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Annu. Rev. Mater. Sci. 1998. 28:271–98
Copyright c
°1998 by Annual Reviews. All rights reserved
THE MATERIAL BONE:
Structure-Mechanical Function
Relations
S. Weiner and H. D. Wagner∗
Departments of Structural Biology and Materials and Interfaces, ∗Weizmann Institute
of Science, 76100 Rehovot, Israel; e-mail: ciweiner@weizmann.weizmann.ac.il;
cpwagner@wis.weizmann.ac.il
KEY WORDS: biomineralization, biomechanics, lamellar bone, mineralized collagen, bone
mineral
ABSTRACT
The term bone refers to a family of materials, all of which are built up of miner-
alized collagen fibrils. They have highly complex structures, described in terms
of up to 7 hierarchical levels of organization. These materials have evolved to
fulfill a variety of mechanical functions, for which the structures are presumably
fine-tuned. Matching structure to function is a challenge. Here we review the
structure-mechanical relations at each of the hierarchical levels of organization,
highlighting wherever possible both underlying strategies and gaps in our knowl-
edge. The insights gained from the study of these fascinating materials are not
only important biologically, but may well provide novel ideas that can be applied
to the design of synthetic materials.
INTRODUCTION
Bone refers to a family of materials each with a somewhat different structural
motif, but all having in common the basic building block, the mineralized
collagen fibril. This family of materials also contains other members, which
for historical reasons, have different names. The better known examples are
dentin, the material that constitutes the inner layers of teeth; cementum, the
thin layer that binds the roots of teeth to the jaw; and mineralized tendons.
Here we review the structure-mechanical function relations of these materials,
highlighting wherever possible the basic underlying themes. We emphasize
the mechanical functions, although some of these materials also fulfill other
271
0084-6600/98/0801-0271$08.00
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272 WEINER & WAGNER
functions. Many bones, for example, are also the major reservoirs of calcium
and phosphate necessary for a wide variety of metabolic functions.
The diversity of structures within this family reflects the fine-tuning or adap-
tation of the structure to its function. This diversity thus provides us with an
invaluable research handle that when used in a comparative way can provide
key insights into the relations between structure and function. This approach,
powerful as it may be, needs to be used with caution. Biological structures are
not necessarily perfectly adapted to function, although the millions of years de-
votedtothefine-tuning of this relation has produced some remarkable solutions
to tough structural-mechanical problems. An exciting prospect for the study
of such biological materials is to identify these “novel” solutions and possibly
apply some to solve problems in synthetic materials. It is also important not to
assume that each member of the family fulfills one or only several functions.
This may well be the case, but the contrary may also occur—the overall design
strategy is to achieve an all-purpose material (the concretes of the biological
world) that will function adequately, if not optimally, under many conditions.
Finally, these biological materials are no different from many synthetic mate-
rials that are required, for example, to function well under compression, but
also on occasion need to withstand serious challenges from impacting and/or
bending stresses. Thus the term function in our title is fraught with difficulty;
unfortunately, so is the term structure.
The basic building block of the bone family of materials is the mineralized
collagenfibril. Itiscomposedofthefibrousproteincollagen in a structural form
that is also present in skin, tendon, and a variety of other soft tissues. The colla-
gen constitutes the main component of a three-dimensional matrix into which,
and in some cases onto which, the mineral forms. The mineral in this family
of materials is dahllite, also known as carbonated apatite (Ca5(PO4,CO
3
)
3
(OH)) (1). The third major component is water. The major components are
intimately associated into an ordered structure, the mineralized collagen fibril.
Their proportions, however, can vary considerably between family members.
The manner in which the building blocks are organized into higher order struc-
tures can also vary, and in fact, this is the basis for differentiating between
the members of the bone family of biological materials. To further complicate
matters, some of these materials are composed of two different organizational
motifs that are juxtaposed, and in turn the whole structure may be folded into
even larger suprastructures (reviewed in 2, 3). Thus there is no meaning to the
term the structure of bone, but rather the structures of these materials have to be
understood both in terms of the differences between family members, and most
importantlyaccordingtohierarchicallevelsof organization. Figure 1 illustrates
the 7 levels of hierarchical organization of the family of mineralized collagen
based materials as we envisage it.
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Figure 1 The 7 hierarchical levels of organization of the bone family of materials. Level 1:
Isolated crystals from human bone (left side) and part of an unmineralized and unstained collagen
fibrilfrom turkey tendonobservedin vitreous icein theTEM (right side). Level2: TEMmicrograph
of a mineralized collagen fibril from turkey tendon. Level 3: TEM micrograph of a thin section
of mineralized turkey tendon. Level 4: Four fibril array patterns of organization found in the bone
family of materials. Level 5: SEM micrograph of a single osteon from human bone. Level 6: Light
micrograph of a fractured section through a fossilized (about 5500 years old) human femur. Level
7: Whole bovine bone (scale: 10 cm).
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274 WEINER & WAGNER
Many measurements of the bulk elastic, plastic, and ultimate properties of
certain members of the bone family of materials have been made. Figure 2 is
a plot of the moduli and strengths of several bone types measured parallel and
perpendicular to the bone long axes. The range of these values reflects many
different variables: the diversity in structures, the orientation of the specimens,
the variations in mineralization extent and porosity, the precise locations of
the specimens, and not insignificantly, the variations in the procedures used for
makingthemeasurements. Itisclearlyimportanttosortoutthe contributions of
all these variables to the bulk mechanical properties—the focus of this review.
Understanding structure-function relations in these materials is therefore a
challenge. We are easily able to measure bulk mechanical properties of some
family members and in some special cases obtain information on certain of
the intermediate hierarchical levels, but how can these be related to the struc-
tures themselves? An in-depth understanding of this subject ideally requires
sorting out the bulk mechanical behavior in terms of the contributions of the
sub-structures at each hierarchical level. Unfortunately, even if we were able to
comprehensively describe these materials in this way, this still would not con-
stitute an adequate analysis, as many of these materials actually change with
time. This in turn affects the mechanical properties. Some of these changes
are in part thermodynamically driven, such as the increase in the sizes of the
crystals, and some are also biologically mediated, such as the determination
of the average proportions of collagen, mineral, and water in a given material.
Furthermore, specialized bone cells actively remove older bone and replace it
with younger bone, which may even have a slightly different structure such that
it is presumably optimized to function in the prevailing stress field at the time
of its formation (4). In this sense, these materials are really “smart.”
