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Ultralight (<10 milligrams per cubic centimeter) cellular materials are desirable for thermal insulation; battery electrodes; catalyst supports; and acoustic, vibration, or shock energy damping. We present ultralight materials based on periodic hollow-tube microlattices. These materials are fabricated by starting with a template formed by self-propagating photopolymer waveguide prototyping, coating the template by electroless nickel plating, and subsequently etching away the template. The resulting metallic microlattices exhibit densities ρ ≥ 0.9 milligram per cubic centimeter, complete recovery after compression exceeding 50% strain, and energy absorption similar to elastomers. Young's modulus E scales with density as E ~ ρ(2), in contrast to the E ~ ρ(3) scaling observed for ultralight aerogels and carbon nanotube foams with stochastic architecture. We attribute these properties to structural hierarchy at the nanometer, micrometer, and millimeter scales.
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DOI: 10.1126/science.1211649
, 962 (2011);334 Science , et al.T. A. Schaedler
Ultralight Metallic Microlattices
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Ultralight Metallic Microlattices
T. A. Schaedler,
*A. J. Jacobsen,
A. Torrents,
A. E. Sorensen,
J. Lian,
J. R. Greer,
L. Valdevit,
W. B. Carter
Ultralight (<10 milligrams per cubic centimeter) cellular materials are desirable for thermal
insulation; battery electrodes; catalyst supports; and acoustic, vibration, or shock energy damping.
We present ultralight materials based on periodic hollow-tube microlattices. These materials are
fabricated by starting with a template formed by self-propagating photopolymer waveguide
prototyping, coating the template by electroless nickel plating, and subsequently etching away
the template. The resulting metallic microlattices exhibit densities r0.9 milligram per cubic
centimeter, complete recovery after compression exceeding 50% strain, and energy absorption similar
to elastomers. Youngs modulus Escales with density as E~r
observed for ultralight aerogels and carbon nanotube foams with stochastic architecture. We attribute
these properties to structural hierarchy at the nanometer, micrometer, and millimeter scales.
The effective properties of low-density ma-
terials are defined both by their cellular
architecture (i.e., the spatial configuration
of voids and solid) and the properties of the solid
constituent (e.g., stiffness, strength, etc.). In the
ultralight regime below 10 mg/cm
terials currently exist: silica aerogels [density r
(1,2)], carbon nanotube aerogels [r4
(3)], metallic foams [r10 mg/cm
and polymer foams [r8mg/cm
(6,7)]. These
materials have a wide range of applications, such
as thermal insulation, shock or vibration damp-
ing, acoustic absorption, and current collectors in
battery electrodes and catalyst supports (8). All of
the ultralow-density materials mentioned above
have random cellular architectures. This random
cell structure results in some beneficial properties
(e.g., high specific surface area and restriction of
gas flow), but generally the inefficient distri-
bution of the constituent results in specific prop-
erties (e.g., stiffness, strength, energy absorption,
and conductivity) far below those of the bulk
material (8). As an example, Youngs modulus,
E, of ultralight stochastic materials scales poorly
with density, generally following E~r
(9), in
contrast to the well-known E~r
relationship for
random open-cell foams with higher relative
densities (8). In large-scale structures, it has been
shown that introducing order and hierarchy can
substantially improve material utilization and re-
sultant properties. For instance, the Eiffel Tower
possesses a relative density similar to that of low-
density aerogels (10) but is clearly structurally
robust. The size difference between the smallest
and largest structural features will determine the
degree of hierarchy that can be achieved. In this
paper, we present a method for creating ordered
hollow-tube lattice materials with a minimum
scale of ~100 nm. Coupled with control over mm-
to cm-scale structural features, this enables us to
bring the benefits of order and hierarchy down
to the materials level. The result is an ultralight-
weight cellular material with efficient material
utilization, a Youngs modulus that follows E~
, and the ability to recover from >50% com-
pression while demonstrating large energy absorp-
tion upon cyclic loading.
The base architecture of our metallic micro-
lattices consists of a periodic array of hollow
tubes that connect at nodes, forming an octahe-
dral unit cell without any lattice members in the
basal plane. Figure 1 illustrates how the micro-
lattice architecture can be distilled into three levels
of hierarchy at three distinct length scales: unit
cell (~mm to cm), hollow tube lattice member
(~mm to mm), and hollow tube wall (~nm to mm).
Each architectural element can be controlled in-
dependently, providing exceptional control over
the design and properties of the resulting micro-
lattice. The architecture determines the relative den-
sity of the lattice, with the absolute density dictated
by the film material.
The fabrication process begins with solid mi-
crolattice templates fabricated by using a self-
propagating photopolymer waveguide technique.
