Bio-Inspired Engineering of Honeycomb Structure - Using Nature to Inspire Human Innovation

Abstract and Figures

Abstract Honeycomb structures, inspired from bee honeycombs, had found widespread applications in various fields, including architecture, transportation, mechanical engineering, chemical engineering, nanofabrication and, recently, biomedicine. A major challenge in this field is to understand the unique properties of honeycomb structures, which depended on their structures, scales and the materials used. In this article, we presented a state-of-the-art review of the interdisciplinary efforts to better understand the design principles for products with honeycomb structures, including their fabrication, performance (e.g., mechanical, thermal and acoustic properties) as well as optimization design. We described how these structural perspectives have led to new insights into the design of honeycomb structures ranging from macro-, micro- to nano-scales. We presented current scientific advances in micro- and nano-technologies that hold great promise for bioinspired honeycomb structures. We also discussed the emerging applications of honeycomb structures in biomedicine such as tissue engineering and regenerative medicine. Understanding the design principles underlying the creation of honeycomb structures as well as the related scientific discovery and technology development is critical for engineering bioinspired materials and devices designed based on honeycomb structures for a wide range of practical applications.
The most representative honeycomb structures from macro-to nano-scale. (A) Hex tower designed by Michel Rojkind (Source:; (B) vertically perforated lightweight heat insulation brick (Source:; (C) honeycomb-cored sandwich panel (Source:; (D) honeycomb-cored airless tire for troopcarrying humvees that prevents thermal damage caused by locally hot spots on the road (Source:; (E) turbine honeycomb seal (Source:; (F) honeycomb mirror for Hubble space telescope (Source:; (G) extruded and sintered ceramic honeycomb (Source: http://www.ikts.; (H) multi-channel ceramic membrane (Photo Source: Membrane Science & Technology Research Center); (I) SEM top view of as-prepared and fully lithiated silicon honeycombs [46]; (J) honeycomb microstructured fluorinated Si surface [47]; (K) channel structure of typical silica microhoneycomb [48]; (L) conceptual scheme where the polyethylene's crystalline fibers grow by means of the mechanisms of mesoporous silica-assisted extrusion polymerization [49]; (M) SEM image: compact structure is sliding above the underneath column with a deformed pillar (2 mm in size) of anodic aluminum oxide nanohoneycomb [50]; (N) SEM image of TiO 2 surface after photoelectrochemical etching under strong (+1.0 V) anodic polarization [51]; (O) schematic illustration of the accordion honeycomb with hexagonal cells consisting of two overlapping squares with a
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Bioinspired engineering of honeycomb
structure – Using nature to inspire human
Qiancheng Zhang
, Xiaohu Yang
, Peng Li
, Guoyou Huang
Shangsheng Feng
, Cheng Shen
, Bin Han
, Xiaohui Zhang
, Feng Jin
Feng Xu
, Tian Jian Lu
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, PR China
MOE Key Laboratory for Multifunctional Materials and Structures, Xi’an Jiaotong University, Xi’an 710049, PR China
Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, PR China
School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
MOE Key Laboratory of Biomedical Information Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
article info
Article history:
Received 29 October 2014
Received in revised form 12 March 2015
Accepted 5 May 2015
Available online 7 July 2015
Honeycomb structure
Bioinspired materials
Sandwich panel
Material processing
Mechanical behavior
Heat transfer
Optimization design
Honeycomb structures, inspired from bee honeycombs, had found
widespread applications in various ﬁelds, including architecture,
transportation, mechanical engineering, chemical engineering,
nanofabrication and, recently, biomedicine. A major challenge in
this ﬁeld is to understand the unique properties of honeycomb
structures, which depended on their structures, scales and the
review of the interdisciplinary efforts to better understand the
design principles for products with honeycomb structures, includ-
ing their fabrication, performance (e.g., mechanical, thermal and
acoustic properties) as well as optimization design. We described
how these structural perspectives have led to new insights into
the design of honeycomb structures ranging from macro-, micro-
to nano-scales. We presented current scientiﬁc advances in
micro- and nano-technologies that hold great promise for bioin-
spired honeycomb structures. We also discussed the emerging
applications of honeycomb structures in biomedicine such as
tissue engineering and regenerative medicine. Understanding the
design principles underlying the creation of honeycomb structures
0079-6425/Ó2015 Elsevier Ltd. All rights reserved.
Corresponding authors at: Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an
710049, PR China.
E-mail addresses: (F. Xu), (T.J. Lu).
Progress in Materials Science 74 (2015) 332–400
Contents lists available at ScienceDirect
Progress in Materials Science
journal homepage:
as well as the related scientiﬁc discovery and technology develop-
ment is critical for engineering bioinspired materials and devices
designed based on honeycomb structures for a wide range of
practical applications.
Ó2015 Elsevier Ltd. All rights reserved.
2. The topology and evolution of honeycomb structures. . . . . . . . ............................... 336
3. Design principle: structure–property relationships . . . . . . . . . . ............................... 339
3.2.1. Mechanics of 2D and 3D macro honeycombs . . . . . . . .......................... 340
3.2.2. Mechanics of micro- and nano-honeycombs . . . . . . . .......................... 345
3.2.3. Mechanics of polymeric and bio-honeycombs . . . . . . .......................... 350
4.1. Fabrication and applications in traditional engineering . . . . . . . . . . . .................... 355
4.2. Fabrication and applications in micro and nanofabrication . . . . . . . . .................... 361
4.3.3. Cell encapsulated honeycomb cellular constructs . . . .......................... 377
5.1. Design and fabrication of hierarchical/hybrid structure . . . . . . . . . . . .................... 382
5.2. Multi-functional design and fabrication approaches. . . . . . . . . . . . . . .................... 385
1. Introduction
Nature is a great and successful laboratory with a database full of effective solutions to many
scientiﬁc and technical problems [1–3]. The ideas from nature have inspired mankind with a series
of novel designs on high-performance materials and systems that function from macroscale to
Q. Zhang et al. / Progress in Materials Science 74 (2015) 332–400 333
nanoscale [4–7]. For instance, one can ﬁnd a variety of porous structures in nature, which play crucial
roles in multifunction realization and system operation in organisms. The majority of artiﬁcial designs
on porous materials has been inspired by nature or can ﬁnd their prototypes in nature [8,9], with
honeycomb being the most representative example. The honeycomb cellular structure, originating
from the natural honeycomb in a nest, consists of uniformly-distributed double-layered hexagonal
cells. The materials for constructing cell walls are beeswax and propolis (a kind of plant resin).
Studies on the characteristics of honeycomb structures have been going on for literally thousands
of years [10–15]. However, honeycomb structures were not incorporated into large-scale applications
in human society until about 70 years ago, after which numerous honeycomb structures made from
various materials emerged, from papers [16,17], to metals [18], then to ceramics [19] and composites
[20]. The technologies used to fabricate honeycomb structures have also been progressively advanced
In view of technological invention, the evolution of honeycomb technology may be divided into
four stages, i.e., interesting and enlightening stage (60 BC-126), exploratory stage (1638–1901),
structure-based application stage (1914–1990), and multi-functional, multi-ﬁeld and multi-scale
rapid development stage (1990–now). During the ﬁrst stage, people wondered about the hexagonal
comb of honeybee for centuries. After experiencing silence for more than 1000 years, the second
industrial revolution drove the exploration of porous structures in nature due to increasing demand
for lightweight structures, and the invention of microscopes offered a proper tool to explore these
magical structures. For example, in 1665, Robert Hook discovered that the natural cellular structure
of a cork is similar to that of a hexagonal honeycomb. Hundreds of years of accumulation in under-
standing the honeycomb structure led to the development of honeycomb technology from a qualita-
tive change in the second stage to a quantitative change in the third stage. In 1914, Höﬂer and Renyi
patented the ﬁrst structural application of honeycomb structures, initiating the structure-based appli-
cation stage. Almost 70 years since then, numerous honeycomb related materials emerged in architec-
ture, aviation, space, transportation and many other engineering ﬁelds, from papers, to metals, then to
composites. The more detailed description of the fatal developments in the history of man-made hon-
eycombs could be found from the open literature, e.g., Bitzer [25,26] and Xiong et al. [25,26].
Since the 1980s, applications of honeycomb structures in engineering ﬁelds (Fig. 1A) had expanded
signiﬁcantly into the architecture ﬁeld, such as the Hex Tower designed by Michel Rojkind in 2005
(Fig. 2A). Besides, new types of honeycomb made from different materials had been designed and
manufactured to facilitate speciﬁc applications. In particular, over the past two decades, we have
witnessed the further expanding of honeycomb structures from engineering ﬁelds to nano and
biomedical ﬁelds (Fig. 1B), such as nanohole arrays in anodized alumina [27], microporous arrays in
polymerthin ﬁlms [28], activated carbon honeycombs [29], and photonic band gap honeycomb
structures [30]. Especially in 1999, the conjecture was ﬁnally proven by Hales [31] that the way bees
build hives is to provide maximum cell space by using a minimal amount of beeswax, indicating that
hexagonal honeycomb structure is the most stable for nature. Recently, Karihaloo and his colleagues
[32] revealed the mechanism for the transformation of circular honeycomb cells in a natural honeybee
comb quickly into rounded hexagonal structures, i.e., the formation of molten viscoelastic wax heated
by ‘hot’ worker bees to ﬂow near the triple junction between neighboring circular cells. This ﬁnding
witnessed a vigorous continuation of the long-standing debates about whether the honeycomb is
an example of blind physics or an exquisite biological engineering.
With the development of electron microscopy technology, new honeycomb structures at micro-
and nano-scales in nature have been increasingly discovered. For instance, numerous examples of
hexagonal or similar patterns have been found in living tissue [14,33,34], cell aggregates [35] and
molecules [36]. In the past several decades, with advances in manufacture technologies, honeycomb
structures have been adapted into different applications, ranging from engineering [37–42] to more
recently biomedicine [43–45], accumulating a rich store of artiﬁcial honeycomb structures at scales
varying from macrometer to nanometer. In Fig. 2, we summarized representative applications of
the most typical artiﬁcial honeycomb structures, which can be divided into three categories depend-
ing on scale, i.e., the traditional engineering ﬁeld, the micro and nanofabrication ﬁeld, and the
biomedicine ﬁeld [36,44–54]. It can be seen that new applications of honeycomb structures have been
constantly launched in the traditional engineering ﬁeld (e.g., Hex tower designed by Michel Rojkind
and airless honeycomb tire), in innovative micro-and nano-scale fabrications (e.g., lithiated silicon
honeycombs [46]), as well as in biomedical applications (e.g., scaffold designed with accordion-like
honeycomb [44]).
In this article, we reviewed the honeycomb structures, with emphasis on their plentiful morpholo-
gies and multifunctional applications, from a multi-scale standpoint. First, we reviewed recent devel-
opments in the design concept of topological structure, including the evolution of honeycomb
structures, and their structure–property relationships in scales from macrometer to micrometer and
nanometer. Then, we summarized the emerging applications of honeycombs as multifunctional
nano- and bio-structures and introduced the relevant fabrication methods. Particular focus was paid
on the load bearing applications with multi-functionalities, including lightweight, heat dissipation,
noise control, catalysis, ﬁltering separation, scaffold, biointerface, and molecular separation. Last,
we provided some insights into their challenges and future perspectives.
Fig. 1. The most representative honeycomb structures from macro- to nano-scale. (A) Hex tower designed by Michel Rojkind
(Source:www.minusﬁ; (B) vertically perforated lightweight heat insulation brick (; (C)
honeycomb-cored sandwich panel (Source:; (D) honeycomb-cored airless tire for troop-
carrying humvees that prevents thermal damage caused by locally hot spots on the road (Source:http://www.resilient-; (E) turbine honeycomb seal (Source:; (F) honeycomb mirror for Hubble
space telescope (Source:; (G) extruded and sintered ceramic honeycomb (Source:http://www.ikts.; (H) multi-channel ceramic membrane (Photo Source: Membrane Science & Technology Research Center); (I) SEM
top view of as-prepared and fully lithiated silicon honeycombs [46]; (J) honeycomb microstructured ﬂuorinated Si surface [47];
(K) channel structure of typical silica microhoneycomb [48]; (L) conceptual scheme where the polyethylene’s crystalline ﬁbers
honeycomb [50]; (N) SEM image of TiO
size of 200 200
m[44]; (P) viable honeycomb building unit [45]; (Q) SEM image of cellular morphology on the surface of ice-
template-induced scaffold [52]; (R) honeycomb formed in the mesh of a hexagonal grid [53]; (S) SEM image of
poly(dimethylsiloxane) star polymer ﬁlm having honeycomb morphology [53] and (T) honeycomb network of anthraquinone
molecules with open pores (diameter 50 angstroms) [36].