The investigations to date of the structure-function relations of the bone fam-
ilyofmaterials are for the most part unable to provideanywherenear a complete
picture of this subject. Despite this inadequacy, we have chosen to organize
this review according to the hierarchical levels of organization. We discuss 5 of
the 7 hierarchical levels, which range in scale from nanometers to millimeters,
in terms of their structures and mechanical properties. These relations in the
more macroscopic structures have been reviewed extensively elsewhere (2,5).
LEVEL 1: THE MAJOR COMPONENTS
Dahllite (carbonated apatite) crystals, type I collagen fibrils, and water are the
major components of the bone family of materials. Whereas dahllite is the only
mineral type in mature bone, type I collagen is by no means the only protein
present. There are two hundred or more so-called non-collagenous proteins
(NCPs) (6), but together they generally comprise less than 10% of the total
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BONE, THE MATERIAL 275
Figure 2 Strength versus modulus of various bone types under different loading modes, in direc-
tions parallel and perpendicular to the bone long axes. The circles and inverted triangles are for
baboon tibia planar (circumferential) lamellar bone and osteonal bone, respectively, measured in
bending (data from 72); the squares, diamonds, and triangles are for human femur osteonal bone,
bovine femur fibrolamellar bone, and bovine femur parallel-fibered bone, respectively, measured
in tension (data from 49); hexagons are for mineralized turkey tendon (gastrocnemius) measured in
tension (data from 47). The insert shows the same values but has an expanded scale. Note that in
the latter, proportionality between strength and modulus arises from a progressive change in ash
weight (mineral content), rather than an increase in structural isotropy.
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276 WEINER & WAGNER
protein content. Although some of these proteins may contribute to the mecha-
nical functions, we have no direct evidence for this. Nor do we know whether
lipids, which may also be present in fairly large amounts in some bones (7),
have any mechanical function.
Dahllite Crystals
The crystals of bone are plate-shaped, with average lengths and widths of
50 ×25 nm (Figure 1; Level 1) (8–10). The crystals are very thin, with thick-
nesses appearing (in transmission electron microscopy; TEM) to be remark-
ably uniform. Small angle X-ray scattering (SAXS) is a more reliable means
of measuring their smallest dimensions, and the results vary from just 1.5 nm
for mineralized tendon up to about 4.0 nm for some mature bone types (11, 12).
These crystals are therefore extremely small—in fact they are probably the
smallest biologically formed crystals known (10). Unfortunately, we still know
very little about their surface atomic structures. An atomic force microscopy
(AFM) study of synthetic apatite shows that the surface is highly ordered and
matches the bulk structure (13). Nor do we know for sure why these crys-
tals are plate-shaped, even though dahllite has hexagonal crystal symmetry.
One proposed explanation is that they grow via an octacalcium phosphate
transition phase (14). Octacalcium phosphate crystals are plate-shaped and
have a structure very similar to apatite, except for the presence of a hydrated
layer.
Reliablemeasurements of the mechanical properties of biologicaldahlliteare
important for understanding bone properties. Measurements on single crystals
have not been made to date, presumably because of their small size. Powders
under pressure or compact polycrystalline materials have been measured usu-
ally by sonic velocity, and the results are compared with measurementsmade on
large geological single crystals (15). Young’s modulus of synthetic powdered
carbonated apatite is 109 GPa, whereas it is 114 GPa for a large single crystal of
hydroxyapatite. We are not aware of a similar measurement made on crystals
extracted from bone.
The Type I Collagen Fibril
Type I collagen is characterized by its fibrous nature, with the fibrils in bone
generally about 80–100 nm in diameter, when measured in the TEM (Figure 1;
Level 1). Their lengths are in effect unknown, because they tend to merge with
neighboring fibrils (16,17). Each fibril is made up of three polypeptide chains
about 1000 amino acids long. These are wound together in a triple helix. A
triple-helical molecule is thus cylindrically shaped, with an average diameter
of about 1.5 nm, and lengths of 300 nm (reviewed in 10,18, 19). The manner
in which they pack to form a fibril is most unusual (19). In an imaginary slice
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BONE, THE MATERIAL 277
Figure 3 Schematic illustrations (not drawn to scale) of the structure of collagen in terms of
the organization of the triple-helical molecules. (a, left side) Slice about 1.5 nm thick through a
fibril, showing the staggered array pattern first proposed by Hodge & Petruska (20); (a, right side)
three-dimensional model showing the alignment of the holes to form a channel (21). (b) Model
showing the proposed location of the platy crystals in the channels (3). The arrows show the three
principal symmetry directions. In parallel-fibered bone, T is in the plane transverse to the bone
long axis and P is in the plane parallel to the natural outer surface of the bone (48).
through a fibril, 1.5 nm thick (i.e. the thickness of one triple-helical molecule),
the triple-helical molecules are all parallel, but their ends are separated by
holes of about 35 nm (Figure 3a). Furthermore, the neighboring triple-helical
molecules are offset or staggered by 68 nm (20). In a second imaginary slice
orthogonal to the first, no offset is present and the triple-helical molecules, as
well as the holes, are aligned (Figure 3a) (21). One key point is that the internal
structure of the fibril does not have radial symmetry but is different in all three
orthogonal directions.
Fibrils almost never exist alone in biological tissues, including the members
of the bone family. They associate with each other to form arrays of aligned
fibrils that make up a larger structure called the fiber. It is thus very difficult
to measure the mechanical properties of an individual fibril. Furthermore, the
packing of fibrils in a fiber may vary from one tissue to another and influence
the mechanical properties.
Water
Water is the third major component of the bone family of materials. The impor-
tanceof water for themechanicalfunctioning of bone cannotbeunderestimated.
Mechanicalmeasurements of dry boneare different fromthoseof wet bone(22).
The water is located within the fibril, in the gaps, and between triple-helical
molecules. It is also present between fibrils and between fibers (23).
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278 WEINER & WAGNER
The Relative Proportions of the Three Major Components
The relative proportions of mineral, collagen, and water vary in a systematic
manner between bone types (24). The volume relationships in particular show
that the collagen content remains basically the same, whereas the increase in
mineral content occurs at the expense of the water content. The average propor-
tions are fixed for any given bone by a complex and only partially understood
biological process. The mineral component, in addition, increases with increas-
ing time, as the crystals continue to grow.
Currey (22, 25) has performed a series of studies of the relationships between
mineralcontent and mechanical properties. The approach hasbeentotest a very
large sample of bones, even though they havedifferent porosities and structures.
The results still clearly indicate that the Young’s modulus of compact bone in
tension shows a strong positive relationship with mineral content (Figure 4)
(25). The ultimate strain and the work under the stress-strain curve decrease
Figure 4 Plot of the calcium content versus Young’s modulus for a large variey of bones (data
from 25).