In this method, a thiol-ene liquid photomonomer
is exposed to collimated ultraviolet (UV) light
through a patterned mask, producing an inter-
connected three-dimensional photopolymer lat-
tice (11). A wide array of different architectures
with unit cell dimensions ranging from 0.1 to >10
mm can be made by altering the mask pattern and
the angle of the incident light (12,13). Here, we
focus on architectures with 1- to 4-mm lattice
member length L, 100- to 500-mm lattice member
diameter D, 100- to 500-nm wall thickness t,
and 60° inclination angle q, similar to the mi-
crolattices depicted in Fig. 1. Conformal nickel-
phosphorous thin films were deposited on the
polymer lattices by electroless plating, and the
polymer was subsequently etched out (table S1).
The autocatalytic electroless nickel-plating reac-
tion enables deposition of thin films with con-
trolled thickness on complex shapes and inside
pores without noticeable mass transport limita-
tions. The ultralight microlattice essentially trans-
lates the deposited nanoscale thin film in three
dimensions to form a macroscopic material where
the base structural elements are hollow tubes. By
controlling the reaction time, a 100-nm-thick uni-
form conformal coating can be achieved, resulting
in a cellular material with a density of 0.9 mg/cm
(Fig. 1). The density is calculated by using the
weight of the solid structure but not including the
Fig. 1. Design, processing, and cellular architecture of ultralight microlattices. (A) Polymer microlattice
templates are fabricated from a three-dimensional array of self-propagating photopolymer waveguides. (B)
The open-cellular templates are electroless plated with a conformal Ni-P thin film followed by etch removal
of the template. (C) Image of the lightest Ni-P microlattice fabricated with this approach: 0.9 mg/cm
(Dand E) Images of two as-fabricated microlattices along with a breakdown of the relevant architec-
tural elements.
HRL Laboratories Limited Liability Company, Malibu, CA 90265,
Department of Mechanical and Aerospace Engineering,
University of California, Irvine, CA 92697, USA.
Division of En-
gineering and Applied Sciences, California Institute of Technol-
ogy, Pasadena, CA 91125, USA.
*To whom correspondence should be addressed. E-mail:
18 NOVEMBER 2011 VOL 334 SCIENCE www.sciencemag.org962
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weight of air in the pores, adhering to the standard
practice for cellular materials. The density of air at
ambient conditions, 1.2 mg/cm
, multiplied by its
volume fraction would need to be added to ex-
press the density of the solid-air composite. This
method to form microlattices allows significantly
more control than typical methods for forming
other ultralightweight materials, such as foams
and aerogels, where nominally random processes
govern porosity formation.
Characterization of the base constituent by
transmission electron microscopy (TEM) revealed
that as-deposited electroless nickel thin films have
an average grain size of ~7 nm, which is consistent
with literature reports (14,15). Energy-dispersive
x-ray spectroscopy confirmed that the film com-
position is 7% phosphorous and 93% nickel by
weight. Because the films were not annealed after
deposition, they remained as a supersaturated
solid solution of phosphorous in a crystalline
face-centered cubic nickel lattice with no Ni
cipitates present (14). The 7-nm grain size ren-
ders electroless nickel thin films harder and more
brittle than typical nano- and microcrystalline
nickel. A hardness of 6 GPa and a modulus of
210 GPa were measured by nanoindentation
and hollow tube compression experiments, re-
spectively (16).
Compression experiments on the as-formed
microlattices showed a nearly complete recovery
Fig. 2. Nickel microlattices exhibit recoverable deformation. (A) Before deformation. (B)15%
compression. (C) 50% compression. (D) Full recovery after removal of load. (E) Optical image of
unit cell unloaded. (F) Example of node buckling under compression. (G) SEM image of node before testing. (H) SEM image of node after six compression
cycles at 50% strain. (The compression test is shown in movie S1.)
Fig. 3. Multicycle compression test results of nickel microlattices.
(A) Stress-strain curves of a microlattice with 14 mg/cm
hibiting recoverable deformation (compare with Fig. 2). (B)
History of compressive modulus, yield stress, maximum stress,
and energy loss coefficient during the first six compression
cycles shown in (A). (C) Stress-strain curve of a microlattice
with a density of 1.0 mg/cm
.(D) Stress-strain curves of a mi-
crolattice with 43 mg/cm
showing deformation more typical
for metallic cellular materials. (E)SEMmicrographofpost-
nanoindentation mark in 500-nm-thick electroless nickel film
demonstrating brittle behavior. SCIENCE VOL 334 18 NOVEMBER 2011 963
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from strains exceeding 50% (movie S1). Figure
2, A to D, provides images of a 14 mg/cm
crolattice sample (L=1050mm, D= 150 mm, t=
500 nm) during compression testing, and Fig. 3A
conveys the corresponding stress-strain curve
measured at a prescribed displacement rate of
10 mm/s. In this experiment, the sample was not
constrained by face sheets or attached to any
compression platens. Because of a small taper
in lattice strut diameter, the deformation typ-
ically initiates at a particular surface. Upon first
compression, the lattice exhibits a compressive
modulus of 529 kPa, with deviations from lin-
ear elastic behavior starting at ~10 kPa. The stress
decreases slightly after the peak, which is as-
sociated with buckling and node fracture events,
and a broad plateau is subsequently established in
the stress-strain curve as buckling and localized
node fracture events spread through the lattice.
