric. The temperature
was monitored with an IR camera (Fluke TiX 580). A temperature profile was
generated using the IR analysis software (Fluke SmartView) showing thatthe temperature drops off to below 45 °C, the glass-transition onset point of
the VS material, at a distance of ∼3 mm from the SMA ribbon center line (SIAppendix, Fig. S11), or about 2.5 mm from the ribbon edge. Thermally responsive fibers can be spaced at least 3 mm apart to avoid thermal cross-talk.
Sensor Response to Temperature. A section of fabric prepared with a printed
ink sensor was placed on a hotplate and heated to 125 °C. Resistance of thesensor was measured during this time while temperature was monitoredwith an IR camera (Fluke TiX 580). Within the operating temperature rangeof our SMA ribbons (100 °C), the maximum increase of the sensor resistanceapproaches 5% (SI Appendix, Fig. S12A), which can negatively impact sensor
readings. In practice, if the sensor is placed at least 3 mm from any heatedfibers the sensor temperature will not exceed ∼36 °C, which correlates with a∼0.9% resistance change (SI Appendix, Fig. S12B).
Sensor Response to Curvature. A section of fabric prepared with a printed ink
sensor was wrapped about insulated tubing of various radii while the resistance
was measured relative to the initial value. Around the tightest curve of radius 3/
4 in, the sensor exhibited a maximal increase in resistance of 28% (SI Appendix,
Fig. S12B). Measurements were repeated three times for each radius.
Sensor Controls. In Fig. 4C we show a section of cloth with antagonistic
bending SMA actuators attached, in conjunction with two small conductive
ink traces printed on opposite faces. With the fabric device fixed at one end,
it was able to curl up and down by cycling between the opposing actuators.
The device naturally relaxed into a neutral center position when neither
actuator was active due to a balance in opposing spring forces in the SMA
wires. The bending motion was detected and measured by monitoring theresistance change in the sensor traces. Data were gathered after cycling thesystem through over 1,000 up-and-down curling cycles to remove any hysteresis in the sensors and fabric.
Tourniquet Cuff Pressure Measurement. The SMA ribbons on the tourniquet
were designed to pinch into a “clover” shape as seen in Fig. 5B, Inset, whichallows compression actuation that is pure bending, rather than requiring linear contraction. As this type of actuation is nonuniform around the circumference of the tourniquet, we elected to measure the tourniquet cuff pressureusing a dynamometer consisting of a soft rubber squeeze bulb affixed to adigital pressure sensor. This provides an approximate “average” pressure, as
opposed to a local maximum at the points where the ribbon pinches inward.
The tourniquet was positioned such that a single SMA ribbon was centeredaround the squeeze bulb, after which that single SMA ribbon was activatedand allowed to constrict, producing sufficient force to significantly deform thebulb. Pressure measurements were repeated three times for each of the threewires, resulting in an average pressure of 1.6 kPa with an SD of 0.08 kPa.
Data Availability. All data are included in the paper and SI Appendix.
ACKNOWLEDGMENTS. Support for T.L.B. and R.A.B. was provided by the Air
Force Office of Scientific Research under award FA9550-16-1-0267.

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cures over a 12-h period. To promote composite homogeneity, experimental
samples were cured on a rotating fixture. These measurements appear to
track the prediction supplied by the Bruggeman effective medium theory(Fig. 3J), using the thermal conductivities of FM (k = 19 W · m−1 · K −1, approximated from ref. 53) and our own measured value for neat epoxy(k = 0.21 W · m−1 · K −1 ). Discrepancies between the experimental and analytical values here may be due to small amounts of residual particle settling orclustering around the platinum wire resulting in a higher local density of FM
than calculated.

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