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BONE, THE MATERIAL 279
with increasing mineral content (22). Interestingly, some of the most unusual
bones at both ends of the mineral content spectrum have somewhat anomalous
mechanical properties. A fascinating example is the rostrum of the whale,
Mesoplodon,whichhas the highestmineral content (87wt%)of all themembers
of the bone family (26). The organization of the crystals is similar to other
bones, yet the collagen content and characteristics are quite different (27).
Mechanical tests show that it is the stiffest (Young’s modulus 49.6 GPa) and
hardestbonetested (28). This raises the interesting possibility that collagen was
presentduring the earlystages of formationofthe rostrum, butwas subsequently
removed, allowing crystals to continue to grow. Do similar processes, albeit
not so severe, occur during the normal ongoing mineralization process?
Mechanical Implications
The three major components of bone have completely different properties. In
this sense the material is clearly a composite. The host organic framework has
a fibrous structure at the level of individual triple-helical molecules, at the level
of fibrils (Level 2), and at the level of assemblages of fibrils (Level 3) that form
fibers. In contrast, within a fibril, the structure is crystalline with orthotropic
symmetry (Figure 3). This implies the presence of three planes of symmetry
orthogonal to each other (Figure 5). The guests in this composite are the plate-
shaped crystals. In this respect, bone should be viewed as a platelet-reinforced
composite (29). To complicate matters further, the atomic lattice symmetry of
the crystals is hexagonal, despite their platy shape. It would be of interest to
know if the mechanical properties of individual crystals are really similar to
those measured from compressed powders. With the advent of new stiff tips
for AFM, measurements of this type may be possible.
Figure 5 Schematic illustration (not drawn to scale) showing (a) an arrangement of mineral-
ized collagen fibrils aligned both with respect to crystal layers and fibril axes. This structure has
orthotropic symmetry. (b) Arrangement of mineralized collagen fibrils with only the fibril axes
aligned. This structure has transversal isotropy.
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280 WEINER & WAGNER
LEVEL 2: THE MINERALIZED COLLAGEN
FIBRIL BUILDING BLOCK
Robinson& Watson’s(30)pioneering TEM study reported thatthe68-nm band-
ing pattern of stained unmineralized collagen fibrils (Figure 1; Level 1) can also
be seen in unstained but mineralized collagen fibrils (Figure 1; Level 2). This
implies that the stain and the mineral are at the same location within the fibril,
i.e. mainly within the gap regions. TEM observations of unstained individual
mineralized collagen fibrils, both after freeze-drying and hydration in vitreous
ice (31,32), showed that the platy crystals are organized in layers that traverse
across the fibril (Figure 1; Level 2). Furthermore, electron diffraction patterns
show that the crystallographic c-axes are well aligned with the fibril long axis;
a relation first observed by Schmidt (33) using polarized light microscopy.
This layered organizational motif has been confirmed using three-dimensional
electron tomography (34), as well as by AFM (35). The layered arrangement
of crystals can be easily accommodated inside the collagen fibril (Figure 3b).
Examinations of individual mineralized fibrils from turkey tendon at different
tilt angles, show that they are ellipsoid in cross-section, with the crystal layers
aligned with the longer axis of the ellipse (31).
As always in the field of bone structure, the static model is an oversimplifi-
cation. Studies of crystal growth in collagen fibrils show that the first-formed
crystalsare indeed in the hole zone(channels)(36, 37) and during the firststages
are confined to this zone (32). However, they continue to grow and penetrate
into the overlap zone (Figure 3) (38). In so doing, they must push aside the
triple-helicalmolecules. Measurements of theaverage distancesbetween triple-
helical molecules in fibers with mineral and those without show a decrease in
distance from about 1.5 to 1.1 nm (39,40). In addition to direct compression,
more space may also be created by partial or (as noted for the whale rostrum)
almost complete removal of the collagen.
Akey question iswhetheran appreciable volumeofcrystals is present outside
the fibrils. Katz & Li (23) ingeniously combined structural and volumetric
informationto infer that in bone an appreciable amount of the mineralisoutside
thefibrils. Loci ofdisorderedcrystals havealso beenobservedin somemembers
of this family (41,42). The extent to which this occurs may vary considerably
between members of the bone family and needs to be better documented.
Mechanical Implications
The organization of the platy crystals in layers across the fibril indicates that
at this level the structure is a platelet-reinforced fibril and is fully orthotropic.
During the early stages of mineralization, the matrix host limits crystal growth
and keeps the crystals separate from each other, at least along the length of the
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BONE, THE MATERIAL 281
fibril. The crystals continue to grow, compressing the triple-helical molecules,
and eventually join together to form extended sheets. At this stage the crystals
can be regarded as having been “straight-jacketed” by the organic framework
(43). Clearly the mechanical properties of the collagen fibrils change consid-
erably under such conditions.
An interesting point concerns the nature and role of the interface between the
reinforcing mineral phase and its embedding protein matrix. It is well known
that the interface plays a critical role in governing specific properties such as
compressive and shearbehavior, fracture modes andtoughness, as well as stress
transferfrom externallyapplied loadsto thereinforcement. Thechemistry ofthe
interface in artificial composites may be tailored for specific functions because
in certain cases a weakerinterface is desirable, whereas in other cases astronger
interface is preferred. The interface between collagen and apatite crystals is
poorly understood. The fact that the collagen framework, directly or indirectly,
both orients and controls crystal growth suggests that it could approximate a
perfect or ideally strong interface. Thus the primary design of such a composite
is probably oriented by nature toward a strong and stiff structure.
LEVEL 3: FIBRIL ARRAYS
In the bone family of materials, mineralized collagen fibrils are almost always
present in bundles or arrays aligned along their lengths (44) (Figure 1; Level 3).
These bundles are, however, not discrete. Fibers from one bundle may fuse with
a neighboring bundle (16). The detailed internal structural organization of the
fibril arrays is another poorly documented aspect of these materials. The major
gaps in our knowledge arise from the fact that the internal organization of each
fibril has an orthotropic structure. Thus understanding fibril array structure,
especially in terms of the mechanical implications, should address the question
of whether the neighboring fibrils are aligned in all three dimensions, i.e. form
an extended crystalline structure or, at the other extreme, are aligned only to
their fibril axes. The difference between these two arrangements is important in
terms of symmetry; one would be fully orthotropic and the other transversely
isotropic (Figure 5). Furthermore, how are the fibril arrays packed to form
large ordered structures, and what is the extent of the order/disorder in these
structures?