Figure 2C shows the microlattice at 50% com-
pression. Upon unloading, the stress drops rapid-
ly but does not approach zero until the platen is
close to its original position. After removing the
load, the microlattice recovers to 98% of its orig-
inal height and resumes its original shape (Figs.
2D and 3A).
The stress-strain behavior corresponding to
the first cycle is never repeated during subsequent
testing. Rather, during a second compression, the
peak stress is absent and the pseudohardening
behavior changes, but the stress level achieved at
50% strain is only 10% lower than that after the
first cycle. Consecutive compression cycles ex-
hibit stress-strain curves nearly identical to those
of the second compression. Stiffness and strength
diminish with cycle number but remain almost
constant after the third cycle (Fig. 3B). The mi-
crolattice also shows significant hysteresis during
compression experiments. For the first cycle, we
estimate the work done in compression to be
4.6 mJ/cm
and the energy dissipation to be
3.5 mJ/cm
(Du/u) of 0.77. This large energy dissipation re-
sults from extensive node microcracking and
thus is limited to the first cycle. After three cy-
cles, a nearly constant energy loss coefficient
of ~ 0.4 is calculated (Fig. 3B). From this esti-
mate, we extract a loss coefficient (tan d)of
~0.16 (17), an order of magnitude higher than
for typical nickel foams (18). Figure 3C shows
the stress-strain response of a 1.0 mg/cm
with larger unit cells (L=4mm,D= 500 mm, t=
120 nm), illustrating that different microlattice
architectures in the ultralow-density regime result
in similar behavior [although this sample under-
went an additional freeze-drying process step that
caused some damage (table S1)]. Increasing the
density and wall thickness eventually led to a com-
pression behavior more typical for metallic cellular
materials. Figure 3D shows the stress-strain curve
for a 43-mg/cm
sample (L= 1050 mm, D= 150 mm,
t= 1400 nm), for which recovery upon unloading
from 50% strain is essentially absent.
Optical examination of the ultralight micro-
lattices during deformation suggests that defor-
mation initiates by local buckling at the nodes
(Fig. 2, E and F). A closer inspection of the
microlattices by scanning electron microscopy
(SEM) shows that cracks and wrinkles are intro-
duced primarily at the nodes during compres-
sion (Fig. 2, G and H). This damage is responsible
for the 1 to 2% residual strain observed after the
first compression cycle, as well as for the drop in
yield strength and modulus during subsequent
compression cycles. Once stable relief cracks
form at the nodes, the bulk microlattice material
can undergo large effective compressive strains
through extensive rotations about remnant node
ligaments, but with negligible strain in the solid
nickel-phosphorous material, thus requiring no
further fracture or plastic deformation. This prop-
erty results in the reversible compressive behavior
thicknesstodiameter ratio is essential for this de-
formation mechanism. Increasing this aspect ratio
leads to excessive fracture and loss of recover-
ability (Fig. 3D).
The rise in stress at strains of ~ 40% (Fig. 3A)
is a result of increased interaction between lattice
members after localized compression at the nodes
and should not be confused with densification,
which in these samples does not occur until strains
exceed 90% (fig. S2).
Similar stress-strain curves as presented in
Fig. 3A are typical for viscoelastic polymer foams
(19) and carbon nanotube forests (20) but not
for metal-based materials, implying a nonconven-
tional loss mechanism is present. Two energy-loss
mechanisms could possibly explain the energy
dissipation during compression cycles: (i) struc-
tural damping because of snapping events (e.g.,
kinking or local buckling of the trusses) and (ii)
mechanical or Coulomb friction between con-
tacting members (or a combination of both). This
mechanical behavior is especially unexpected con-
sidering the relatively brittle nature of the constit-
uent electroless nickel thin film, as evidenced by
the formation of cracks near a residual indenta-
tion mark (Fig. 3E) and the rapid collapse upon
single hollow truss member compressions (16).