2. The topology and evolution of honeycomb structures
2.1. The topology of honeycomb
Honeycomb structures of interest here are composed of plates or sheets that form the edges of unit
cells, with their diameters ranging from tens of micrometers to tens of millimeters. Most honeycombs
are closed cell structures. These unit cells are repeated in two dimensions to create a cellular solid.
Based on this kind of distribution, the more common honeycomb structures can be arranged to create
triangular, square, hexagonal or circular shapes (Table 1). Each of the ﬁrst three topologies is efﬁcient
at supporting structural loads, especially the shear loads encountered in panel bending [38]. These
three classes of periodic cellular metals can now be fabricated from a wide variety of structural alloys.
Generally speaking, the relative density, which is the ratio between the density of the cellular
structure and that of the solid, is an important factor to describe the properties of honeycomb. By
identifying a unit cell and deriving the volume fraction occupied by metal, it is very easy to obtain
the relative density.
Recent advances in micro-/nano-fabrication and biomedicine have led to the emergence of circular
honeycomb topologies (Table 1). Meanwhile, recent advances in topology design and fabrication have
led to the emergence of lattice truss structures with open-celled honeycomb topologies, such as dia-
mond textile, diamond collinear lattice, and square collinear lattice. Those structures can be fabricated
by a fused deposition modeling process or a wire lay up process followed by transient liquid phase
bonding. The fabrication approaches can be found in some review articles [38,55].
2.2. The evolution of honeycomb structures
Honeycomb with hexagonal cells has the most common structure amongst cellular materials, and
has been successfully fabricated by using a variety of technologies and materials. In reality, however,
to meet the speciﬁc needs for different applications, hexagonal honeycomb structures had evolved
into many new ones in the man-made world, leading to rapidly increasing diversity from traditional
engineering to micro- and nano-fabrication then to biomedicine. Here, we summarized the evolution
of honeycomb structures (Fig. 3) to achieve such speciﬁc requirements as strengthened performance,
simpliﬁed process, reduced cost, or enhanced multi-functionality.
In the traditional engineering ﬁelds, depending on speciﬁc applications, the shape of honeycomb
cells had evolved from hexagonal to square [38], triangular [56], columnar [57] or other related shapes
[58] (Fig. 3A). For example, honeycombs with rectangular or hexagonal cells are satisfactory conﬁgu-
rations for forced convective heat transfer, while triangular honeycomb posses better mechanical
performance (in-plane stiffness/strength) over various mechanical loading conditions [59]. Based
(A) (B)
Fig. 2. Number of annual publications on (A) ‘honeycomb’, (B) ‘honeycomb’, nano
and tissue engineering
.Source: Science
Citation Index Expanded [Sci-EXPANDED].
upon the two distinct analytical methods, i.e., homogenization theory and discrete network approach,
Torquato et al. [60] investigated the effective linear elastic properties of honeycombs with various cell
shapes including square, hexagonal and triangular cells. Cross-property bounds relating to bulk mod-
ulus and other elastic moduli to thermal conductivity were obtained. To regulate or reinforce superior
performance in one aspect, stretching or compressing or shearing of hexagonal microporous arrays
Table 1
Unit cells and relative densities of honeycomb topology structures.
Unit cell shape Relative density
Hexagonal honeycomb q=q
Square honeycomb q=q
Triangular honeycomb q=q
Circular-cored hexagonal honeycomb q=q
(continued on next page)
along the K and M axes by a certain factor led to highly over-expanded (OX) [61], rectangular [62],
reentrant hexangular [63] and asymmetrical hexangular cells [64,65] (Fig. 3B). The OX cell is obtained
based on the standard hexagonal cell via extending along the K direction, resulting in a rectangular cell
conﬁguration in the M direction. Relative to hexagonal honeycombs, the OX conﬁguration increases
the shear properties in the W direction but decreases the ones in M direction. In addition, combining
the above structures generates new structures such as the square supercell constructed by combining
squares and triangles [66] and the Kagome cell [67] (Fig. 3C). To provide exceptional formability and
low cost, honeycomb structures have been developed from basic cell shapes such as hexagon, square
and triangle, to variations such as ﬂex-core [68], double-ﬂex [69] and reinforced hexagonal cells
(Fig. 3D). The ﬂex-core cell enables an exceptional formability in compound curvatures due to the
anticlastic curvature is reduced and free of buckling the cell walls. Once curvatures were formed very
tight radii, the shear strengths for ﬂex-core cell are higher than that for hexagonal cores with equiv-
alent density. Since the ﬂex-core with a unique large cell exhibits desirable formability and relatively
higher speciﬁc compression properties, the double-ﬂex cell is found to be the most formable
To enhance multi-functionality, truncated-square [58], reentrant hexangular core [63] and chiral
honeycombs [70] were exploited, Fig. 3E. Compared with the macro honeycombs in traditional
engineering, a large number of honeycomb structures besides the ones listed in Fig. 3 exist in
micro- or nano-fabrication and biomedical ﬁelds, partly due to their high sensitivity to manufacturing
and handling conditions. Baggetto et al. [46] reported that a regular hexagonal honeycomb structure
adopted a striking change, with a wall thickness, height and wall-to-wall spacing respectively of
250 nm, 1.1
m and 4.8
m, becoming highly curved as a function of Li contents when at full lithiation
(Fig. 4). In nanoscale liquid crystals, the columnar liquid crystals often exhibit a two-dimensional (2D)
periodic hexagonal honeycomb conﬁguration designed by self-organizing T-shaped molecules.
Sometimes distorted variants also exist, such as rectangular or oblique [71]. Chen et al. [72] reported
two topological classes: a periodically-distributed cylinders with identical size and cross-section
shape of pentagon and an conﬁguration of cylinders with a ratio in numbers of 2:1 for square and
triangular cross-sectional shape. Fig. 5 demonstrates a variety of 2D honeycomb-like structures, most
of which are constructed by T-shaped molecules, facial amphiphiles and rod-like molecules.
As microporous ﬁlms formed from poly(e-caprolactone) or polyacrylamide could be mechanically
deformed, it is possible to form various geometric patterns upon mechanical deformation. Nishikawa
et al. [73] reported that such geometric patterns as elongated hexagons, rectangles, squares, and
triangles could be obtained upon compression or stretching of hexagonal micro polymer ﬁlms,
Fig. 6. The patterning of micromeshes may be applied to fabricate micropatterned soft-materials for
cell culture. Wan et al. [74] fabricated microporous honeycomb-patterned ﬁlms from commercially
available polystyrene. Upon increasing the additive content in chloroform solvent, the shape of the
pores gradually changed from near-spherical to ellipsoidal (Fig. 7), with interfacial tension of the
Table 1 (continued)
Unit cell shape Relative density
Circular-cored square honeycomb q=q
studied system identiﬁed as a main factor for pore shape modulation. Four periodic patterns were
found in 2D soft materials where uniform circular holes are distributed [75]. As shown in Fig. 8,
mechanical instability is observed between expanded and compact periodic conﬁgurations.
3. Design principle: structure–property relationships
Through thousands of years of exploration, we have gone beyond the traditional awareness of the
exceptionally high mechanical strength as the only characteristic of honeycomb structures, and have
gradually deepened our understanding of multifunctional design principle for honeycomb structures.
The focus of this section, therefore, is on the relationships between topological structure and the
mechanical, thermal and acoustic properties for a variety of honeycomb structures. Other physical,
chemical and biological properties of honeycomb structures are closely related to their preparation
process and speciﬁc applications, and thus are discussed in Section 4.
Fig. 3. Periodic honeycombs with various cell shapes. (A-a) Regular hexagonal cell; (A-b) square cell; (A-c) triangular cell; (A-d)
columnar cell; (B-a) OX cell [61]; (B-b) rectangular cell [62]; (B-c) reentrant hexangular cell [63]; (B-d) asymmetrical
honeycomb [64,65]; (C-a) square supercell constructed from mix of squares and triangles [66]; (C-b) Kagome cell [67]; (D-a)
ﬂex-core cell [68]; (D-b) double-ﬂex cell [69]; (D-c) reinforced hexagonal cell (Source:; (E-a)
truncated-square cell [58]; (E-b) trichiral cell [70]; (E-c) tetrachiral cell [70] and (E-d) hexachiral cell [70]. K and M denote two
arbitrary vector axes in space.
3.1. Honeycomb conjecture
The mathematical structure of honeycombs has intrigued mankind for thousands of years. The
honeycomb conjecture was proposed by Pappus of Alexandria (c. 290–c. 350) with his ﬁfth axiom,
which states: ‘‘any partition of the plane into regions of equal area has perimeter at least that of the regular
hexagonal grid’’. This isoperimetric property of hexagonal honeycombs continues to intrigue
mathematicians today. The conjecture was ﬁnally proven by Thomas Hales [31,76]. His article
‘‘Cannonballs and Honeycombs’’ [77] described a modern version of the ancient observation in 2D.
In three dimensions (3D), not the bee’s honeycomb but the Voronoi cells of the body centered cubic
is possibly the most efﬁcient design, as shown by FejesTóth and others [78–80].
3.2. Mechanics of honeycomb structures
3.2.1. Mechanics of 2D and 3D macro honeycombs
The in-plane mechanical behaviors of regular hexagonal honeycomb and its derived structures
have been intensively investigated as reﬂected by the large number of research papers on this topic.
The main inﬂuencing factors such as material [81], structure type [82,83], porosity and relative density
Fig. 4. (A) SEM images in top and tilted view of (a) as-prepared honeycombs before lithiation (as the dashed line depicted) and
(b) fully lithiated silicon honeycombs. (B) Morphological changes of the Si honeycomb structure as a function of Li content. The
ﬁgure depicts the potential proﬁle for Si honeycombs upon lithiation (a) and delithiation (b) measured at 75
during the
ﬁrst cycle [46].
Fig. 5. (A–J) Topological isomers of plane tiling in various honeycomb-like networks forming two groups: lower row is the facial
amphiphiles and upper row is the rod-like molecules with two polar end groups and lateral nonpolar chains (bolaamphiphiles)
Fig. 6. Topological conﬁgurations observed in a stretched microporous ﬁlm of PCL: (A) hexagonal conﬁguration before
stretching; (B) elongated hexagons; (C) rectangular pattern; (D) square-like pattern and (E) triangle-like pattern [73].
Fig. 7. SEM images of polystyrene/poly(N,N-dimethylaminoethyl methacrylate) ﬁlms using chloroform (A and B) or
tetrahydrofuran (C and D) as solvent: (A and C) top view and (B and D) cross-sectional view [74].
[84–86] have been studied. For instance, Zhu and Mills [81] theoretically analyzed in-plane uniaxial
compression of regular honeycombs made from a broad range of materials (from polymer to metal),
which was found to signiﬁcantly depend on material type. A deterministic approach was adopted by
Fleck and Qiu [82] to predict the fracture response of elastic-brittle 2D lattices, and found that
hexagonal honeycombs deform by bar bending while triangular honeycombs deform predominantly
by the stretching of the constituent bars due to high nodal connectivity. It has been established that
honeycombs having triangular, Kagome, and diamond cells are extension-dominated, beneﬁcial for
the design for high modulus; while the design for ﬂexible structures require honeycombs to have
the cell shapes of square and hexagonal due to they are bending-dominated [82,83].
Most existing analytical studies assume the mechanics of honeycomb structures to be a 2D
problem. Earlier models on metallic hexagonal honeycombs [86] are only suitable for aluminum
honeycombs with relative densities less than 0.05, where the dominated failure mode is the elastic
buckling. As the relative density exceeds 0.1, yielding and plastic buckling of cell walls become the
dominant modes of failure under in-plane compression [84,85]. For honeycomb core sandwich panels,
as the core deformation is dictated considerably by thin face sheets, the role of core height and face
sheet (skin) and the mechanics of sandwich panel as a 3D problem cannot be ignored [87,88].
Further, with widespread engineering applications (e.g., energy absorption), the stress state involved
in practical design often becomes complex, therefore the biaxial in-plane compression and crushing of
honeycombs [89,90] have received increasing attention.
Fig. 8. Three groups (rows) of the arrangement patterns of circular holes for honeycombs, where each row is restricted to four
given conﬁgurations: (A) tilings; (B) expanded undeformed porous structures (green-shaded regions) and (C) compact (buckled,
denoted in green-shaded) porous structures caused by uniaxial compression [75].