The mineralized tendons of large birds, especially those from the easily
obtainable domestic turkey, have been studied in most detail at this level. These
tendons are essentially arrays of type I collagen fibrils that reach macroscopic
(millimeters) dimensions. They undergo mineralization starting from one end.
A TEM study by Nylen et al (37) reported that if the appropriate specimen
preparation conditions are used, the fibrils are intimately associated and the
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282 WEINER & WAGNER
banding patterns in neighboring fibrils are in register with each other (Figure 1;
Level3). Thus thetendonfibril array is clearly highly orderedintwo dimensions
downto a resolutionoftens of nanometers. These observationsdo not, however,
address the question of three-dimensional order.
Traub et al (32) used electron diffraction patterns of the crystals in sec-
tions of turkey tendon to demonstrate that locally (over an area of 0.3 µm)
the crystal layers in several neighboring fibrils are aligned in all three dimen-
sions. The alignment must be good (better than ±15◦) because the diffraction
pattern repeats itself every 30◦, as expected from the crystal symmetry. A
three-dimensional TEM tomographic study of bone from a chick tibia also
showed local alignment of crystal layers in adjacent fibrils (45). Sonic velocity
measurements in three orthogonal directions of macroscopic specimens show
significant differences (46), implying that orthotropic order at the fibril level
may well extend to millimeter distances. This in turn implies that the mechan-
ical properties should also be different in all three directions.
Mechanical measurements of macroscopic-sized mineralized tendons have
been made using sonic velocity (46) and in tension (47). The tension measure-
ments show the expected strong dependence on mineral content. The stress-
strain curves, however, have an S-shape, except for the most mineralized sam-
ple, which behaves like other more mineralized members of this family. The
S-shapeis attributedtotheunfolding ofa higherorderpackingstructure(crimps)
known to be present in unmineralized collagen (19). Interestingly the presence
of more mineral appears to eliminate this structure (47). The unmineralized
tendons have low average modulus values of 67 and 103 MPa, whereas the
mineralized tendons have average values ranging from 162 to 825 MPa (Figure
2). We caution against extrapolating these measurements to other members
of the bone family, as even the most mineralized tendon is poorly mineralized
(less than 50 wt%) compared with most bones (46).
Another member of the bone family of materials with a structure similar to
tendon is parallel-fibered bone. As its name implies, it is composed of arrays of
mineralized fibrils aligned along their fiberaxes, but its mineral content (around
65 wt% ) is much higher than mineralized tendon and is more representative
of most bone types. To date there has been no detailed study of the three-
dimensional structure of this bone type, althoughSEM observations support the
notion that it too has long-range orthotropic order (48). The hardness values
in three orthogonal directions are quite different (48). In the plane parallel to
the macroscopic bone outer surface (periosteum) (P in Figure 3b), the hardness
values are 480 ±60 MPa2, and in the transverse (T in Figure 3b) and radial
planes,thevaluesare705 ±90 and 600 ±60MPa2, respectively(1 kg/mm2=
9.81 MPa). The extent of anisotropy is probably much greater because the
structure is not perfectly regular to micron-scale dimensions. If these values
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BONE, THE MATERIAL 283
are extrapolated down to the nanometer scale of the individual mineralized
fibril (Figure 3b), the highest hardness values occur when the triple-helical
molecules are indented in the plane perpendicular to the fibril axis, and the
crystals are indented edge-on. The lowest values occur when the crystals are
indented face-on and in the direction in which crystal layers are separated by
four layers of triple-helical molecules (P in Figure 3b). It is extremely difficult
to study this bone type using more informative mechanical tests, because it is
generallyintimately associatedwith another bonetype (lamellarbone). Asingle
measurement(49)(Figure 2) shows that this boneishighlyanisotropic. Clearly,
we need to improve our understanding of the elastic and ultimate properties of
parallel-fibered bone, as fibril arrays form the basis of all the structural types
in this family.
Even though the information is sparse, the mechanical implications are clear.
Mineralized fibril arrays are highly anisotropic, with the highest modulus val-
ues in tension and, especially, in compression in the direction parallel to the
fibril long axes. Thus the basic building module of this family of materi-
als is anisotropic, both in structure and in mechanical properties. This may
have advantages for some functions but has clear disadvantages for others. At
the next level of organization, the structural diversity might be at least par-
tially rationalized in terms of extents of anisotropy or isotropy of the different
sturctures.
LEVEL 4: DIVERSITY IN FIBRIL ARRAY
ORGANIZATIONAL PATTERNS
At Level 4 the conspicuous diversity in structure occurs, with fibril arrays
organized in a variety of patterns. Of course, this does not imply that structural
diversity does not exist in Levels 1, 2, and 3. The fibril array patterns of four
of the most common members of this family are shown in Figure 6. For a
more comprehensive description of diversity in fibril array organization see
Francillon-Vieillot et al (50) and Pritchard (51).
Pattern 1: Arrays of Parallel Fibrils
This pattern is essentially the extension of the Level 3 structure into the micron
and even millimeter scale size range. We mentioned above two occurrences of
this structural pattern, namely mineralized tendons and parallel-fibered bone. It
is also found in some fish scales and in the skeletons of fish and amphibia (51).
The presence of mineralized tendons in the legs of large land-bound birds such
as turkeys is somewhat unusual but convenient for study. Far more common
is the phenomenon of tendons (called Sharpey’s fibers) that are mineralized in
the zone of attachment to the bone or tooth surface (16,50).
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284 WEINER & WAGNER
Parallel-fibered bone is characteristically found in the bovid family . During
early development, bone of this type is formed very rapidly. Parallel-fibered
bone is first laid down with the fibrils more or less parallel to the bone long axis.
Fairly large sausage-shaped spaces are left between successive layers of newly
forming bone. These spaces are subsequently filled with another bone type
(lamellar bone) (2). The combination of the two is referred to as fibrolamellar
bone(also known as plexiformbone). As was noted in the discussionofLevel 3,
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BONE, THE MATERIAL 285
we know little about the internal three-dimensional structure of these parallel
fibril arrays at the level of crystal layers and fibril organization.
The highly anisotropic structure of parallel fibril arrays has the obvious ad-
vantage that they can be aligned in specific directions to optimize their me-
chanical functions. The attachment of a tendon to a bone surface with the
contact zone stiffened by mineralization is a good example of this adapta-
tion. The elastic properties are optimized in a given direction, and the stiff-
ening of the structure essentially fixes the orientation. Parallel-fibered bone
has a much higher modulus value (around 26 GPa) in the direction parallel to
the axis of long bones, as compared with the orthogonal directions (around
11 GPa) (49) (Figure 2). We noted above (Level 3) that Ziv et al (48) measured
Vickers microhardness of parallel-fibered bone on three orthogonal planes,
with the highest values also being on the plane perpendicular to the fibril axes
(T in Figure 3b) and with different but lower values on the other orthogonal
planes.