The brittle nature of the film arises from its nano-
grained microstructure (~7 nm) that hinders plastic
deformation by dislocation motion (21). How-
ever, at the bulk scale microlattices exhibit com-
pletely different properties, because the cellular
architecture effectively transforms this brittle thin
film into a ductile, superelastic lattice by enabling
sufficient freedom for deformation and tolerance
to local strains through formation of stable relief
Plotting the relative compressive modulus,
, of various fabricated microlattices versus
their relative density, r/r
, shows that the modulus
scales with (r/r
(Fig. 4). This scaling law in-
dicates bending-dominated mechanical behavior
similar to open-cell stochastic foams (8). In con-
trast, other materials with densities < 10 mg/cm
such as aerogels and carbon nanotube (CNT)
foams, exhibit a steeper scaling of E/E
(Fig. 4) (22,23), because of inefficient load transfer
between ligaments. (Incidentally, this also affects
the structural stability of a self-supporting cellular
material, imposing a lower bound on density.) We
notice that, although the relative modulus of
topologically designed periodic lattice materials
[such as octet-truss lattices (24)] typically scales
linearly with relative density (25,26), we do not
expect the same scaling for the microlattices
described here because of the absence of struts in
the basal plane (26) and the ultrathin-walled
hollow nodes, both of which facilitate localized
bending deformation (Fig. 2F). Nonetheless, the
marked improvement in mechanical efficiency
over any other existing ultralightweight material,
achieved by controlling both dimensions and
periodicity of the architecture, enabled a self-
supporting cellular material with a relative density
an order of magnitude lower than previously re-
alized. Further, by transforming a brittle Ni-P thin
film into a three-dimensional cellular material and
designing a hierarchical cellular architecture at three
Fig. 4. Relative compres-
sive modulus (defined as
the measured Youngsmod-
ulus, E,dividedbythe
Youngs modulus of the
constituent solid, E
lected cellular materials
at low relative density.
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distinct length scales, we demonstrated the emer-
gence of entirely different mechanical properties.
In addition to possible applications for an ultra-
light material with high energy absorption and
recoverability, we anticipate that these results will
help reshape our understanding of the interac-
tion between material properties and structural
References and Notes
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Basotect V3012 (2007),
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Properties (Cambridge Univ. Press, Cambridge, 1997).
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Metall. Mater. Trans. A 37A, 2939 (2006).
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(Butterworth-Heinemann, Burlington, MA, 2000), p. 43.
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Acknowledgments: The authors gratefully acknowledge
the financial support by Defense Advanced Research
Projects Agency under the Materials with Controlled
Microstructural Architecture program managed by
J. Goldwasser (contract no. W91CRB-10-0305) and thank
J. W. Hutchinson and C. S. Roper for useful discussions.
A patent application regarding the structure and
formation process of the ultralight microlattices has been
submitted to the U.S. Patent and Trademark Office.
The polymer waveguide process has been patented (U.S.
Patent 7,382,959, U.S. Patent 7,653,279, and U.S.
Patent 8,017,193), but the template can be fabricated
in other ways.
Supporting Online Material
Materials and Methods
Fig. S1
Table S1
Movie S1
25 July 2011; accepted 12 October 2011
Silica-Like Malleable Materials from
Permanent Organic Networks
Damien Montarnal, Mathieu Capelot, François Tournilhac, Ludwik Leibler*
Permanently cross-linked materials have outstanding mechanical properties and solvent resistance,
but they cannot be processed and reshaped once synthesized. Noncross-linked polymers and
those with reversible cross-links are processable, but they are soluble. We designed epoxy networks
that can rearrange their topology by exchange reactions without depolymerization and showed
that they are insoluble and processable. Unlike organic compounds and polymers whose viscosity
varies abruptly near the glass transition, these networks show Arrhenius-like gradual viscosity
variations like those of vitreous silica. Like silica, the materials can be wrought and welded to make
complex objects by local heating without the use of molds. The concept of a glass made by
reversible topology freezing in epoxy networks can be readily scaled up for applications and
generalized to other chemistries.
Thermoset polymers such as Bakelite must
be polymerized in a mold having the
shape of the desired object because once
the reaction is completed, the polymer cannot be
reshaped or reprocessed by heat or with solvent.
In contrast, thermoplastics, when heated, can flow,
which permits extrusion, injection, and molding
of objects. Depending on the chemical nature of
the plastic, during cooling, solidification occurs
by crystallization or by glass transition. During
vitrification, as the temperature is lowered below
the glass transition, the viscosity abruptly in-
creases in a narrow temperature range, and the
material becomes so viscous that it behaves
essentially like a solid with an elastic modulus
of about 10
to 10
Pa (1). Nevertheless, com-
pared to processable plastics, cross-linked poly-
mers have superior dimensional stability; have
high-temperature mechanical, thermal, and envi-
ronmental resistance; and are irreplaceable in many
demanding applications, such as in the aircraft
industry. High-performance coatings, adhesives,
rubbers, light-emitting diode lenses, and solar cell
encapsulants are made of permanently cross-linked
polymer networks as well.
Making covalent links reversible could pro-
vide a way to combine processability, reparability,
and high performance (26). Networks with bonds
able to break and reform (79) or to exchange
pairs of atoms (10) can relax stresses and flow.
The challenge is to allow rapid reversible reac-
tions at high temperatures or by a convenient
stimulus and to fix the network at service condi-
tions. In this context, cleavage or exchange reac-
tions by addition-fragmentation in the presence of
radicals offer interesting possibilities (5,1114).