To meet the needs of sandwich construction and maximizing its energy absorption capacity in the
out-of-plane direction, extensive studies have been performed to investigate the out-of-plane
mechanical behavior of honeycomb structures [91]. Again, material, structure type and porosity
(relative density) are identiﬁed as the main inﬂuencing factors [85,92]. Under out-of-plane compres-
sion, the most common honeycombs are aluminum foil honeycombs (relative density
and heavy duty metal honeycombs (relative density
>5%) such as those processed via extrusion
[23] and square honeycombs made of stainless steel [94,95]. For the former, the honeycomb cells
buckle elastically, producing the ﬁrst deformation at the pressure head end (without face sheet,
Fig. 9A) [96] or mid-height (with face sheet, Fig. 9B) [97], and crush by progressive formation of folds.
Yang and Qiao [98] proposed a model to predict the corresponding crushing wavelength and core
crushing strength. For the latter, the cells exhibit the axial–torsional buckling mode (Fig. 9C), i.e.,
the vertical nodal axis remains straight, while cell wall segments rotate around this axis [99]. Kim
and Christensen [92] compared the mechanical performance of three core types (triangular, hexago-
nal, and star cell) and found that the triangular core has the same stiffness as the other two cores, but
lower compressive and shear buckling strengths. Nevertheless, the highest ﬂexibility is found in the
star cell core, beneﬁcial for the engineering design for curved sandwich constructions.
Great attention had also been paid to the mechanical properties of honeycombs when subjected to
different types of external loading, including in-plane tension [100], in-plane biaxial compression,
out-of-plane transverse shear [101,102], peel [103], uniaxial tension [104], three- and four-point
bending [105], combined in-plane compression and shear [106], combined out-of-plane compression
and shear [93], creep [107], fatigue [108], dynamic shear and, recently, low- and high-velocity impact
[109,110]. Generally, deformation of honeycombs under these loadings can be interpreted by combin-
ing three different modes: ﬂexing, stretching and hinging [111]. For the ﬂexure mode, the cell walls act
like ﬂexures and are modeled as cantilever beams whose ends are ﬁxed and guided respectively
(Fig. 10A). For the stretching mode, cell walls are assumed to be like shock absorbers that only stretch
along their length without variation in angle or rotation (Fig. 10B) [111]. With hinging mode, the cell
wall does not elongate or bend; the deformation in cells is merely caused by the variation in angle
between cell walls. This in mechanism indicates that either global shear or local bending contributes
to the hinging mode (Fig. 10C) [111].
Fig. 9. Out-of-plane compression of metal honeycombs: (A) beginning of deformation in hexagonal honeycomb panel from
lower support [96]; (B) honeycomb cells at a certain stage of crushing [97]; (C) axial torsional buckling mode of stainless steel
square-honeycomb (viewed from top) [99].
(a) (b)
Fig. 10. (A) Deformed honeycomb cell walls with linear-elastic extension or compression; (a and b) bending caused separately
by loading in X
and X
directions [86]. (B) Stretch-resulted deformation in hexagonal cells due to applied tensile load in (a) D2
(direction 2) and (b) D1 (direction 1), where the right side presents the cell wall with applied forces [111]. (C) Hinging-resulted
deformation in hexagonal cells: (a) global shear and (b) local bending [111].
Within the density range of 20–300 kg/m
, honeycombs usually outperform other cellular materi-
als in terms of both stiffness and strength under compression or shear (Fig. 11)[112,113]. Moreover,
the superiority of honeycombs also holds in other mechanical properties, including bending resistance
[114–116], energy absorption [117], and shock resistance [118]. To further improve the mechanical
performance, composite and auxetic honeycomb structures have been exploited. For example,
composite structures such as foam ﬁlled hexagonal honeycombs [96,119] and honeycomb-ﬁlled single
and bitubular polygonal tubes [120] have been developed for enhanced energy absorption. Reentrant
hexangular cores with negative Poisson ratios [57], as a kind of auxetic honeycombs, exhibit improved
mechanical properties, including shear strength, indentation resistance and fracture toughness,
compared to conventional honeycombs.
3.2.2. Mechanics of micro- and nano-honeycombs
The advances in nanotechnology have signiﬁcantly accelerated the development and understand-
ing of honeycomb structures with micro- or nano-sized cells, potentially having widespread
Fig. 11. The relationship between the material density and the mechanical performance of (A) compressive stiffness/strength
and (B) shear stiffness/strength summarized by Ashby [112,113].
applications due to large surface area to volume ratio [121]. Balsa wood [122–125] and anodic porous
alumina (AAO) [50,126–129] are perhaps the most famous micro- or nano-scale honeycombs.
Balsa wood with a density ranging from 40 to 380 kg/m
has a cellular microstructure with approx-
imately hexagonal cross-sections of a typical micro-honeycomb. The micro-honeycomb allows large
deformations, leading to high speciﬁc energy dissipation capacity. To quantitatively determine the
mechanical properties of balsa wood and qualitatively clarify its deformation mechanisms, several
uniaxial quasi-static compressive investigations in both longitudinal and transverse directions
[122,130–134] have been performed (see Table 2). As a pioneering work, it is found by Easterling
et al. [132] that the balsa wood shares the same mechanisms with honeycomb in terms of compressive
deformation loaded along and across the grain (analogous to out-of-/in-plane direction in a honey-
comb). Further, it is suggested by Gibson [134] that the simple honeycomb model may be sufﬁcient
for determine the Young’s moduli and compressive strength of woods along and across the grain.
Recently, Silva and Kyriakides [122] conducted extensive experiments on the compressive response
of balsa wood in axial, radial and tangential directions, and systematically described the macroscopic
and microscopic deformation mechanisms (Fig. 12A). The shear [123] and dynamic compression
behavior [124,125] of balsa wood have also been investigated (see Table 2).
Anodic porous alumina (AAO) [50,126–129,135], nanoporous silica [136–141], and mesoporous
honeycomb-shaped activated carbon [142] were well-known nano-scale honeycombs. To maintain
microstructural integrity in practical applications, characterizing their mechanical properties was of
great importance. For transversely isotropic nano-honeycombs, ﬁve elastic constants were needed,
namely, Young’s moduli E
and E
, Poisson ratio
, and shear moduli G
and G
. However, it
was challenging to obtain these properties given the small cell size of nano-honeycombs. Built upon
an earlier work [129], Jeon et al. [135] attempted to experimentally determine the mechanical prop-
erties of microscopic brittle specimens of transversely isotropic nature by ﬁve independent tests using
the Nano-UTM and a nano indenter, as shown in Fig. 13. Ng et al. [126] studied AAO honeycomb sub-
jected to nanoindentation along its axial direction and micron-sized pillar of AAO under compression,
and observed a unique mode of deformation that the AAO honeycomb is either severely deformed or
Table 2
Mechanical behavior of micro- and nano-honeycomb materials.
Materials Pore size Loading methods Failure mode Ref.
Balsa wood 30–70
m Compression Buckling and kink band
Balsa wood 30–70
m Shear Cracks [123]
Balsa wood 30–70
m Modiﬁed Kolsky bar Buckling and kink band
Bending and shear [121,151]
Anodic porous alumina 31 nm Tensile test in Nano-
UTM and ﬂexural
testing in AFM
Elastic modulus [129]
Anodic porous alumina 25–35 nm Tensile and bending
Elastic modulus [135]
Anodic porous alumina 70 nm Compression Severe layer distortion
at the pillar’s head
Anodic porous alumina 70 nm, 20–80 nm Nanoindentation Bilinear and median
Anodic porous alumina 25–35 nm Bending fatigue Rectangular fracture
35 nm, 80 nm Compression Brittle crushing [136]
Nano-structured glass
3 nm Simulated
Mesoporous silica 5 nm Unilateral external
Destroy [138]
Mesoporous silica Nanoindentation Elastic modulus,
remained apparently elastic. The results shown in Fig. 12B demonstrated that AAO is promising as a
sacriﬁcial shielding or supporting material in applications involving mechanical contact with other
components, e.g., thin ﬁlm sensors. Nanoindentation was also employed to understand the deforma-
tion behavior of AAO honeycombs [126,127]. Further, the fatigue properties of nanohoneycombs were
of prime importance in creating stable products for a range of potential applications [128].
Fig. 12. (A-a) Photograph showing evidence of kink band in balsa wood ðq=q
¼0:150Þ. (A-b) Micrograph of balsa wood
showing concertina axial folding of crushed tracheids for
= 0.063 [122]. (B-a) Comparison of compressive stress–strain
responses of a 1
m column fractured at around 30% strain and a 700 nm column without noticeable facture till 80% strain.
(B-b) Schematically demonstration of the stress–strain curve [50]. (C-a) Bending fatigue life data and prediction curves of
nanohoneycomb. (C-b) SEM image of fractured surface in anodic porous alumina [128].
Fig. 13. Schematic display of ﬁve independent tests to experimentally determine the mechanical properties of nanohoneycomb
specimens: (A-a) tension, (A-b) three-point bending, (A-c) cantilever bending, (A-d) indentation in 1-direction, and (A-e)
indentation in 3-direction. Tensile test of nanohoneycomb beam specimen by Nano-UTM: (B-a) general view and (B-b)
nanohoneycomb mounted on a metal plate. Bending ﬁxture: (B-c) overall feature, (B-d) three-point bending, and (B-e)
cantilever bending. MTS nanoindentation: (B-f) overall view and (B-g) indenter tip holder and sample [135].
Concerning ordered mesoporous materials such as silica, many researchers focused on their rigidity
and structural stability under stressing [139,143–145]. The mechanical stability of ordered meso-
porous silica can be mainly characterized by its elastic modulus, depending on the porous structure
and the consolidation extent of silica. The elastic modulus (E
) of thin ﬁlms with honeycomb-like
porous structure has been measured with the technique of nanoindentation [139], while the crushing
strength of nanosized hexagonal silica honeycombs with different pore sizes has also been measured.
Good agreement has been achieved between experimental measurements and predictions using
theoretical model originally for macroscopic hexagonal ceramic honeycombs [136]. Further, higher
consolidation has been found to provide a more rigid structure, helpful for eliminating the more
hydrothermally sensitive pore surface Si–OH bonds to the beneﬁt of the formation of more
hydro-resistive Si–O–Si bonds [146,147]. Several methods have been developed to enhance pore wall
consolidation, e.g., surfactant removal processes [140,146], silica nanoparticle [141], salt [148] or
alumina additives [149], and humidity treatments [150].
At the micrometer or nanometer scale, the size-dependent effect plays a vital role in the mechan-
ical behavior of honeycombs [121,151]. For example, Zhu [151] found that strain gradient and surface
elasticity dominates honeycomb elastic properties at micrometer and nano-meter scale, in respective.
Joonho et al. [121] employed the asymptotical expansion framework and the numerical homogeniza-
tion method to predict the elastic properties of honeycombs in micro and nano scale by introducing
the surface elasticity. They found that the mechanical property such as bending stiffness and
shear stiffness was dependent upon the size of honeycomb and may attributed to the atomic bonding
reconstruction at micro/nano-sized honeycomb surfaces.
Fig. 14. (A) Experimental images of a square lattice (10.97 mm center-to-center spacing) at different levels of macroscopic
compressive strain: (a) 2%, (b) 7%, (c) 8%, and (d) 10% [157]. (B) Experimental images of a porous lattice under compression of
= 0.25 [152]. (C-a) SEM image of uniform pattern transformation in a square lattice following the polymerized acrylic acid in
the pores. (C-b) AFM topographical image of the transformed pattern. (C-c) SEM image show of the regular transformation
pattern (inset showed 2D fast Fourier transform) due to large-scale periodic conﬁnement of mechanical instabilities [160]. (D)
Halftoned disks with axisymmetric metrics, with patterned sheets programmed to generate (a) a piece of saddle surface, (b) a
cone with an excess angle, (c) a spherical cap and (d) a cone with a deﬁcit angle [155].
3.2.3. Mechanics of polymeric and bio-honeycombs
Owing to the elastic nature of polymeric and bio-honeycomb structures, their mechanical
behaviors are signiﬁcantly different from other honeycomb solids, e.g., the completely reversible
transition in buckling instability and the unusual negative Poisson ratio (Fig. 14)[152]. Further, the
buckling-based morphological changes induce dramatic change not only in relevant physical
properties such as phononic property [153,154], but also in biomedical applications [155]. In tissue
engineering, the structure such as 2D or 3D porous structure, micro-/nano-ﬂuidic channels, and
microenvironment experienced by cells cultured on the surface of the porous structure can be dynam-
ically tuned by buckling-based reversible changes in morphology.