Pattern 2: Woven Fiber Structure
This pattern is in many respects the antithesis of pattern 1. The fibrils are
arranged into bundles, some with rather large diameters (up to 30 µm) and
many with much smaller diameters (51). The fibril bundles are loosely packed
and poorly oriented, particularly in the case of the small-diameter bundles
(Figure 6b). There is also a large proportion of non-collagenous material in
woven bone (16,51). Treatment of woven bone with NaOCl to remove the
accessible organic material reveals a pattern of spherical mineral clusters, with
←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
Figure 6 Four of the most common fibril array patterns of organization. SEM micrographs
of fractured surfaces and schematic illustrations (not drawn to scale) of the basic organizational
motifs. (a) Array of parallel fibrils. SEM: mineralized turkey tendon (scale: 0.1 mm). Schematic
illustrationshowing the localizedorthotropic symmetryof afibril bundle. (b) Woven fiber structure.
SEM: outer layer of a 19-week old human fetus femur. (Micrograph provided by X Su. Also
published in Reference 52.) Schematic illustration showing fibril bundles with varying sized
diameters arranged in different orientations. (c) Plywood-like structure present in lamellar bone.
SEM: fracture surface of a baboon tibia showing the prominent fourth (large arrowhead) and fifth
(small arrowhead) sub-layers (63,72). Schematic illustration showing the five sub-layer model
described in (63) with sub-layers one (right hand side), two, and three arbitrarily composed of one
fibril layer each, whereas sub-layers four and five are composed of four fibril layers each. Note that
the fibrils in each layer are rotated relative to their neighbors (depicted by the change in direction
of the ellipsoid cross-section), following the rotated plywood model (67). (d) Radial fibril arrays.
SEM: human dentin fractured roughly parallel to the pulp cavity surface. The tubules (holes) are
surrounded by collagen fibrils that are all more or less in one plane. Schematic illustration of the
fibril bundles arranged in a plane perpendicular to the tubule long axis. Within the plane they have
no obvious preferred orientation.
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286 WEINER & WAGNER
little evidence of the mineralized collagen fibrils (16). Thus both the matrix
and the mineral are disorganized.
Su et al (52) recently revealed a degree of structural complexity, hithertofore
unrecognized in human fetal woven bone. The initially formed layers of woven
bone are indeed disordered. The extent of order in terms of fibril alignment,
however, increases as the spaces between the initially formed layers are filled
in. Furthermore, the rate of mineralization is very rapid. Measurements of
the microhardness and elastic modulus (4–17 GPa) of these layers using a
nanoindenterreflect this mineralizationprocess and intheolder specimens show
clearanisotropywhen comparing cross- and longitudinal-sections. Wovenfiber
structure may well be disordered as compared with other structural patterns at
this level, but this disorder does not result in isotropic properties.
Woven bone is common in the skeletons of amphibia and reptiles, as well
as in the skeleton of the mammalian embryo (51). During development, the
latter is replaced by other bone types. Embryonic woven bone is probably not
weight-bearing (except for gravity). It is also formed relatively rapidly. Woven
bone is also the first bone type to be formed after fracture or in other pathologic
circumstances, i.e. situations in which rapid formation is a prime concern.
Pattern 3: Plywood-Like Structures
This pattern is characterized by sets of parallel fibrils and/or fiber bundles
present in discrete layers, with the fibril orientation in each layer being different
(Figure 6c). The analogy of this bone structure type to plywood was first made
by Weiss & Ferris (53). The analogy to laminated composites is also evident
(54).
Plywood-like structural motifs are very common in nature and present a fas-
cinating variety of numerical puzzles, each of which probably has an insightful
structure-function relation. Bouligand (55) and Giraud-Guille (56) have not
only enumerated many of these structures, but have also pointed out some of
the structural misinterpretations that arise when oblique sections through these
structures are studied. In certain bone types, for example, this led to the incor-
rect proposal that collagen fibrils have arc-like curvatures (57).
The simplest plywood-like structure encountered in the bone family of ma-
terials has parallel fibril arrays oriented orthogonally to each other in alternate
layers. This motif occurs frequently in certain fish scales, many of which (but
not all) are fully mineralized (58). It is also the basic structural pattern of ce-
mentum, the material that bonds tooth dentin to the jaw bone (59). Orthogonal
plywood was first reported to be present in lamellar bone by Gebhardt in 1906
(60). Closer examination of the structure reveals far more complexity. In lamel-
larbone, the thicknesses ofallthe layers arenotthe same. A thinlayer or lamella
is often followed by a thick one (61). Thus a pair of such thin/thick lamellae
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BONE, THE MATERIAL 287
constitutes the basic repeating unit. More careful examination of the plywood
structures of such lamellar units in human bone revealed that there is a tran-
sition zone between the thin and thick lamellae (62). In many lamellar bones
this transition zone is fairly well developed, and it is clear that the structure is
not composed of simple orthogonal plywood-like material. Giraud-Guille (57)
analyzed the structures of these more complex plywood patterns and showed
that the fibril arrays in successive layers progress from one direction through
intermediate angles to the orthogonal direction. She referred to these structures
as twisted plywood.
Weiner et al (63) made a detailed study of collagen organization in the lamel-
lar bone from rat femurs, using cryomicrotomed and vitrified thin sections (64)
of demineralized material cut parallel to the lamellar boundary. This prepa-
ration procedure avoids the inevitable tissue distortion due to dehydration and
hence the difficulty of interpreting obliquely cut sections. They observed that
successive layers of parallel fibrils in a thin/thick lamellar unit processed by
an angle of roughly 30◦from one layer to the next. They proposed a model
in which a lamellar unit is composed of five such sub-layers (Figure 6c). The
fact that there are five and not six sub-layers oriented progressively every 30◦,
means that the lamellar unit structure is not symmetrical (65). Comparisons
of lamellar bone from different animals showed that in some cases sub-layers
one and four were thicker than the others, giving rise to the overall appear-
ance of a thin/thick orthogonal lamellar unit structure. In other cases, however,
the five sub-layers are roughly of equal thickness, giving the impression of a
continuous structure, more analogous to twisted plywood (63). Although not
enough information is currently available on the generality of the five sub-layer
lamellar unit model, it conceptually offers a synthesis for all lamellar bone
types described. The main variable in terms of collagen fibrils is the different
thicknesses of the sub-layers, rather than the angle of procession from one layer
to the next. Note, however, that not all investigators of the lamellar structure
concur with the Gebhardt plywood model. See Marotti (66) for an alternative
model.