Scott et al. demonstrated photoinduced plas-
ticity in cross-linked polymers (11). Similarly,
reparability and self-healing can be induced either
thermally (13) or photochemically (15,16)in
radical systems. However, these systems undergo
unavoidable termination reactions that limit re-
versibility of the networks.
In parallel, a completely different concept
based on chemical equilibrium between bond
breaking and reforming without irreversible side
reactions has been developed (1720). In these
systems, heating has two effects: It displaces
the equilibrium toward depolymerization and it
accelerates the bond breaking and reforming rate
(8,9). The advantage of such reversible links is
that both above-mentioned effects act together to
bring fluidity and thus processability (5,1719).
They are, however, detrimental to the network
integrity and performance. Chen et al.haveshown
that to avoid flow and creep at service temper-
atures, one can rely, as in thermoplastics, on glass
transition to quench the system (17). Unfortu-
nately, the systems based on chemical equilibri-
um between bond breaking and reforming are
sensitive to solvents because in the presence of a
solvent, the chemical equilibrium is displaced
toward network depolymerization and dissolu-
tion (19).
We sought to show that reversible networks
can flow while maintaining their integrity and
insolubility at high temperature. The idea is to
Matière Molle et Chimie, UMR 7167 CNRS-ESPCI, Ecole
Supérieure de Physique et Chimie Industrielles, 10 rue
Vauquelin, 75005 Paris, France.
*To whom correspondence should be addressed. E-mail: SCIENCE VOL 334 18 NOVEMBER 2011 965
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... Recent and formidable progress in additive manufacturing and 3D printing boosted research in the field [3,4], giving way to the fabrication of high precision micro-/nanoarchitectured cellular materials of complex geometries [4]. In this context, micro-/nanolattice materials consisting of periodically arranged beams or tubes of micrometer/nanometer dimensions exhibit unprecedented stiffness-to-weight ratio [11][12][13][14][15][16]. In general, the Young's modulus, E, typically scales as the density cubed ρ 3 in foams, aerogels and other cellular materials with randomly distributed porosity [17][18][19]. ...
... In general, the Young's modulus, E, typically scales as the density cubed ρ 3 in foams, aerogels and other cellular materials with randomly distributed porosity [17][18][19]. On the other hand, E scales as ρ 2 in periodic hollow-tube microlattices with octahedral basic cells [11], as ρ 1.6 in octet-truss geometry [12], or even linearly with ρ for well-chosen hierarchical architectures [13,15]. ...
... Recent and formidable progress in additive manufacturing and 3D printing boosted research in the field [3,4], giving way to the fabrication of high precision micro-/nanoarchitectured cellular materials of complex geometries [4]. In this context, micro-/nanolattice materials consisting of periodically arranged beams or tubes of micrometer/nanometer dimensions exhibit unprecedented stiffness-to-weight ratio [11][12][13][14][15][16]. In general, the Young's modulus, E, typically scales as the density cubed ρ 3 in foams, aerogels and other cellular materials with randomly distributed porosity [17][18][19]. ...
... In general, the Young's modulus, E, typically scales as the density cubed ρ 3 in foams, aerogels and other cellular materials with randomly distributed porosity [17][18][19]. On the other hand, E scales as ρ 2 in periodic hollow-tube microlattices with octahedral basic cells [11], as ρ 1.6 in octet-truss geometry [12], or even linearly with ρ for well-chosen hierarchical architectures [13,15]. ...
We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative of mechanically isotropic materials low connectivity, mechanically isotropic materials with high connectivity, and mechanically anisotropic materials with intermediate connectivity. Introducing disorder generates spatial fluctuations in the elasticity tensor at the local (joint) scale. Proper coarse-graining reveals a well-defined continuum-level scale elasticity tensor. Increasing disorder aids in making initially anisotropic materials more isotropic. The disorder impact on the material stiffness depends on the lattice connectivity: Increasing the disorder softens lattices with high connectivity and stiffens those with low connectivity, without modifying the scaling between elastic modulus and density (linear scaling for high connectivity and cubic scaling for low connectivity). Introducing disorder in lattices with intermediate fixed connectivity reveals both scaling: the linear scaling occurs for low density, the cubic one at high density, and the crossover density increases with disorder. Contrary to classical formulations, this work demonstrates that connectivity is not the sole parameter governing elastic modulus scaling. It offers a promising route to access novel mechanical properties in lattice materials via disordering the architectures.
... Architected materials have demonstrated static mechanical properties 8 superior to those of traditional materials or composites, such as light weight 26 , high specific stiffness 27 and near-theoretical strength 28 . Beyond the linear elastic regime, architected materials can exhibit further programmable structural transformations and nonlinear responses induced by mechanical actuation. ...