With subjected to different levels of uniaxial compressive strain, the mechanical instability of por-
ous structures in millimeter-scaled distribution was investigated by Mullin and coworkers [156] (see
Fig. 14A). New patterns and super elastic behaviors [75,157] were observed at post-deformation trans-
formation of other lattices with circular voids. Pattern deformation due to buckling instabilities in por-
ous structures with periodically-distributed pores persists at micro-/nano-scales, in a wide range of
porous structures with various porous geometries and lattice symmetries. Such pattern deformation
can be induced by light [158], solvent swelling [154,159,160] (Fig. 14C), or even temperature [155]
(Fig. 14D). For example, Zhang et al. [159] presented pattern deformation in a microporous elas-
tomeric poly(dimethylsiloxane) structure consisted of circular pores (pore diameter varying in the
range of 350 nm to 2 mm) distributed in a square array. Such responsive buckled complex surfaces
can also be designed as constant Gaussian curvature (spherical cap, saddle and cone) or zero mean
curvature (Enneper’s surfaces) by using halftone gel lithography [155].
3.3. Heat transfer
Honeycomb structures have attracted signiﬁcant interest for thermal management applications,
either as thermal barriers or heat dissipaters. In general, three fundamental modes of heat transfer are
present in honeycombs, namely, conduction, convection (natural and forced convection), and radiation.
According to different thermal situations, these modes are usually found to couple with each other.
3.3.1. Conductive heat transfer
In the absence of convection and radiation, heat transport across a honeycomb solid is dominated
by solid and gaseous conduction. Prediction of its effective thermal conductivity is, in principle,
straightforward by treating the honeycomb as a two-phase material. The effective thermal conductiv-
ity in either axial or lateral direction of the honeycomb has been analytically and numerically inves-
tigated [161–164]. Considering both solid and gaseous conduction, Groppi and Tronconi [164] derived
the effective thermal conductivities of a honeycomb with square cells in both axial (k
) and lateral
) directions. For honeycombs made of metal solids, heat conduction through the gas phase is neg-
ligible since the gaseous conductivity (10
W/mK) is signiﬁcantly lower than the solid ones
W/mK). Based on this assumption, Lu and Chen [162] obtained a general correlation for the axial
and lateral effective thermal conductivities of honeycombs having different cell shapes (Fig. 15),
Þ ð1Þ
where c
is the coefﬁcient accounting for the tortuous shape of the cell wall. For axial effective thermal
conductivity c
always equal to 1 regardless of the cell shape, whereas c
is strongly related to cell
shape in the lateral direction. Recently, Yang et al. [165] proposed a fully analytical model for effective
thermal conductivity of honeycombs, achieving the good prediction for honeycombs with various pore
shapes for the full porosity range. They incorporated an analytical expression for shape factor based on
the circularity which corrects the deviation caused from the non-circular (or non-spherical) pore
inclusion into the Laplace heat conduction equation.
3.3.2. Convective heat transfer
Natural convection. Dating back to 1965, studies had focused on natural convective heat transfer in
a honeycomb positioned in the axial direction (Fig. 16A), for its predominant application in ﬂat-plate
solar energy collectors. In such applications, honeycombs with low-conducting and thin cell walls
are placed the absorber plate and the cover glass to suppress the global natural convection in the
chamber. As a result, heat loss from the absorber plate to the cover glass via natural convection is
Fig. 15. Honeycomb structures with different cell shapes to study morphology dependent effective thermal conductivity: two
packings of equilateral triangles of (A) inline and (B) stagger; two packings of squares of (C) inline and (D) stagger; (E) closely
packed circles [161].
(A) (B)
Fig. 16. (A) Illustration of natural convection heat transfer in honeycomb structure in ﬂat-plate solar energy collectors [170];
(B) illustration of forced convection heat transfer in honeycomb structure [171]; (C) comparison of thermal performance
between honeycombs with other state-of-the art heat dissipation materials [170], and (D) illustration of radiation heat transfer
in honeycomb core sandwich panel.
signiﬁcantly reduced by introducing the honeycomb. Following the ﬁrst study of natural convective
heat transfer in honeycombs by Hollands [166], numerous experimental and numerical studies
[167–170] have demonstrated the high efﬁciency of honeycombs for reducing the heat loss in
ﬂat-plate solar energy collectors.
Forced convection. When positioned in the lateral direction, a honeycomb core sandwich can be
used as an efﬁcient heat dissipation material by passing cooling ﬂuid through its continuous open
channels (Fig. 16B). In this case, the cell walls of the honeycomb act as ﬁns to dissipate heat deposited
at the facesheet of the sandwich. Considering heat conduction in honeycomb solids coupled with
forced convection, Lu [171] developed a corrugated wall heat transfer model for honeycomb embed-
ded with cooling ﬂuid ﬂow inside. Using this corrugated wall model, Lu’s group studied and optimized
various inﬂuencing parameters of honeycomb structure with experimental validation [172,173], e.g.,
cell shape, porosity, surface area density, overall geometrical dimensions, and material properties. It
was found that friction factor depends only on surface area density and cell shape of porous structure,
whereas heat transfer performance is affected by a variety of parameters including cell shape, surface
area density, porosity, thermal conductivity, and overall dimensions.
Besides analytical investigations, McDowell and co-workers developed different numerical meth-
ods (ﬁnite element and ﬁnite difference) for forced convection in honeycomb structures [170].
From a design point of view, their studies mainly concentrated on the optimization of honeycombs
with rectangular cells by functionally grading cell size along the height to enhance both structural
and thermal performances.
Ideally, a heat dissipation material should attain more heat transfer at the least expense of pump-
ing power to drive the ﬂuid ﬂow. In this regard, both the heat transfer and pressure drop performances
are important for a heat dissipation material. The high surface area density of a honeycomb enables
superior heat transfer. Meanwhile, the single ‘‘easy ﬂow’’ passage in the honeycomb leads to much
lower pressure drop than other heat dissipation materials having high surface area density, e.g., metal
foams with stochastic micro-structure [171]. Consequently, under the criteria of given pumping
power, honeycomb structures outperform other state-of-the art heat dissipation materials, including
metal foam, woven textile and lattice-frame material (Fig. 16C) [170].
3.3.3. Radiative heat transfer
In the 1950s, the employment of sandwich panels with axial honeycomb cellular cores in ﬂight
vehicles as outer skins led to great demand in studying the heat transfer through these structures
during aerodynamic heating [162,172]. For such high temperature applications, radiation between
the facesheets and the honeycomb core is coupled to solid conduction (Fig. 16D). Using numerical sim-
ulations, Swann and Pittman [173] obtained a semi-empirical relationship for the effective thermal
conductivity of combined radiation/conduction in the honeycomb core as a function of geometric
parameters and material properties. Subsequently, this semi-empirical relationship was used
throughout the aerospace industry as a standard model for determining combined conductive/
radiative heat transfer in panels with axial honeycomb cores. In the combined radiation/conduction
heat transfer mode, the contribution of radiation is determined by the exposed surface temperature
and the thermal conductivity of cell wall. For instance, Lu and Chen [162] found that for honeycomb
cellular metals with hexagonal cells (k
> 200 W/mK), heat transfer is mainly by conduction via solid
cell walls, and the inﬂuence of thermal radiation was found to be negligible even at a relatively high
temperature around 600 K; however, for materials with a thermal conductivity less than 1 W/mK
typically involved in thermal insulation applications, even at relatively low temperatures (310 K),
radiative heat transfer contributes half of the total heat transfer.
3.4. Acoustic property
When a sound wave strikes a structural surface, the total incident sound energy is divided into
three parts including scattering sound, absorbed energy and transmitted sound. The transmitted
sound is an indication of acoustic performance of the structure as a noise barrier (i.e., sound insula-
tion) between separating spaces. The absorbed energy characterizes the sound absorption capability
associated with thermal-viscous effects, resonance dissipation mechanism and so on. Therefore, the
following discussions on the acoustic property of honeycomb structures focus separately on sound
insulation and sound absorption.
3.4.1. Sound insulation
Owing to their high stiffness to weight ratio, honeycomb structures are widely used in aerospace
industry (e.g., fuselage linings of airplane [174]). Advances in ﬁnite element models for complex
honeycomb sandwiches have led to the rapid growth of computational requirement due to the
increased cells. For this reason, the whole structure is usually regarded as a layered plate medium after
homogenization [175]. As a pioneering work, Kurtze and Watters [176] investigated the sound
transmission loss (STL) of sandwich structures to design a more quieter wall than the traditional thick
single wall. Three types of characteristics governing motion are identiﬁed from lower to higher fre-
quency, including bending of whole structure, shear deformation of core and bending of facesheet.
As shown in Fig. 17A, the typical STL versus frequency curve of a ﬂat sandwich plate exhibits four dif-
ferent regions controlled separately by stiffness, resonance, mass and coincidence [177]. This indicates
that panel stiffness dominates STL curve trend until the start of the lowest order resonance. At about
twice the ﬁrst order resonance frequency, mass inertia begins to play a primary role, ending at the
coincidence frequency related to bending stiffness and incidence angle. Compared with one layer ﬂat
plate, honeycomb sandwiches have a similar resultant graph but more design variables such as
thickness of facesheet or core structure [178]. It is found that the key to design quieter honeycomb
sandwiches is to maintain a sub-sonic bending wave speed over as great frequency range as possible
[179]. Apart from continuum models, great efforts have also been devoted to investigating honeycomb
structures using detailed analytical models [180], ﬁnite element method [181], and spectral ﬁnite
element method [182]. Remarkably, these detailed models are able to reﬂect discretized and periodic
characteristics of the honeycomb, which is especially important for wave propagation analysis rather
than STL prediction.
(B) (a) (b) (c)
Fig. 17. (A) Typical sound transmission loss (STL) spectrum for a ﬂat plate [177], (B) representative honeycombs with high
sound absorption coefﬁcients: (a) hexagonal chiral lattice [186], (b) honeycomb structure with local resonators [194], and (c)
schematic of perforated board and honeycomb layer system [198].
In summary, the sound insulation performance of a macro honeycomb structure is related to
vibration response of the whole structure, identical to a conventional ﬂat plate for physical mech-
anism. However, things become different for micro and nano structures [183] since the mechanical
properties of these structure turn to be size-dependent. Thus, new constitute relations (e.g., non-
local elasticity theory [184]) instead of classical continuum models are required to account for
the size effect. For example, the wave characteristics of single-walled carbon nanotubes were
investigated using nonlocal elasticity [185], which indicated the limitation of applicability of local
continuum models. But whether at the macro or micro scale, the main goal to investigate STL of a
honeycomb structure is to predict its unitary dynamic response theoretically or numerically as
accurate as possible.
3.4.2. Sound absorption
In the past two decades, artiﬁcial periodic materials (also known as phononic crystals [186]) have
attracted great attention due to the existence of elastic (or acoustic) wave band gaps. For instance, as
shown by Ruzzene and Tsopelas [187], a honeycomb sandwich plate with different geometry param-
eters can generate periodic impedance mismatch to form a bending wave band gap. Phani et al. [188]
investigated four planar lattices: hexagonal honeycomb, Kagomme lattice, triangular honeycomb, and
square honeycomb. In the high frequency range, the spatial ﬁltering effect due to anisotropy is consis-
tent with geometry symmetry. Generally, the mechanism of band gap formation is attributed to Bragg
scattering and localized Mie scattering resulting from periodic elements. For example, Sánchez-Pérez
et al. [189] showed that an array of rigid cylinders in air with square lattice conﬁguration generated
complete acoustic band gaps in the range of audible frequencies (Fig. 17B-a). Similarly, complete band
gaps are achieved with honeycomb water–steel photonic crystals [190]. It is worth noting that the
band gap from Bragg scattering mandated the structural periodicity to be on the same order as the
incident acoustic (or elastic) wave, thus a low-frequency wave can only be attenuated by acoustic
crystals with larger size [191].
Fortunately, another band gap mechanism denoted as a local resonance has been identiﬁed [192],
offering attractive perspective to realize high STL at low frequencies. For example, a thin
membrane-type metamaterial (weight <3 kg/m
) attached by periodic metal circular disks was
designed and fabricated [193]. For such artiﬁcial structures, numerical and experimental results
demonstrated that an average STL of more than 40 dB could be accomplished from 50 Hz to
1000 Hz. Further, by changing the metal disks to asymmetric rigid platelets, a new kind of metama-
terial (as shown in Fig. 17B-b) was proposed recently [194], realizing almost unity sound absorption
coefﬁcient. From the existing results, we can anticipate that a honeycomb structure with local reso-
nance cells is promising for sound absorption applications.