The plywood pattern of lamellar bone incorporates another “novel” (for the
world of synthetic materials) structural feature. The fibril arrays that make up
one sub-layer of the lamellar unit also have an internal crystalline or three-
dimensional structure (Level 2). Examination of the orientations of the crystal
layers within each of the sub-layers reveals a progressive rotation from the first
sub-layer adjacent to the lamellar boundary, where the crystal layers appear
to be parallel to the boundary, to the fourth and fifth sub-layers, where they
are at a high angle to the boundary. Weiner et al (67) therefore referred to
this as rotated plywood (Figure 6c). Unfortunately, it has not been possible to
accurately measure the rotation angles. Note that as the rotation is always in
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288 WEINER & WAGNER
one direction, this results in a lamellar unit being asymmetric—an important
pointwhen considering its mechanical behavior. Suchstructures are fascinating
for scientists and engineers who usually design composite materials containing
single fibers or fiber bundles that have radial symmetry. Layers of platelets
within the fibril do not have radial symmetry, and thus an additional degree
of freedom is introduced. This could be used for tailoring purposes. Recent
model studies deal with such problems in some detail (29,68,69).
Lamellar bone may appear to be the ultimate in structural sophistication
when it comes to plywood patterns. It is probably not. Consider the pattern of
the unmineralized scale of the primitive coelacanth fish (70). A detailed and
insightful analysis of the successive orientations of the fibril orientations from
layer to layer shows that in every pair of layers the fibrils are orthogonally ori-
ented and that in successive pairs the orientations rotate progressively in a given
direction. In fact, if every alternate layer is regarded as a set, then the angular
progressionis regular.It would be fascinating to understandthemechanicalpro-
perties of the scale in relation to its structure. The elastic properties could possi-
bly be modeled by means of conventional laminate analysis (54), but other
properties such as strength and toughness are more difficult to understand.
Lamellar bone with its rotated plywood structure is very common, especially
in mammals, and is the most common bone type in humans. Thus from an
anthropomorphic point of view it is very important. However, it is difficult to
study the mechanical properties of the structure per se because planar arrays
of lamellae are not generally available in the sizes required for standard tests
(≈15 mm ×1mm×1 mm). What is generally available in these sizes are
lamellaefolded intocylinders(osteons; see Level5), orsausage-shapedlamellar
cylinders in parallel-fibered bone.
Ziv et al (48) measured the microhardness values of planar circumferential
lamellar bone from the rat tibia in many different orientations with respect to
the rotated plywood structure. The results clearly reveal anisotropy, with the
highest values found in the plane perpendicular to the long axis of the bone
(around 830 MPa) and lower values in the orthogonal planes (685–735 MPa).
However, the extent of anisotropy is much less when compared with parallel-
fibered bone of similar mineral content. This implies that the rotated plywood
structure results in a material that is more isotropic than the building block from
which it is constructed, an important strategy adopted by this material. This
in turn may reflect the requirement for lamellar bone to withstand compressive
forces in many directions, unlike parallel-fibered bone, which is optimized
in one direction. The microhardness study also revealed the asymmetry of
the rotated plywood structure, raising the fundamental mechanical question
of how this asymmetry does not result in the weakening of the structure by
buckling.
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BONE, THE MATERIAL 289
Figure 7 Plots of the flexural modulus and nominal work-to-fracture of baboon tibia (a) planar
(circumferential) lamellar bone and (b) osteonal bone versus orientation of the specimen relative
to the whole bone long axis. 0◦—the long axis of the specimen is parallel to the long axis of the
bone; 90◦—the long axis of the specimen is perpendicular to the bone long axis. In all cases, stress
was applied perpendicular to the natural bone outer surface and the measurements were made in
the three-point bending mode. Data from Liu et al (72).
An invaluable opportunity to study planar arrays of lamellar bone in three-
pointbendingarosewhena section of baboon tibia (followingtreatment withan
anti-osteoporotic drug, alendronate) (71) was found to have extensive volumes
of circumferential lamellar bone (72). Specimens were examined in four differ-
ent orientations relative to the bone long axis and were clearly anisotropic with
respect to the flexural modulus, bending strength, fracture strain, and nominal
work-to-fracture. The highest values were always obtained when the loading
axis was perpendicular to the long axis of the bone, namely in the direction in
which the greatest compressive forces are normally applied in this bone. The
extent of anisotropy for the flexural modulus is around 1.8 (the ratio in the two
orthogonal directions), whereas for the nominal work-to-fracture it is as large
as 22 (Figure 7a). The structure has somehow resulted in the ultimate proper-
ties being very anisotropic and distinctly favorable for the direction in which
most natural challenges to the bone will occur vis-a-vis fracture, namely with
stress being applied perpendicular to the bone long axis. When this occurs, the
fracture plane is tortuous, with the crack following either the lamellar bound-
ary planes or the plane perpendicular to the natural surface. The latter fracture
surface is almost featureless and resembles a ceramic (Figure 8b). In the un-
natural situation, when the long axis of the specimen is orthogonal to the bone
long axis, the fracture plane reveals the lamellar structure (Figure 8a). The
challenge now is to relate both the elastic and the ultimate properties of planar
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290 WEINER & WAGNER
Figure 8 SEM electron micrographs of the surfaces of planar (circumferential) lamellar baboon
tibia bone after fracture in (a)90
◦orientation, and (b)0
◦orientation (see Figure 7).
arrays of lamellar bone to its structure. The gaps in our current understanding
of the structure, especially of the lamellar boundaries themselves, preclude a
comprehensive analysis.
Pattern 4: Radial Fibril Arrays
This pattern is characteristic of the bulk of dentin, the material that forms the
inner layer of teeth. The collagen fibrils are almost all in the plane parallel
to the surface at which dentin formation takes place in the pulp cavity (73).
Within this plane, however, the fibril bundles are for the most part randomly
to poorly oriented, depending on the specific tooth and the location within the
tooth (Figure 6d).
Thecrystal organizationfollowstwo quite distinctpatterns: (a) Withincolla-
gen fibrils in dentin, c-axes are oriented parallel to the fibril long axes (74), and
the crystals are in layers across the fibril (75). (b) In loci presumably between
fibrils, the crytals have a random orientation and/or radiate out from the center
of a locus (41, 76). In human root dentin, there is a preferred c-axis orientation
in the collagen fibril plane, but there are also many crystals with c-axes oriented
in all directions. This is presumably the result of both crystal organizational
types being more or less equally represented (77). Furthermore, TEM obser-
vations of bundles of collagen fibrils show that the crystal layers are not always
aligned between neighboring fibrils (75).