Rationally designed architected materials have attained previously untapped territories in materials property space. The properties and behaviours of architected materials need not be stagnant after fabrication; they can be encoded with a temporal degree of freedom such that they evolve over time. In this Review, we describe the variety of materials architected in both space and time, and their responses to various stimuli, including mechanical actuation, changes in temperature and chemical environment, and variations in electromagnetic fields. We highlight the additive manufacturing methods that can precisely prescribe complex geometries and local inhomogeneities to make such responsiveness possible. We discuss the emergent physics phenomena observed in architected materials that are analogous to those in classical materials, such as the formation and behaviour of defects, phase transformations and topologically protected properties. Finally, we offer a perspective on the future of architected materials that have a degree of intelligence through mechanical logic and artificial neural networks. Architected materials are a class of materials with structures intermediate in scale between atomic arrangement and bulk dimensions; this additional degree of freedom enables unique properties and functionalities. This Review describes the state of the art in architected materials that are responsive to various stimuli.
... This may open new routes to conceptualise novel applications in soft robotics, bioengineering and actuator systems. Additionally, due to a generalised formulation, it may set the basis for metallic lattice structures manufacturing design (Schaedler et al., 2011). ...
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The breakthrough in additive manufacturing (AM) techniques is opening new routes into the conceptualisation of novel architected materials. However, there are still important roadblocks impeding the full implementation of these technologies in different application fields such as soft robotics or bioengineering. One of the main bottleneck is the difficulty to perform topological optimisation of the structures and their functional design. To help this endeavour, computational models are essential. Although 3D formulations provide the most reliable tools, these usually present very high computational costs. Beam models based on 1D formulations may overcome this limitation but they need to incorporate all the relevant mechanical features of the 3D problem. Here, we propose a mixed formulation for Timoshenko-type beams to consistently account for axial, shear and bending contributions under finite deformation theory. The framework is formulated on general bases and is suitable for most types of materials, allowing for the straightforward particularisation of the constitutive description. To prove validity of the model, we provide original experimental data on a 3D printed elastomeric material. We first validate the computational framework using a benchmark problem and compare the beam formulation predictions with numerical results from an equivalent 3D model. Then, we further validate the framework and illustrate its flexibility to predict the mechanical response of beam-based structures. To this end, we perform original experiments and numerical simulations on two types of relevant structures: a rhomboid lattice and a bi-stable beam structure. In both cases, the numerical results provide a very good agreement with the experiments by means of both quantitative and qualitative results. Overall, the proposed formulation provides a useful tool to help at designing new architected materials and metamaterial structures based on beam components. The framework presented may open new opportunities to guide AM techniques by feeding machine learning optimisation algorithms.
... In such a case, hydrogels of cellular fibrous networks can readily improve mechanical properties and exhibit a significant response when pressure is applied. [180][181][182][183][184] Respective swelling/shrinkage and expansion/contraction are apparent upon the application of external pressure on hydrogels containing large mono-domains. A study reports the incorporation of a mechanical shearing technique for synthesizing half ester nanocrystallized cellulose (CNC). ...
Understanding the surrounding atmosphere and reacting accordingly with a precise action are always fascinating features of a material. Materials that pose such responsiveness are called smart materials. Currently, research studies on smart materials are being accelerated exponentially around the world; this is also true for smart hydrogels. Smart hydrogels with various chemically and structurally responsive moieties exhibit excellent characteristics of reacting under different environmental conditions such as pH, temperature, light, electric field, and magnetic field as well as biological and chemical stimuli. These smart hydrogels are drawing the attention of researchers for a wide range of applications, for instance, in designing biomedical, industrial, agricultural, electrical, healthcare, and hygienic products. This review encompasses the latest developments in the field of smart hydrogel synthesis based on their unique features and different aspects of their responsive behaviors. Additionally, this paper covers some of the recent strategies for tuning special functional properties of smart hydrogels for targeted applications.
Planar lattice metamaterials, such as periodic beam networks, are often considered as the micropolar continuum, where each material point has two translational degrees of freedom and one rotational degree of freedom. The joints through which bars are linked to one another are generally approximated as rigid. This study focuses on lattices with complex-structured deformable joints. The deformation field in each joint is obtained by conducting structural analyses. Once the “stiffness matrix” of the joint-centered unit cell is obtained by the finite element method, it can be used as the input for the standard procedure of calculating micropolar elastic moduli that are based on the equivalence of strain energy. As a result, effective moduli can be expressed in a semi-analytical form, meaning that only the cell structural stiffness is given numerically. The present model is validated by comparison to the FEM simulations. Particularly, the auxetic and anisotropic properties are discussed for various lattice metamaterials with deformable joints. We then take the obtained effective moduli as inputs to the in-house micropolar FEM code and obtain results agreeing well with the FEM structural simulations.