Normal honeycomb structures exhibit negligible sound absorption because the damping
coefﬁcient of the commonly used materials is small. Nonetheless, honeycomb structures can be
transformed into excellent sound absorbers by introducing viscous-thermal dissipation or
Helmoholtz resonance mechanisms [195]. One simple and direct way is to ﬁll the honeycomb cav-
ity with polyurethane (PUR) foam [196] or ﬁbrous sound absorptive material [197]. Apparently, the
sound absorption coefﬁcient of the whole structure mainly depends on the ﬁlled sound absorption
materials. Besides the ﬁlling materials, the facesheet of honeycomb sandwiches can be replaced by
a microperforated board to improve sound absorption [198]. The small (1 mm) holes on the face-
sheet together with the honeycomb structure composed a typical Helmoholtz resonator which
could absorb sound energy in a narrow frequency band (Fig. 17B-c). Moreover, if the concept of
microperforatation is applied, a wide band absorption may be achieved without using the ﬁbrous
or porous ﬁlling material [199].
Overall, different from the sound insulation performance, the sound absorption capability of a
honeycomb structure is less affected by its overall dynamic response which may be size-dependent
for small scale problems. The decisive factor on the ﬁnal absorption coefﬁcient mainly depends on
speciﬁc physical mechanisms, e.g., Bragg scattering, local resonance or Helmholtz resonance.
Therefore, the critical scientiﬁc issues of an acoustic honeycomb structure are related to its mechan-
ical property and absorption mechanism for sound insulation and sound absorption, respectively.
4. Fabrication methods and applications
Naturally-occurring honeycombs have attracted great interests due to their distinct formations stud-
ied by scientists for centuries, where advances in engineered (artiﬁcial) honeycombs have been largely
motivated by their broad applications. For instance, macro-honeycombs have been used not only in
sandwich panels [38] but also adopted for many other applications such as energy absorption [57], air
directionalization [25], thermal management [171], sound absorption [197], light diffusion [200] and
magnetic shielding [201]. In recent years, a wide range of manufacturing processes have also been devel-
oped to fabricate micro/nano-honeycomb structures and their evolutional structures that are more
affordable and functional for traditional engineering ﬁelds as well as emerging biomedicine.
4.1. Fabrication and applications in traditional engineering
Based on thousand years of exploration and the last hundred years of development in engineering,
honeycombs have been extensively utilized in various traditional engineering ﬁelds (civil engineering,
transportation, mechanical engineering, chemical engineering, etc.) because of their multifunctional
characteristics including light-weight construction, thermal insulation [170,202,203], and energy
absorption [204–206]. The practical applications of man-made honeycombs focus primarily on: (i)
ultralight weight design associated with high strength and low density, such as lightweight compo-
nents used in architectural, automobile and aerospace structures, (ii) high impact energy absorption
applications such as armors and helmets, and (iii) high macroscopic shear yield strength applied to
non-pneumatic tires. In the following sections, typical examples of these applications are presented.
4.1.1. Architectural engineering
Typical honeycomb structures applied in architectural engineering include honeycomb architec-
ture, construction materials, and building decorations. Honeycomb architecture leads an innovative
trend in architectural system, giving the conceptual design of a hexangular tube construction.
Honeycomb type buildings with different shapes (Fig. 18A) exhibit superiority in energy-saving,
environment-friendly, and earthquake-proof characteristics. Two representative examples of honey-
comb architecture are Mexico city-based architect Michel Rojkind’s new project and the Metropol
Parasol project in Seville, Spain, by Jurgen Mayer H. Architects that is completed in 2009 created a real
buzz. Further, two glass towers wrapped in a dramatic honeycomb structure will soon be under con-
struction. There will be the world’s largest wooden structure in the city’s Santa Fe district; it has 35
stories and can house 180 duplex apartments with a hotel and gardens on the upper ﬂoors.
The application of honeycomb structures can be found in such construction materials as honey-
comb bricks and transparent insulation (Fig. 18B). Detailed review on the analysis and evaluation of
transparent insulation for building applications can be found in Ref. [207]. In addition to honeycomb
construction materials, the highly competitive honeycomb transparent insulation is also used in solar
collectors [170], roof cover system [208] and integrated collector storage [209], as well as in space
heating and day lighting for buildings [210]. Heat transfer takes place through a honeycomb transpar-
ent insulation by coupled radiation and conduction.
On closer examination, increasingly more honeycomb elements have been adopted for designing
building decorations (Fig. 18C). Sometimes these elements work beyond the ornament function, with
the versatile honeycomb-like shelving and Hedler MaxiBrite honeycomb as two examples. Each build-
ing unit of a modular honeycomb-like furniture system was made from expanded polypropylene
ARPRO, which is in nature a type of plastic foam with high mechanical performance. A box, a seat
or a step can be obtained by a single building unit, while putting them together by special clips,
multiple building units can be achieved including the shelving units, partitions with built-in storage,
and storage boxes. The Hedler MaxiBrite honeycomb is used as a metal reﬂector due to increased
contrast and brilliance b suppressing stray light.
4.1.2. Transportation
With the rapid development of transportation industry, honeycombs have been widely used in this
ﬁeld especially for aerospace and mass transport.
Honeycomb paulownia surfboard. One of the attractions of honeycomb paulownia surfboards,
kayaks and boats is the honeycomb pattern cored out to lighten the board, providing a tight platform
for a 1.8 mm 3ply of bamboo to be used as the only deck skin (Fig. 19A). No ﬁber glass but gum
Fig. 18. Representative honeycomb structures in architecture: (A-a) Mexico City-based architect Michel Rojkind’s new project;
(A-b) Metropol Parasol project; (A-c) KAUST Breakwater Beacon designed by Urban Art Projects; (A-d) versatile honeycomb-like
shelving with odd-shaped blocks (; (B-a) ClayFix
Heat Isolation
Mortar (; (B-b) typical greenhouse conﬁguration with honeycomb insulation [449];
(C) building decorations with honeycomb design structures: (C-a) versatile honeycomb-like shelving; (C-b) Disney store
modular honeycomb design; (C-c) Swedish birch and rosewood wine rack; (C-d) Hedler MaxiBrite honeycomb; (C-e) and (C-f)
collectables remixed with real honeycombs.
turpentine and wax is used to seal it, which is the small environmental impact compared to ﬁber glass
products that are associated with pollutants and long decomposition time.
Tires with non-pneumatic honeycomb structure. Pneumatic tires have several disadvantages, includ-
ing: (i) catastrophic damage caused by ﬂat while driving, (ii) requirement for maintenance of air pres-
sure, (iii) complicated manufacturing processes, and (iv) non-uniform contact pressure distribution
[211]. For instance, in Iraq, the explosion of improvised explosive devices (IEDs) can easily blow out
the Humvee tires, leading to directly kill the soldiers. That worries the U.S. Army and makes them
to look for a novel mode that can prevent tire blew out or keep running after suffering a ﬂat tire.
To solve this problem, a company named Resilient Tech recently put forward a new prototype that
replaces the key part of a tire with a non-pneumatic honeycomb structure. Besides, several tire engi-
neers also attempted to develop non-pneumatic tires (NPT) through using polygon typed lattice
spokes to replace the pneumatic tire (Fig. 19B) [212,213]. Kim et al. [214] explored the structural per-
formance of a NPT with 3D lattice spokes by performing numerical simulation of the contact pressure
Fig. 19. (A) Honeycomb paulownia surfboard (lightweight surfboard with honeycomb CNC (computer numerical controlled))
routing wooden (; (B) tire with a non-pneumatic honeycomb structure (http://www.resilient-; (C) illustration of non-pneumatic tire with hexagonal lattice spokes [214]; (D) replacing homogeneous material with
cellular material to reduce hysteretic energy loss; (E) conceptually-designed morphing wing with reentrant hexagonal
honeycomb core; and (F) imported pressure load on airfoil with re-entrant honeycomb core [224].
on the NPT and found that 3D hexagonal cellular spokes have a higher out-of-plane stiffness than 2D
spokes under targeted load and a lower mass. As demonstrated by the model for determine the
in-plane linear elastic behavior for honeycomb, high shear ﬂexure properties could be achieved by
properly-designed reentrant hexangular cells with negative Poisson ratios (Fig. 19D) [215]. One of
the latest contributions of this study is the design of a non-pneumatic wheel using topology optimiza-
tion route, with the goal of matching its static stiffness [216].
Honeycomb sandwich as the most prevalent lightweight structure. Honeycomb sandwiches are the
most prevalent lightweight structure (Fig. 20). The requirement for lightweight structural materials
in transportation industry especially for aerospace and aircraft applications (Table 3) have evoked
great need for the development of honeycomb structures [217–225].
A variety of materials have been used as basic materials to fabricate honeycombs, including paper-
board, ﬁberglass, carbon ﬁber reinforced plastic, nomex reinforced plastic, Kevlar reinforced plastic,
polypropylene and metal (usually aluminum). Metal-based honeycombs are conventionally fabricated
by the expanded honeycomb manufacturing process and the strip slotting process. Hexagonal honey-
combs are typically manufactured from aluminum alloys by an expansion manufacturing process that
results in two of the six cell walls having double thickness. This manufacturing method can only pro-
duce uniform hexagonal hollow structures with small relative density (
60.03). Alternatively, Côté
et al. [99] and Radford et al. [226] introduced a strip slotting process to manufacture high-density
stainless steel square honeycombs with relative density
> 0.03.
Due to the advantages of cost effective, environmental stability, ease of processing and recycling,
polypropylene (PP) becomes a promising candidate material for sandwich constructions. PP honey-
comb has the favorable properties [223] such as lightweight, impact resistance, excellent bonding,
corrosive resistance, recycling ability and thermal insulation, leading to a more promising utilization
Fig. 20. Number of annual publications on ‘honeycomb’ and ‘sandwich’. Source: Science Citation Index Expanded [Sci-
Table 3
Honeycomb sandwich structures used in transportation industry.
Core material Product Ref.
Aluminum F/A-18 Aircraft [217,218]
Nomex H/C Aircraft, vehicle [219,220]
Carbon/epoxy composite Small aircraft [221,222]
Polypropylene (PP) Vehicle [223]
Carbon/epoxy laminate Airfoil [224,225]
in transportation applications compared with honeycombs made from nomex, polypropylene and alu-
minum, balsa wood and cellular foams. Cabrera et al. [227] reported that 100% PP tubular honeycomb
cores sandwiched panels can be fabricated with keeping the mechanical properties of all the PP sheets.
Through optimizing the governing factors including environmental temperature, core material and
copolymer ﬁlm under a peel test, the bonding strength where the core joined with the facesheet
can be optimized. It is demonstrated that the foam-to-facesheet bond is more homogeneous due to
a higher surface contact area [224].
4.1.3. Mechanical engineering
Lightweight large-scale space-based mirror (Fig. 21A and B). Refractive optics has been used for
space-based optics, where the mirrors must follow strict requirements of functionalities and
operations. In addition, they must be lightweight and simultaneously have adequate mechanical
strength to withstand a high launch acceleration. The development of lightweight large-scale mirror
is essential for the precision performance and efﬁciency of an optical system. Compared to the
mechanically cumbersome solid mirrors, honeycomb designs using lightweight frame as the support-
ing structure can reduce the mirror weight by 8% [228]. Honeycomb structures with regular hexago-
nal, square and triangular cells can be fabricated by machine tooling and near net forming processes
[57]. Back to the 1980s, metals (e.g., aluminum and beryllium) and glasses (e.g., ULE, Zerodur) were
the primary choice of materials to fabricate the space-based mirrors. Since the 1990s, with the
development of materials science, the substitute materials such as fused silica, single or multi crystal
silicon and silicon carbide have been developed [229,230], prospering the ﬁeld of manufactory and
Honeycomb seals (Fig. 21C). Seals are widely used in turbine and compressor construction to
enhance aerodynamic efﬁciency by reducing leakage loss in the gap between the rotating and station-
ary parts. Since the 1980s, honeycomb seals with hexahedral cellular structure have been frequently
used as replacement for the conventional labyrinth seals to ensure a minimum gap loss and increased
strength in turbomachinery [231,232]. Among all the geometrical parameters of honeycomb seal, the
sealing clearance and honeycomb cell size are the most important factors in the design process
[40,233–244]. In particular, the Dresser-Clark company for the ﬁrst time uses them as end seals for
high-pressure centrifugal compressors [245]. In contrast to the labyrinth seals, the tip seals with a
honeycomb lands can mitigate the rotor wear while providing a durable interface that enhanced
the engine efﬁciency [232].