Dentin structure is therefore highly anisotropic because the collagen fibrils
are essentially confined to one plane. In terms of crystal organization, how-
ever, the extent of anisotropy is much less. Other highly anisotropic features of
dentin are the tubules, which pass through the structure from the pulp cavity
to the region close to the dentin-enamel junction (Figure 6d). These holes oc-
cupy about 10% or less by volume of the bulk dentin and are oriented roughly
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BONE, THE MATERIAL 291
perpendicular to the collagen fibril plane. Therefore, it is surprising that stud-
ies of the elastic modulus of dentin have revealed no significant anisotropy in
relation to the structure (78, 79). This could, in part, be due to the difficulties of
testing such small specimens. Studies of dentin microhardness do reveal signif-
icant variations between locations on one plane within the tooth (78). Because
of this variation, detection of anisotropy in dentin using microhardness must
be made at one specific location. Wang & Weiner (75) performed such tests on
human dentin sectioned in different directions and confirmed that dentin is es-
sentially isotropic. In structural terms, we suspect that the essentially isotropic
elastic and hardness properties are derived mostly from the crystal organiza-
tion. We note that there is a large proportion of essentially unoriented crystals
and that even in fibril bundles, the crystal layers of neighboring fibrils are not
aligned. It is also noteworthy that in contrast to the elastic properties, the frac-
ture properties of dentin are anisotropic, with the crack preferably following
the plane in which the mineralized collagen fibrils are present (80).
Mechanical Implications
Level 4 structural organization is in many respects the heart of the subject. It
is at this level that structural diversity would appear to be optimized to func-
tional need. We can surmise that mineralized tendons are strong in tension,
lamellar bone is built to withstand stresses in many directions, and dentin is
structured to withstand compressive forces in one prevailing direction, and
so on. Nonetheless, it is evident that serious gaps in our knowledge exist,
both with respect to data on the micromechanical properties of these materials
(aside from hardness) and in terms of understanding the structure. One reason
for the former is the difficulty in acquiring large enough samples of the mate-
rial comprised only of the particular structural type of interest for mechanical
testing. We suspect that the enormous natural diversity in this family of ma-
terials has not been thoroughly explored and that suitable materials may be
available, albeit from exotic sources. With good data in hand on structure and
mechanical properties, the problem of relating structure to function will be less
formidable.
LEVEL 5: CYLINDRICAL MOTIFS—OSTEONS
Bones themselves, as opposed to dentin, cementum, scales, and most miner-
alized tendons, often undergo internal remodeling. This process involves the
excavating out of large tunnels by teams of specialized cells called osteoclasts.
These tunnels are then refilled by osteoblasts, starting with the deposition of a
thin layer of cement on the existing excavated surface, followed by layers of
lamellar bone. The process stops when the tunnel is almost completely filled,
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292 WEINER & WAGNER
leaving a narrow channel at the center that functions as a blood vessel (5)
(Figure 1; Level 5). In fact, other even smaller capillary-like features (canali-
culi) are also built into the structure. These canaliculi are numerous and house
the cells (osteocytes) that remain within the bone material itself. The canaliculi
tend to radiate out from the central blood vessel. Thus the structure of an osteon
is basically onion-like in cross-section with layers of lamellae surrounding a
central hole; in longitudinal section they are cylindrical (Figure 1; Level 5).
The osteon also contains many elongated pores.
A brief note on confusing terminology (5): The osteonal structures are also
called Haversian systems, erroneously named after John Havers who actually
discovered the lamellae in 1691 (81). van Leeuwenhoek discovered the osteons
in 1693 (82). These structures are also often referred to as secondary osteons to
differentiate them from similarly shaped structures that are laid down de novo,
e.g. in the spaces between the parallel-fibered bone in fibrolamellar (plexiform)
bone (50).
The widespread phenomenon of remodeling is itself a good indication that
it must be important. Despite the hundreds of years that have elapsed since the
osteons were identified, we do not have a complete understanding of the advan-
tages, including possible mechanical benefits, that this process affords. Many
studies have compared the mechanical properties of secondary osteonal bone
with primary bone (83,84). The primary bone usually used was fibrolamellar
(plexiform) bone, which is comprised of both parallel-fibered bone and primary
osteons. Secondary osteonal bone composed of cylindrical arrays of lamellae
should be compared with primary lamellar bone comprised of planar arrays of
lamellae. The latter, as noted above, is not naturally available in large enough
quantities for standard mechanical tests. Liu et al (72), however, recently stud-
ied such planar lamellar arrays in an unnatural bone produced as a result of
treatment by alendronate and have compared it to osteonal bone taken from the
same baboon tibia, albeit from the opposing side of the mid-shaft. Figure 7b
shows the results for the flexural modulus and the nominal work-to-fracture
in four different orientations of osteonal bone. The basic trends and absolute
values are similar to those of planar lamellar bone (Figure 7a), except for the
off-axis values, where in the latter, the differences between the curves are a
little larger than the on-axis values. It is difficult to definitively ascribe this dif-
ference to a particular aspect of the rotated plywood structure, but it may well
be related to the presence of a prominent fifth sub-lamella in the lamellar unit
of baboon tibia that is oriented 30◦from the bone long axis (Figure 6c). This
asymmetry would be canceled out in a cylindrical structure (Figure 9). In fact,
this canceling out effect of the asymmetry due to the folding of the lamellae into
cylinders may well be one of the important mechanical advantages of osteonal
bone over bone composed of planar lamellar arrays. In general, however, it can
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BONE, THE MATERIAL 293
Figure 9 Schematic illustration (not drawn to scale) of a cylindrical osteon-like structure with the
five sub-lamellar model superimposed. The orientation of the sub-layers is reversed on opposite
sides of the cylinder, thus balancing the asymmetry of the lamellar structure. Figure from Liu et al
(72).
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294 WEINER & WAGNER
Figure 10 Flexural stress-strain curves of baboon tibia measured in three-point bending at 0oand
90◦(see Figure 7). The heavy lines are for planar (circumferential) lamellar bone and the thin lines
for osteonal bone. Data from Liu et al (72).
be concluded that the elastic properties are mostly due to the lamellar structure
itself and not to the folding of lamellae into cylinders.