Template-assisted electrodeposition is a promising microscale additive manufacturing technique allowing to deposit pure metals with high resolution. To allow the application-relevant design of metamaterials, it is necessary to establish microstructure-mechanical property relationships under extreme conditions. In this work, a novel process based on two-photon lithography was used to synthesize arrays of nanocrystalline nickel micropillars and complex microlattices. This allowed high throughput mechanical testing using a newly developed in situ nanoindenter at unprecedented combination of cryogenic temperatures (160 to 300K) and strain rates (0.001 to 500s⁻¹). Strain rate sensitivity was found to increase from ∼0.004 at 300K to ∼0.008 at 160K. Thermal activation analysis showed a decrease in activation volume from 122b³ at 300K to 45b³ at 160K and an activation energy of 0.59eV in line with collective dislocation nucleation as the rate limiting mechanism. Transmission Kikuchi Diffraction allowed quantifying microstructural changes during deformation. As such, a deformation map along with the responsible deformation mechanisms has been ascertained for additively micromanufactured nanocrystalline nickel at unique combinations of extreme temperatures and strain rates. Further, rate-dependent compression of microlattices and complementary finite element simulations using the results from micropillars as constitutive models exemplified the promise of such metal microarchitectures in space and aviation applications.
With increasing interest in the rapid development of customized ceramic electronics, hybrid additive manufacturing (HAM) technology has become a competent alternative to traditional solutions such as printed circuit boards and cofired ceramic technology. Herein, the novel HAM technology is proposed by combining a dispensing three-dimensional (3D) printing process and selectively laser-activated electroless plating for fabricating 3D fully functional ceramic electronic products. An appropriative 3D-printable and metalizable low-temperature cofired ceramic slurry is developed to build the green body of ceramic electronics. After the debinding and sintering process, the 3D ceramic structure can be selectively laser-activated and then electrolessly plated to achieve electronic functionality. The thickness of the plated copper layer approaches 10 μm after 4 h of plating, and the electrical conductivity is 5.5 × 107 S m-1, which is close to pure copper (5.8 × 107 S m-1). To reduce the surface roughness of the laser-activated ceramic surface and thereby enhance the conductivity of the copper layer, the laser parameters are optimized as a 1250 mm s-1 scan speed, a 0.4 W laser power, and a 20 kHz laser-spot frequency. A high-power 3D light-emitting diode circuit board with an internal cooling channel is successfully developed to prove the feasibility of this HAM technology for customizing fully functional 3D conformal ceramic electronics.
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Electrochemical devices that harvest or store electrical energy are indispensable to our daily life and are currently of growing importance in the future prosperity of the world economy. The sol–gel technology has contributed substantially to the development of electrode materials and electrocatalysts, particularly in terms of the synthesis of nano-sized and/or nanostructured particles. As with the other application fields, nanomaterials with enriched active surface sites can enhance electrode performance, and hence, have been substituted for the classical low-surface-area electrodes like rods and plates. However, the powdery nanomaterials need to be fixed on an electrode substrate in a mixture with binders and conductive agents, which imposes several drawbacks especially in fundamental research. In this context, free-standing and binder-free monolithic electrodes bearing rationally designed nanostructures have emerged as advanced electrode materials based on the concept of incorporating the nanomaterials into the classical bulky electrodes. This review focuses on the recent progress in porous monolithic electrodes with special concern for those with three-dimensionally interconnected porous structures prepared via the sol–gel processes accompanied by phase separation. In addition to the synthesis and pore control for various electrode materials, the insights garnered from the electrochemical investigations on the porous monolithic electrodes are overviewed. Graphical abstract
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Mechanical metamaterials with zero or negative Poisson’s ratio were subject to increasing research interest over the last few years. Their energy absorption capabilities make them suitable for impact and dampening applications, such as personal protection equipment or packaging materials. The variable porosity and unusual mechanical properties also make them applicable in drug delivery systems and wound management. Herein, we present an extension to common auxetic structures, including tetra-chirals and tetra-antichirals. By introducing an asymmetry in the design of their unit cell, Poisson’s ratio can be varied over a broad range. Specimens with a selected amount of asymmetry were additively manufactured with a thermoplastic polyurethane using fused filament fabrication. Compression tests were performed to investigate the influence of the asymmetry on Poisson’s ratio and the compression modulus. Two different numerical models were employed using ABAQUS to describe the mechanical properties of the structures and were verified by the experiments. The numerical models are based on three-point bending test data. Both asymmetric designs show an influence of the asymmetry onto Poisson’s ratio, resulting in variable Poisson’s ratio, porosity, and compression modulus.
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We describe the fabrication of ultralow-density carbon nanotube (CNT) foams that simultaneously exhibit high electrical conductivities and robust mechanical properties. Our approach utilizes carbon nanoparticles as a binder to crosslink randomly oriented bundles of single-walled CNTs. The resulting CNT foams are the stiffest low-density nanoporous solids reported and exhibit elastic behavior up to strains as large as ∼ 80%. The use of the carbon binder also allows bulk electrical conductivity to be maintained at low densities.