Functional honeycomb cores. Over the past few decades, honeycomb cores as functional mechanical
components have been used successfully for electromagnetic shielding [61,246,247]; ﬂow direction-
alization of ﬂuid (typically air and water) ﬂow in a various ducts and channels (typically winder
tunnel) [25]; and heat exchange [248]. Metal [248,249], reinforced plastic, Nomex paper and compos-
ite or hybrid materials [24,250] are the common materials used in making these honeycombs by
expansion, extrusion, extrusion and sintering processes. Aluminum honeycomb is by far the most
versatile and widely used. Aluminum honeycombs with properly designed cell sizes and cell depths
can attenuate the decibel level in a wide range of sound frequency and thus have been used for radio
frequency shielding. In addition, aluminum honeycombs covered by Cr(III) corrosion-resistant coating
materials have also been used to directionalize ﬂow. Recently, based on a hierarchical architecture
[24], carbon nanotube-reinforced polymer foam has been ﬁlled into the cells of aluminum honeycomb
to enhance the electromagnetic absorption. This new material is found to be superior to the existed
material for electromagnetic absorption in the gigahertz range, setting the stage for multifunctional
sandwich panels that has such a mass efﬁciency to combine high electromagnetic absorption with
mechanical stiffness and thermal management.
Intelligent (smart) structures. Honeycomb structures have been used extensively for designing
intelligent (smart) structures. For instance, based on the in-plane deformation of the honeycomb with
reentrant hexangular cells, Muraoka and Sanada [251] introduced a novel term ‘‘honeycomb link mech-
anism’’ and according to this link mechanism, a compact design of an efﬁcient displacement ampliﬁer
distributed in array for piezoelectric actuators was proposed. Zhang et al. [252] demonstrated a new
piezoelectric composite transducer according to the ceramic honeycomb structure, which nearly elim-
inated the piezoelectric d(33) response of the ceramic and exhibited exceptionally high hydrostatic
Fig. 21. Photograph of (A) honeycomb-supported core for the backup primary mirror of Hubble space telescope, (B) SiC space-
based mirror, and (C) honeycomb seal segment ( Honeycomb core: (D) stainless steel shielded
waveguide vent panel, (E) honeycomb ceramic for catalyst support monolith, and (F) Nomex paper honeycomb. (G) Schematic
of honeycomb with a cell shape of reentrant hexagon and in-plane deformation pattern of their single hexangular cell, and (H)
patterned honeycomb plate and its ﬁnite element analysis to show the deformation with only one end ﬁxed.
piezoelectric response. Hassan et al. [253] illustrated a novel concept of honeycomb structure with
hexagonal and auxetic topology. You et al. [254] designed a composite smart antenna structure with
high gain and wide bandwidth, and lightweight feature. Here, the honeycomb-cored sandwich construc-
tion acted as the basic supporting structure due to its high strength and low density.
4.1.4. Chemical engineering
Honeycombs have been used in a range of chemical engineering applications such as particulate
ﬁlter [255], concentrator, catalytic combustor [256,257] and catalytic reactor [258] for chemical pro-
cesses. There exist several excellent reviews on the wide use of ceramic honeycombs as catalyst sup-
port, particulate ﬁlter for vehicular emission control and other chemical industrial applications such as
NOx reduction, efﬂuent concentrator, catalytic combustion and chemical processes [19]. Groppi and
Tronconi [259] focused their review on the utilization of novel monolithic catalysts as a substitution
of conventional catalyst pellets (packed beds). The high thermal conductivity of the novel monolithic
catalysts provides beneﬁts for gas/solid exothermic chemical processes in externally cooled tubular
reactors. Recently, their applications touch upon the areas of environmental chemistry such as waste
water treatment [260], heat regenerators [261] and solid oxide fuel cell [262].
Typically, ceramic honeycombs (Fig. 22A) possess hexagonal, square and triangle parallel channels.
By conventional extrusion processes, the materials exploited to manufacture these ceramic honey-
combs are cordierite [263,264], aluminum titanate [257], mullite [265], corundum, zeolite [266],
and their compound [265,267]. Compared with conventional ceramics, they have the characteristics
of low thermal expansion, high thermal shock resistance, large surface area, and corrosion resistance.
Compared to ceramic honeycombs, metallic honeycombs have important metal properties such as
good thermal conductivity, electrical conductivity, and fracture toughness. In addition, FeCrAl alloys
with excellent oxidation resistance have been used in various applications under temperatures as high
as 1200 °C. FeCrAl honeycombs (Fig. 22B) exhibit huge potential to substitute ceramic supports for
exhaust gas catalyst and fuel cells [268].
4.2. Fabrication and applications in micro and nanofabrication
With the rapid development of nanotechnology, honeycomb cell structures at the nanometer and
micrometer scales have been fabricated using various methods [57]. A review of recent work on
ordered porous materials by Davis [269] suggested that ordered porous materials (normally with
honeycomb structures) possess exceptional properties, which lead to applications ranging from the
traditional catalysts and adsorbents to the emerging ﬁelds. Generally, porous materials with pore sizes
on the order of 50 nm to 1 mm are of great interest for applications in superhydrophobic surfaces [57],
photonics [270,271], optoelectronics [272], and microelectronics [273,274]; while ordered meso-
porous solids with a pore size of 2–50 nm are of more importance for ﬁelds such as catalysis [275],
sensors [276], separation media [277], adsorbents [278], and templates for material synthesis [279].
Molecule-sized porous solids like hexagonal honeycomb lattices with pore sizes smaller than 2 nm
are graphene and carbon-nanotubes [280,281], crystalline materials [282], etc. Here we focus our
review on typical honeycombs varied by pore size and material type, as well as their emerging
(A) (B)
Fig. 22. Topologies of extruded and sintered (A) ceramic honeycombs and (B) FeCrAl honeycombs [249].
4.2.1. Typical micro- and nano-honeycombs Oxide ﬁlms with micro-/nano-scale pore sizes. Anodic aluminum oxide (AAO) ﬁlms are the ﬁrst
man-made nanohoneycomb fabricated through a 2-step anodization process (Fig. 23A). The focus of
nanoporous AAO has been placed on surface and structural engineering as well as emerging applica-
tions as reviewed by Jani et al. [283]. To tailor the surface morphology, Barela et al. [284] developed a
complex structure with high aspect ratio by a single-step wet etching of AAO substrate. Because of the
ease and low cost in fabrication, AAO ﬁlms (Fig. 23B-a) have found broader applications in the emerg-
ing ﬁelds compared to conventional honeycomb structures, such as solar cells [285], magnetic storage
devices [286], catalysts [287], carbon nanotubes [288], capacitive humidity sensors [289] and metal
nanowires [290,291]. In addition, multifunctional oxide ﬁlms such as TiO
oxide (Fig. 23B-b) and silica
oxide (Fig. 23B-c) have been explored to realize certain functionalities. For instance, TiO
nano-honeycombs fabricated by a photoetching reaction along the c axes of rutile TiO
present regu-
larly ordered quadrangle cells with a few hundred nanometers in width and several micrometers in
depth depending on the crystallographic orientation. The topological characteristics of TiO
nano-honeycombs including the large area-to-volume ratio and high crystallites enable the utilization
in photoelectronic devices such as photocatalysts and dye sensitized solar cells [51]. Micro-sized honeycomb-patterned polymer ﬁlm. In recent years, micro-sized honeycomb ﬁlms
have shown great potential in electronics [292], catalysts [293], photonics [294], superhydrophobic
surfaces [295], and optical sensing [296]. Ever since star-shaped polystyrenes (PS) and
poly(para-phenylene)-b-PS block copolymers were synthesized in the year of 1994 [297], the
breath-ﬁgure approach [57] has been widely utilized for the manufacture of polymer ﬁlms with hon-
eycomb structures. This method is simple, inexpensive and robust in the fabrication of highly ordered
honeycomb ﬁlms compared to other methods such as lithography [298], soft lithography [299],
self-assembly [300,301] and transcription [302,303]. Detailed review about the breath-ﬁgure
Fig. 23. (A) Schematic of the fabrication process of nanohole array-type metals: (a) honeycomb-like alumina as the parent
mode, (b) deposition of metals under vacuum evaporation, (c) injection and polymerization of methylmethacrylate, (d)
poly(methyl methacrylate) negative type, (e) electroless metal deposition, and (f) honeycomb-like nano array [27]. (B-a)
Morphological images in top and cross-sectional view of the as-prepared AAO ﬁlm after 10 h processing of second step
anodization in 0.3 M oxalic acid [126]. (B-b) SEM image of TiO
surface after photoelectrochemical etching under strong (+1.0 V)
anodic polarization [51]. (B-c) SEM image of cross-section and channel morphology structure of a typical silica microhoney-
comb [48].
formation of self-assembled polymeric- and nanoparticle-based micro- and nanostructures was given
by Bunz [304]. Escalé et al. [305] also reviewed recent developments in the preparation of elaborate
functional honeycomb polymer ﬁlms by the processing approach of breath-ﬁgure (Fig. 24), and the
advances in the design concepts and technologies of functional polymeric surfaces having either
stimuli-responsive or super-hydrophobic properties. Mesoporous honeycombs. Mesoporous honeycombs (e.g., mesoporous honeycomb membrane
and mesoporous silica nanoparticle) are classiﬁed based on cell shape: columnar cells (low porosity)
and hexagonal cells (high porosity). Ordered mesoporous silica ﬁlms are typical columnar honey-
combs, attracting great attention for their superior low-dielectric property. A great number of studies
have focused on enhancing their mechanical properties to fulﬁll the need for broad applications [57].
For example, Jung et al. [306] found that the mechanical properties of such ﬁlms are affected by pore
ordering and ﬁlm density. For a ﬁlm with random pore geometry, the elastic modulus is positively cor-
related to ﬁlm density. While for a modiﬁed mesoporous silica ﬁlm with periodic pore distribution, a
negative correlation is observed within a certain density range, which can be advantageous to low-k
materials. The interests in ordered mesoporous materials with hexagonal honeycomb structures
arouse due to their uniform pores, large surface-area-to-volume ratio, particularly attractive as cata-
lysts for the synthesis of crystalline linear polyethylene nanoﬁbers [54] and hydrodesulfurization of
petroleum resides [307]. Representative mesoporous materials include siliceous hexagonal SBA-15
and MCM-41, cubic MCM-48 and KIT-6 (with lamellar (MCM-50) well-deﬁned structure) (Table 4).
The mesoporous silica SBA-15 template from a tri-block copolymer in strong acidic media has been
intensively studied in view of its good hydrothermal stability and well-deﬁned geometry.
Particularly, the pore width of SBA-15 can be adjusted from 5 to 30 nm according to the synthesis
route, given the accommodation of the bulky reactants and products within a reaction. Molecule-sized honeycombs. Honeycomb patterns at molecule levels maximize net intermolec-
ular separation while preserving the molecular rows, thus holding great potential in catalytic,
electronic, mechanical and biological applications. The mechanism for molecule assembly into
Fig. 24. Schematic illustration and SEM image of (A) the breath ﬁgure method and the honeycomb ﬁlm, (B) the peeling
processing, and (C) the pincushion structure [305].
honeycomb patterns is attributed to the molecular structure and intermolecular bonding characteris-
tics (Fig. 25A) [36]. Trimesic acid is one of the typical assembling molecules that has been extensively
studied to form ordered 2D honeycomb networks. Ye et al. [308] summarized 1.1-nm pore diameter
hexagonal and other derivative porous networks (Fig. 25B) generated by assembling trimesic acid, and
gave a uniﬁed unit cell model describing the whole family of its assembling structures. Crystalline
structures with the introduction of metal–organic framework contained honeycomb pores of
1.0–2.0 nm in diameter (Fig. 25C) (Table 5) and surface areas up to 3000 m
[282,309]. Such mate-
rials with exceptionally high surface areas are of critical importance, addressing one of the biggest
challenges involving porous media and holding great potential for various applications related to
catalysis in chemical engineering, separation technologies and the development and utilization of
gas storage [57]. Low-dimensional porous materials with honeycomb structures. Typical low-dimensional
honeycomb-structured materials include photonic crystal ﬁbers [57], self-assembled honeycomb
polyurethane nanoﬁbers [310], nanohoneycomb-structured glass ﬁbers [137,310], hexagonal
nanotubes and nanorods, and grapheme and its allotropes [311]. For example, the photonic band
gap structures of photonic crystal ﬁbers improve the optical properties of conventional materials
through the method of wavelength-scale morphological microstructuring. Knight et al. [312] fabri-
cated a photonic crystal ﬁber with extra air holes in an otherwise regular honeycomb pattern of holes
(Fig. 26A-a), and demonstrated that its guided modes with extraordinary properties are supported by
the waveguide. Coffey [313] also demonstrated new types of microstructured optical ﬁbers such as
multicore, multimode and hollow core endowed by high porosity honeycomb-spatial properties,
targeting next-generation systems with better ﬁber capacity (Fig. 26A-b). Kievsky and Sokolov
[314] found that microscale silica ﬁbers fabricated using self-assembly technique have a
nanohoneycomb-structured glass ﬁber, with a hexagonal cross-section of 2
m and a length of
m(Fig. 26C). These new ﬁbers can be used as self-healing composite [137,310], chromatography,
drug delivery, manufacturing nanowires, and nanoreactors for ‘‘1D’’ chemistry. In addition, there is
densely-packed graphene in a honeycomb crystal lattice; and the graphene serves as the basic
structural element of graphite, charcoal, carbon nanotubes and fullerenes [311,315]. Through various
techniques such as wrapping, rolling and stacking, the graphene can be fabricated into 0D buckyballs,
1D nanotubes and 3D graphite (Fig. 26D) [311], respectively.
4.2.2. Emerging applications Super-hydrophobic surfaces. Super-hydrophobic surfaces endowed by unique porous micro- or
nano-structures possess high contact angles and extremely low ﬂow resistance, which is promising for
a broad range of engineering applications such as self-cleaning [5], deicing [316,317], corrosion
resistance [318], and resistance on current conduction [319]. Cassie and Baxter [320] proposed that
hydrophobic or even super-hydrophobic surface can be achieved by constructing topographic
structures, where honeycomb and its derived structures have received much attention. Li et al.
[321] proposed the possibility of fabricating honeycomb-like aligned carbon nanotube (ACNT) ﬁlms
with a hierarchical structure (Fig. 27A and B) through capillary effects. Mishchenko et al. [316]
Table 4
Mesoporous honeycomb structures.
Mesoporous solid Space group Pore diameter (nm) Structure Ref.
MCM-41 P6mm 2–5 Hexagonal 1D channel [277]
MCM-48 Ia3d 2–5 Bicontinuous 3D
SBA-15 P6mm 5–10 Hexagonal 1D channel
SBA-16 Im3m Min 1–6; max 4–9 Body center arrangement of cages
SBA-1 Pm3n 2–4
SBA-3 P6mm 2–4 Cubic 3D
MSU P6mm 2–5 2D hexagonal
HMS P6mm 2–5 2D hexagonal
fabricated a silicon membrane with honeycomb-shaped pores (Fig. 27C and D) by reactive ion etching,
overcoated with a nanonail architecture of a 7.4-
m-thick organic self-assembled monolayer or
ﬂuoropolymer. These super-hydrophobic surfaces can avoid ice accumulation on aircrafts or other
structures, which may cause danger and require extra deicing procedures that are expensive and
environmentally unfriendly.
Fig. 25. Some typical molecule-sized honeycomb structures. (A-a) (Left) STM image of the anthraquinone molecules assembled
in a honeycomb network on a Cu(11 1) surface. (Right) Model of the ðﬃﬃﬃﬃﬃﬃﬃﬃ
unit cell. (A-b) A row (left) and a vertex
(right) assembly of anthraquinone molecules [36]. (B1) STM images of coverage-induced evolution of the H
(n= 1–8 and
1) self-assembling structures. (B2) Corresponding unit cell models for experimentally observed assembling structures in (B1)
[308]. (C-a) Local environment of Co
; (C-b) azide-bridged (EE and EO) honeycomb layer; and (C-c) Bpg-bridged 3D structure
Table 5
Representative crystalline materials with honeycomb structures.
Material Main framework composition Structure Pore size
Co(N3)2(bpg).Sn meso-R,â-bi(4-pyridyl) glycol (bpg)
Square, honeycomb, and
1.36 [282]
MOF-177 Six-membered rings 1.08 [309]
Q. Zhang et al. / Progress in Materials Science 74 (2015) 332–400 365 Energy conversion. To develop micro honeycomb structures with excellent mechanical
properties and high speciﬁc surface area has become the focus of 3D design of lithium-ion batteries
and efﬁcient solar harvesting devices [322,323], including cathode [46], electrolyte [324], and anode
Fig. 26. (A-a) Cross-section of photonic crystal ﬁber with close-packed hexagonal pattern [312]; (A-b) SEM image of Hollow-
core photonic bandgap ﬁber [313]; (B-a) SEM image of array of ﬂower-patterned hexagonal disk of b-NaYF4. (B-b) SEM images
of the top- and side-view of the disk. (B-c) and (B-d) SEM image of array of b-NaYF4 hexagonal nanotube and nanorods,
respectively [317]. (C) Self-assembly synthesized glass ﬁbers: (a) large-area SEM image (bar size 22
m); (b) zoomed image (bar
size 5
m); (c) schematic show of nano conﬁguration within the ﬁber; and (d) TEM image showing a 3 nm periodicity
distribution near the ﬁber edge. (D-a) Graphene as mother of all graphitic forms such as buckyballs, nanotubes and graphite
[311]; and (D-b) High resolution TEM image of graphene [315].
[325]. To improve the storage capacity of Si negative electrode materials and cycling life of Li-ion
micro-batteries, Si honeycombs on micro- and nanometer scales are fabricated by photolithography
and etching (Fig. 4), which can undergo striking mechanical deformations, achieve higher cycling life
and reduce wall cracking by tailoring the thickness and length of cell walls [46]. Kotobuki et al. [324]
employed the sol–gel method to fabricate a 3D battery using ceramic electrolyte with two types of LLT
) honeycomb structure (Fig. 28). This structure reduces internal cell resistance and
improves the discharge capacity to 7.3
operated at 1.1 V. Li et al. [325] prepared
honeycomb graphitic-carbon ﬁlms containing an array of 75 nm diameter pores, and found that these
honeycomb carbon ﬁlms dramatically improve rate capabilities relative to thin carbon ﬁlms used as
-insertion anodes. In addition, a porous material with hierarchical pore sizes at micro-, meso-
and macrometer scales has been proposed to be ideal for overall performance enhancement [48].
For this, ‘‘ice templating’’ method was employed to synthesize nanoporous materials with
micro-honeycombs (Fig. 28B), where the ice crystals grow within the precursor and act as a template
during the freezing of their parent hydrosols or hydrogels unidirectionally.
Recently, Yin et al. [322] reported is a fundamentally new strategy for the design of
next-generation high-power energy storage devices. Based on the principle of ‘‘breath ﬁgure’’ method
[297,326], they successfully developed a scalable self-assembly strategy to create bioinspired
hierarchical structures (microscale honeycomb structure, see Fig. 29D) composed of functionalized
graphene sheets, optimizing ion transport and increasing the reversible capacity up to 1600 mA h/g
(the highest level ever reported for the pure carbon materials, see Fig. 29F and G). Besides, Yin
et al. [323] applied a novel approach to create free-standing hierarchical porous graphene structures,
which show a large area of uniform honeycomb structure and favor holding functional nanoparticles
Fig. 27. (A) SEM image of large-area near-honeycomb pattern aligned carbon nanotubes, consisting of hexagonal honeycomb.
(B) Higher magniﬁcation SEM image of typical honeycomb-like pattern. Ice accumulation on (C) ﬂat aluminum and (D)
honeycomb microstructured ﬂuorinated Si surface.
to form multi-functional composites. Via utilizing such kind of multi-functional composites (combina-
tion of the graphene-based free-standing ﬁlms with TiO
nanoparticles), they successfully solved one
of the bottlenecks to increase the conversion efﬁciency in photovoltaic devices, leading to increasing
the efﬁciency of light conversion in solar energy conversion applications. Photonics. Typical photonic band-gap materials had 2D photonic lattice structures, usually rep-
resented by honeycomb nano-structures [270], honeycomb photonic bandgap ﬁbers [30], and artiﬁcial
compound-eye-like structures with honeycomb-shaped microlenses [328]. The search for photonic
band-gap materials evoked considerable efforts in the past several years. For example, Meade et al.
[329] showed through theoretical modeling that a honeycomb nano-structure of air cylinders in
dielectric provided a photonic band gap for all directions normal to the cylinders. Gourley et al.
[270] experimentally demonstrated that through the fabricating method of electron beam lithography
using Al and Ga, honeycomb nano-structures are capable of possessing stable structures and nonradia-
tive surface recombination; besides, they found that the resonant coupling of light into/out of the
lattice occured at selected wavelengths satisfying the Bragg condition. Inspired by insect eyes, Liu
et al. [328] explored a simple method to fabricate honeycomb-shaped microlenses on curvilinear
surfaces by the femto-second laser microfabrication and the thermomechanical bending process
(Fig. 30). Over 7600 hexagonal-shaped microlenses with a diameter of 50
m were fabricated on a
hemispherical poly(methyl methacrylate) shell. The wide ﬁeld-of-view imaging using the microlens
array reached up to 162°.
Fig. 28. (A) The honeycomb structure of LLT membrane: (a) half honeycomb with 400 holes on one side and (b) full honeycomb
with 200 holes on each side; the hole size was 180
m. Cross-sectional (c) SEM and (d) EDS images of
cell [324]. (B) SEM image of single crystal TiO
electrode prepared by reduction at: (a) 650 °C for 4 h, (b)
700 °C for 4 h, and (c) 1000 °C for 1 h [327].
368 Q. Zhang et al. / Progress in Materials Science 74 (2015) 332–400 Microelectronics. Honeycombs are widely found in microelectronic devices typically made
from semiconductor materials, such as transistors [330], capacitors [331], inductors [332], resistors,
diodes, insulators, and conductors. Zhang et al. [333] successfully synthesized a 2D NiO
nano-honeycomb by thermal annealing of Ni thin ﬁlm deposited onto a silicon substrate for micro-
electronics and micro-systems. This opened the door for the integration of nano-honeycombs and
micro-systems, leading to nano-scale functional devices. Sazio et al. [334] utilized a hybrid technology
to fabricate a large-air-fraction ﬁber with honeycomb-structure holes to a germanium-ﬁlled honey-
comb MOF (microstructured optical ﬁber) by chemical vapor deposition (Fig. 31). Micro/nano sensors. A micro- or nano-sensor is an extremely small element that is capable of
picking up and relaying environmental information of biological, thermal, chemical [335], and other
forms of signals [336], which are subsequently sent to a processor. Nanotechnology enables designing
sensors that are much smaller, have less power consumption, and are more sensitive than the current
macrosensors. Nano sensors work by sensing the interaction of molecules, processing and transmit-
ting the data with electrons, and storing the information in nanoscale structures. A variety of
honeycomb-structured materials have been explored as substrates for sensor applications. For exam-
ple, Chen et al. [337] designed a Phenylboronic acid segregated honeycomb-patterned porous ﬁlm for
glucose sensing. Kumeria et al. [338] employed nanoporous anodic aluminum oxide to design inter-
ferometric micro-sensor to detect volatile sulfur compounds and hydrogen sulﬁde gas. Walt and
co-workers [339,340] proposed the design of optical multisensor arrays based on optical ﬁbers, where
(B) (E)
(F) (G)
Fig. 29. Conﬁguration and electrochemical properties of the honeycomb structures: (A and B) photograph of the honeycomb
ﬁlm/honeycomb-patterned on the glass/copper foil; (C and D) SEM images of honeycomb-patterned ﬁlm prepared from 1 mg/
mL of the GO/DODA complex on the silicon wafer; (E) cross-sectional SEM image of the honeycomb-patterned ﬁlm on the
copper foil; (F and G) capacity versus cycle number for the honeycomb ﬁlm and non-patterned ﬁlm at a current density of
50 mA/g showing charge (square, black) and discharge (circle, red) (the insets are the corresponding SEM images) [322].
bundles of optical ﬁbers with terminal parts covered with ﬂuorescent polymeric dyes (Fig. 32) were
employed to collect signals from the multi-sensor. Upon the interaction with many types of gases,
the polymers changed their structure, causing wavelength shifts of emitted light. Graphene, composed
of a single layer of carbon atoms packed into a 2D honeycomb lattice, has been recently found to be
promising as a low electrical noise material [341], prospering the ﬁeld of ultra-sensitive and ultra-fast
electronic sensors. With a single atom thick, graphene indirectly contacts with the substrate, making
the interface state govern the sensing. Nano-sensors designed based on this principle have shown
promise in detecting external deposited agents with ultra high resolution [57]. Environmental engineering. Free-standing, three-dimensional (3D) ordered porous graphene
structure e.g., honeycomb-patterned layer makes an essential step in utilizing the advantages of
graphene nanosheets for macroscopic applications, especially the environmentally engineering appli-
cations such as antibacterial applications and water treatment [342,343]. Yin et al. [323] introduce a
low-cost facile, simple, environmentally-friendly strategy to create free-standing hierarchical porous
Fig. 30. (A) 3D proﬁle of microlenses on top of hemispherical shell, obtained using a laser confocal microscope. (B) Cross-
sectional proﬁle of a microlens shown in (a). (C) Schematic of fabrication process. (D) SEM observation of the morphology of the
molding template; the scale bar was 50
m. (E) Imaging performance of microlens array, obtained via a 5objective lens [328].
graphene with uniform honeycomb structures via an ‘‘on water spreading’’ method [344]. They exper-
imentally proved such free-standing hierarchical honeycomb ﬁlm to be antibacterial without any
additional antibacterial agent (see Fig. 33). The fabricated honeycomb ﬁlm does not contaminate
the surrounding environment and is capable of avoiding the possible leaks. The advantage of ﬂexibil-
ity, mechanical stiffness and especially antibacterial property of free-standing hierarchical honeycomb
ﬁlm makes it essential potential for environmentally-friendly water treatment.