Finite Element Analysis (FEA) was used to model viscoelastic effects in the compression of polyurethane (PU) foam. Modelling of the impact compression of foam cubes predicted that a compressed region propagated through the sample, causing step increases in the stress traces. Modelling of head impacts on gymnastic ‘crash’ mats, made of PU chip foam, revealed that the majority, but not all, of the energy losses could be attributed to the polymer viscoelasticity. The Gibson-Ashby micromechanics model was used to show that the hysteresis in a viscoelastic foam could be higher than in the parent polymer. A wet Kelvin foam, with a better foam geometry, was then used for viscoelastic analysis. The lattice of uniform-sized cells, in a Body Centred Cubic array, were compressed in the [111] direction. With the PU treated as a linear viscoelastic material, the predicted hysteresis in the cyclic stress-strain curve was slightly smaller than that measured for a PU flexible foam.
The mechanical properties (the moduli and collapse strengths) of three-dimensional cellular solids or foams are related to the properties of the cell wall, and to the cell geometry. The results of the analyses give a good description of a large body of data for polymeric foams.
The velocity and attenuation of ultrasonic waves were measured in nanostructured silica aerogels as a function of frequency, density, gas pressure within the pores and elastic strain. The sound velocity was found to be independent of frequency. For the density dependence of the elastic modulus a scaling law was observed for each class of specimens with exponents ranging from 2.0 to 3.6. The gas pressure strongly influences the sound velocity only for aerogels with densities below 30 kg m−3. Aerogels exhibit elastic non-linearity of an unexpected kind: the sound velocity decreases with increasing static compression. This is attributed to structural properties of these materials. The ultrasonic attenuation of silica aerogels is found to be lower than that of other highly porous materials. The main contributions under ambient conditions are the interaction between the pore gas and skeleton, and the water content, which is typically about 5 wt.%. Evacuated and heat treated specimens show elastic hysteresis with a loss tangent of about 10−3. This value is compared with preliminary data derived from creep measurements.
Cellular solids include engineering honeycombs and foams (which can now be made from polymers, metals, ceramics, and composites) as well as natural materials, such as wood, cork, and cancellous bone. This new edition of a classic work details current understanding of the structure and mechanical behavior of cellular materials, and the ways in which they can be exploited in engineering design. Gibson and Ashby have brought the book completely up to date, including new work on processing of metallic and ceramic foams and on the mechanical, electrical and acoustic properties of cellular solids. Data for commercially available foams are presented on material property charts; two new case studies show how the charts are used for selection of foams in engineering design. Over 150 references appearing in the literature since the publication of the first edition are cited. It will be of interest to graduate students and researchers in materials science and engineering. © Lorna J. Gibson and Michael F. Ashby, 1988 and Lorna J. Gibson and Michael F. Ashby, 1997.
An analysis was performed to establish a relationship between specific damping capacity and loss angle for materials with arbitrary loss angle. The motivation for this work is that the usual relationship is only valid for low loss materials and leads to some confusion when the specific damping capacity is greater than one. In this paper, two equations for specific damping capacity are derived that are valid for all values of loss angle. One equation uses the usual definition of specific damping capacity as dissipated energy per cycle divided by maximum stored energy. The other equation defines specific damping capacity as dissipated energy per cycle divided by work done per cycle. The latter equation has the desirable property of varying between zero and one. The analysis done in the time domain is extended to include analysis of hysteresis curves as well.
In this study, amorphous Ni-P films were deposited by electroless plating under different pH values. Their mechanical properties and deformation behavior were then investigated by instrumented nano-indentation. With increasing pH value of the plating solution from 3.75 to 6.0, the hardness and elastic modulus of the obtained Ni-P films increased from 6.1 GPa and 146 GPa to 8.2 GPa and 168 GPa respectively. From the load-indentation depth curve, the Ni-P films were found to yield at an indentation depth of 8 nm. By microstructural examination around the indented regions, early-stage plastic deformation of the amorphous Ni-P films was verified through the formation and extension of shear bands with a spacing of several tens of nanometers. Within the shear bands, flow dilatation-induced intense shear localization was expected and resulted in crystallization in the amorphous matrix. The critical shear stress and energy release rate required for the initiation of early-stage plastic yielding of the Ni-P films were calculated to be about 1.4 GPa and 3.0 J/m2 respectively, both of which increased with pH values.
A new class of cellular micro-scale truss structures formed from a three-dimensional interconnected pattern of self-propagating photopolymer waveguides were presented. The diameter of the waveguide was dependent on the exposed area and the length was primarily dependent on the incident energy of the light and the photo-absorption properties of the polymer. The diameter of the resulting waveguide is found to be slightly larger than the diameter of the single aperture as the prolonged exposure causes the waveguide to thicken. The micro-truss structure is 7.8 mm in height and features a repeating octahedral-type unit cell. The microstructures with increased and reduced open volume fraction are possible such that the upper bound on open volume fractions determined by the self-supporting ability of the structure while lower bound limited by the ability to remove the uncured monomer after the polymerization process.