4.3. Fabrication and applications in biomedicine
Honeycomb structures are also commonly found in biological ﬁelds (Table 6). Taking DNA
structures as an example, there are two types of unpredictable DNA–lipid complex: the
spaghetti-like bilayer-coated DNA complex and the densely packed honeycomb complex. May and
Ben-Shaul [345] demonstrated that the spaghetti-like bilayer-coated DNA complex is only marginally
stable while the densely packed honeycomb complex is stable over a wide range of composition struc-
tures. For cell/tissue morphogenesis, microscope studies have shown that the orderly packing retinal
pigment epithelium cells form a layer in the back of the eye behind the retina, representing
Fig. 31. (A) Unﬁlled honeycomb MOF template (scale bar, 5
m); (inset) schematic show of inward surface growing at a
uniform rate normal to the local side (green arrows). (B) Honeycomb template after germanium deposition (scale bar, 5
Fig. 32. Schematic of fabricating the matrix of gas-sensitive ﬂuorescent polymer microspheres at the end of an optical
waveguide. Inset: micrograph of ‘‘honeycomb’’ structure of the butt-end surface of the waveguide before and after application
of polymeric microspheres [339,340].
characteristic honeycomb-like structure [34]. Recently, the emerging applications of honeycombs in
biomedicine have encouraged further research activities although most were preliminary applications
in biomedicine [34,35,345–348]. In this section, we review these applications, with focus on tissue
engineering and regenerative medicine, biosensors and bioelectronics, bioadsorption and biocatalysis,
and drug release.
Fig. 33. Antibacterial properties of the free-standing honeycomb ﬁlm: (A and B) Laser scanning confocal microscopy images of
green ﬂuorescent protein labeled Pseudomonas aeruginosa PAO1 bioﬁlm on (A) graphene honeycomb ﬁlm and (B) graphite
surface after 48 h incubation; the green, red and blue spot represent live, dead and EPS kit, respectively; SEM images of green
ﬂuorescent protein labeled Pseudomonas aeruginosa PAO1 bioﬁlm on (C) graphene honeycomb ﬁlm and (D) graphite surface
after 48 h incubation [323].
Table 6
Typical applications of honeycombs in biomedicine.
Methods Material Cells Applications Ref.
Film scaffold Surfactant-free water
PLGA Osteoblast-like MG63 Cell culture
Surface – Nanoculture
MPCs 3D cell culture [375]
Directed self-assembly NHF, KGN NHF, KGN Tissue
3D scaffold Direct-write assembly pHEMA Primary rat hippocampal
Cell culture [374]
Ionotropic gelation Alginate ECs, HSMCs Co-culture
pHEMA = poly(2-hydroxyethyl methacrylate).
PLGA = poly(lactide-co-glycolide).
MPCs = human bone marrow-derived mesenchymal stem/progenitor cells.
NHF = normal human ﬁbroblasts.
KGN = human granulosa cells.
ECs = endothelial cells.
HSMCs = human smooth muscle cells.
4.3.1. 2D honeycomb-patterned substrates
Mesoscopically honeycomb-patterned porous 2D substrates (e.g., honeycomb ﬁlms), with submi-
cron to micron pore sizes, are of particular interest for biomedical application as biointerface [349],
cell culture substrates [350–353], separation membranes for blood cells [354], immobilization of
biomolecules [355], dialyzer [356,357] and oxygenator membranes [349]. To design honeycomb
substrates for biomedical applications, great efforts have been devoted to developing grafting and
cross-linking honeycomb ﬁlms [351]. For example, Connal and Qiao [53] reported preparation of
hierarchically porous poly(dimethylsiloxane)-based honeycombs by forming honeycomb-structured
porous polymer ﬁlms on non-ﬂat honeycomb grid surfaces (Fig. 34A). Zhang et al. [358] developed
a highly efﬁcient breath ﬁgure approach that enables the fabrication of highly ordered honeycomb
ﬁlms prepared over large non-planar honeycomb grid surfaces, which may facilitate commercial
utilization of the micro-fabrication technique for a variety of surfaces. Further, it has been found that
the more important factor for affecting the occurrence of cracking during the formation of honeycomb
ﬁlm is not the glass transition temperature but the Young’s modulus of a polymer (Fig. 34B).
Honeycomb-patterned substrates have been employed in an early stage for cell culture [352,353].
To explore the effect of honeycomb pattern on cell behavior, hepatocytes were cultured on polymer
subtracts with various honeycomb patterns fabricated by self-organization technique [57]. The hepa-
tocytes are ﬂattened with cultured on a ﬂat ﬁlm, where actin ﬁlaments spreading around the regions
(Fig. 35A and B); while hepatocytes form spheroids when cultured on a honeycomb ﬁlm with actin
ﬁlaments located inside the edge of the spheroid pattern (Fig. 35C and D). However, endothelial cells
cultured on the honeycomb ﬁlms exhibit greater spreading and ﬂattening capabilities (Fig. 35E and F)
[359]. Besides honeycomb patterns, the texture of the substrate also plays an important role in cell
behavior. For instance, Fukuhira et al. [360] demonstrated that NIH3T3 ﬁbroblasts cultured on
honeycomb patterned poly(
-lactide) ﬁlm fabricated with dioleoylphosphatidylethanolamine show
better cell proliferation compared those that on ﬁlm fabricated with copolymer of dodecylacrylamide
and o-carboxyhexylacrylamide. Sunami et al. [57] reported that the honeycomb ﬁlm with
site-selectively adsorbed ﬁbronectin plays a key role in cell adhesion and proliferation. These ﬁndings
reveal that honeycomb-patterned ﬁlms are suitable to act as 2D substrate for cell culture or 2D
scaffold with enhanced cell adhesion and proliferation.
4.3.2. 3D honeycomb scaffolds
Today, tissue engineers are attempting to engineer virtually every human tissue, including carti-
lage, bone, heart valves, nerves, muscle, bladder, liver, etc. Besides, due to the complex cell microen-
vironments with different physical and biochemical properties, there is no surprise that cell behaviors
in 3D culture are unexpectedly different as compared to those in 2D culture [361–363]. In particular,
to understand the effect of organized 3D cell microenvironments on neuronal cell development, engi-
neering of 3D cell microenvironments is needed to imitate neuronal cells and mimic their surrounding
native microenvironment. New tissue engineering strategies mainly aim on designing 3D porous
biomaterial scaffolds to provide a 3D structure to enhance nutrient delivery, as well as mechanical
support for cell behaviors (e.g., attachment, proliferation and differentiation), and their architecture
deﬁnes the ultimate shape of the newly grown soft or hard tissue [364,365]. Among various 3D porous
biomaterial scaffolds, 3D honeycomb scaffolds have attracted great attention due to their high poros-
ity and good mechanical performance, which render them great potential as 3D porous scaffolds for
tissue engineering and regenerative medicine.
Early scaffolds were not fabricated with precise porous architecture. Hutmacher [55,366] gave the
ﬁrst report on various honeycomb scaffold architectures manufactured by a promising rapid prototyp-
ing (RP) technology – fused deposition modeling (FDM) for tissue engineering applications (Fig. 36A).
The research results show that these highly reproducible and economical honeycomb scaffolds have
good mechanical properties [367,368], as well as excellent biocompatibility with human ﬁbroblast
and periosteal cell culture systems [367]. FDM has attracted wide attention [369], and made an
enormous inﬂuence on the extending development of such honeycomb rapid prototyping technique
series as extrusion-based RP techniques, three dimensional printing, selective laser sintering, stere-
olithography, microstereolithograph, electron beam melting, and selective laser melting [370,371].
Recently, Fratzl group made an important impact, and the theoretical and experimental study of
Fig. 34. (A) SEM image of the honeycomb morphology for: (a) honeycomb grid with hexagonal cells in the scale of 600 mesh;
(b) honeycomb with hexagonal cells formed on surface in the scale of 600 mesh; (c) image of replica-molding honeycomb (b) is
the parent mode); (f) 1000 mesh square honeycomb grid; (g) surface-embossed honeycomb with 1000 mesh square; (h) image
of replica-molding honeycomb (g) is the parent mode; (i) 2000 mesh square honeycomb grid; (j) surface-embossed honeycomb
with 2000 mesh square; (k) image of replica-molding honeycomb (j) is the parent mode [53]. (B) SEM image of polymer ﬁlm
with honeycomb morphology prepared from star polymer on (a–d) planar and (e–h and e
) non-planar honeycomb grid
substrates. Scale bars: (a–d) 10
m, (e–h) 100
m, (e
cross- and square-shaped honeycomb hydroxyapatite scaffolds supports that the pore shape of scaf-
folds also contributes signiﬁcantly to control the kinetics of tissue deposition [372,373]. These results
suggest that the optimization of pore shapes may improve the speed of ingrowth of bone tissue into
porous scaffolds (Fig. 36B).
High performance honeycomb scaffolds provide important material basis on tissue engineers and
regenerative medicine. In addition to Hutmacher and Fratzl groups’ outstanding contribution to
honeycomb application on biomedical engineering, other related applications are introduced as
follows. Shepherd et al. [374] fabricated 3D micro-periodic square honeycomb scaffolds by
direct-writing assembly of photopolymerizable poly(2-hydroxyethyl methacrylate) hydrogel ink.
The hydrogel honeycomb scaffolds is a preferred culture system with kind of robust and biocompat-
ibility for primary hippocampal neurons, facilitating 3D in vitro studies of hippocampal neurons and
other sensitive cell types. For cancer study, 3D cell culture improved the prospect of treating cancer
with gene therapy [361]. Miyagawa et al. [375] used a micro-fabricated honeycomb scaffold with
diameter of approximately 2–3
m to induce spheroid formation of human bone marrow-derived
mesenchymal progenitor cells and promote efﬁcient adipogenic differentiation. For myocardial repair
(A) (B)
(E) (F)
Fig. 35. SEM image of hepatocytes and CLSM image of actin localization in adhered hepatocytes at 72 h after culture on (A and
B) ﬂat ﬁlm and (C and D) honeycomb ﬁlm where approximate 100
m spheroids was spread. There were not deformation and
detachment of spheroids from honeycomb ﬁlm could be observed [346]. (E) SEM and (F) CLSM image of vascular endothelial cell
on honeycomb ﬁlm [359].
by tissue-engineered grafts, present scaffolds such as non-woven poly(glycolic acid) (PGA) mesh and
collagen foam are structurally incompatible with the anisotropy features of recapitulating cardiac.
Novel microfabrication techniques have thus been developed to create porous, elastomeric 3D
scaffolds with accordion-like honeycomb microstructure [376]. Due to its controllable stiffness and
anisotropy, accordion-like honeycomb is able to sustain the structural–mechanical limitations of
prevalent scaffolds, beneﬁcial for the grafts with aligned heart cells and mechanical properties that
more closely resemble native myocardium (Fig. 37). Subsequently, through the approach of laser
ablation and oxygen plasma-mediated