Thisis not thecasefor the ultimate properties. Acomparison of typical setsof
stress-straincurvesfor planar lamellar arrays and cylindrical lamellar structures
(Figure 10), shows obvious differences in the fracture behavior. The osteonal
bone reveals far more damage-related features and a pronounced tailing effect
(72). The latter is related to the observation that following massive fracture,
the two pieces of the osteonal bone always remain attached, whereas the planar
lamellar bone fractures cleanly into two halves. This may afford important
biological benefits. The natural wound healing process of a fractured bone can
onlytake place if the twosegments are in closeproximity. Otherwiseaso-called
non-union fracture occurs that will heal only with surgical intervention. There
may well be other, yet to be discovered, mechanical benefits of osteonal bone
compared with planar arrays of lamellae. In principle, it is possible to predict
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BONE, THE MATERIAL 295
the elastic constants of osteons or arrays of osteons, using Lekhnitskii’s work
on fully orthotropic solids (85). Although algebraically difficult, this should
be feasible, providing the data for the basic physical parameters (the relative
weight or volume content, the various elastic constants of the components, etc)
are available.
LEVEL 6: SOLID VERSUS SPONGY BONE,
AND LEVEL 7: WHOLE BONES
Figure 1, Level 6, is a photograph of spongy bone associated with solid or com-
pact bone. Figure 1, Level 7, is a photograph of a whole bone. A vast literature
exists on both subjects (e.g. 4), which relates the mechanical properties to the
material bone, as well as to their overall structures and shapes. This is beyond
the scope of this review. For an overview of the subject, readers are referred
to Currey (2), and for a more biological perspective to Martin & Burr (5). For
a fascinating as well as historical view, the chapter on bone in Thompson’s
classic book is recommended (86).
CONCLUDING COMMENTS
Progress is being made on understanding the structure-mechanical function re-
lations in the bone family of materials. Although many gaps in our knowledge
exist, especially when the structure is considered in terms of its 7 hierarchical
levels, our theoretical understanding of these relations and predictive capabili-
ties are slowly improving. The more we learn, the more we realize thatthere are
striking similarities between bone and man-made polymers and composites and
that materials sciences can benefit from the basic work that has been performed
inthe bone fieldand vice versa. Simpleexamples are thehigh-molecular-weight
organic fibers such as aramids (Kevlar) or polyethylene. They are structurally
organized like tendons, from the molecular level up. In both the biological and
the synthetic materials, the structural and evidently mechanical anisotropies
are highest at the molecular scale, but are progressively reduced as the scale
increases through sub-fibrillar and fibrillar arrays, up to the micrometer level
(the single fiber). At higher levels, both bone and man-made composites have
structures and physical properties that show progressively less anisotropy. This
occurs, for example, when large arrays of single fiber-based plies or lamel-
lae are arranged into layered or laminated structures at various angles. This
is an important characteristic of structural design in nature and synthetically
by humans, which in both cases is motivated by the fact that complex macro-
scopic structures are usually not designed uniquely for a single type of stress,
but rather against stresses of various types, applied in various directions. The
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296 WEINER & WAGNER
design criteria, therefore, are varied rather than single-valued, and structural
complexity is unavoidable. This effect also results in the gradual loss of a
formal link between the various physical properties at higher and higher orga-
nizational levels. For example, by using a scaled-upmodel it may be possible to
predict the stiffness of a fibril based on that of a single molecule, but it is much
more difficult to predict the stiffness of a macroscopic composite structure from
the stiffness of a molecule. The prediction of strength is even more difficult
because of the higher sensitivity of that property to the presence of defects.
Extensive work has been performed in the field of composite materials to
predict elastic constants, mostly of complex laminated structures in planar or
cylindrical form; e.g. see the laminate theory in Reference 54. In principle,
rather complex cases such as the predictions of the elastic constants of osteons
or arrays of osteons may also be dealt with using Lekhnitskii’s work on fully
orthotropic solids (85). We wish to emphasize, however, that especially in the
case of biological materials and structures, models can only lead to simplified
results,inview ofthe inherent variabilityof material andgeometricalproperties,
the aging effects, and our current lack of detailed information of the structures
and the properties at the smaller scales. In the case of bone, this structural
complexityappears invarious often subtle forms. One important example is the
interplay of fibrils and laminates at all levels. The power of theoretical models
to bridge gaps in our knowledge is possibly the greatest at the level of the single
lamella or of the parallel fibrillar arrays, and it is precisely at these levels that
experimental results are still lacking, dueto the technical difficulties involved in
testingvery small specimens. Models for boneofvariousdegrees ofcomplexity
have indeed been proposed over the years, based mostly on concepts developed
in the field of composite materials (29,49, 87–93). However, only a few of
these models incorporate platelet-or ribbon-shaped reinforcement and take into
account some of the detailed geometrical and structural features (29,68,69).
There is clearly a great need for additional careful experimental work with very
small specimens with well-defined structures (72,94).
The family of mineralized collagen-based materials presents a variety of
structures that represent solutions to demanding mechanical requirements. The
study of the structure-mechanical function relations in such materials is a fasci-
nating subject in its own right and may provide novel ideas that can be applied
to the improvement of synthetic materials.
ACKNOWLEDGMENTS
We thank Lia Addadi, Udi Akiva, Talmon Arad, Danmei Liu, Ilana Sabanay,
Wolfie Traub, Rizhi Wang, and Vivi Ziv for their invaluable contributions to
our knowledge of bone. We also thank Shoshana Neumann for her help in
preparing this manuscript. This study was supported by U.S. Public Service
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BONE, THE MATERIAL 297
Grant DE06954 from the National Institute of Dental Research. SW holds the
IW Abel Professorial Chair of Structural Biology.
Visit the Annual Reviews home page at
http://www.AnnualReviews.org.
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Annual Review of Materials Science
Volume 28, 1998
CONTENTS
Jahn-Teller Phenomena in Solids,
J
. B. Goodenough 1
Isotropic Negative Thermal Expansion,
A
rthur W. Sleight 29
Spin-Dependent Transport and Low-Field Magnetoresistance in Doped
Man
g
anites,
J
. Z. Sun, A. Gu
p
ta 45
High Dielectric Constant Thin Films for Dynamic Random Access
Memories
(
DRAM
)
, J. F. Scott 79
Imaging and Control of Domain Structures in Ferroelectric Thin Films via
Scanning Force Microscopy, Alexei Gruverman, Orlando Auciello,
H
iroshi Tokumoto 101
InGaN-Based Laser Diodes, Shuji Nakamura 125
Soft Lithography, Younan Xia, George M. Whitesides 153
Transient Diffusion of Beryllium and Silicon in Gallium Arsenide, Yaser
M
. Haddara, John C. Bravman 185
Semiconductor Wafer Bonding, U. Gösele, Q.-Y. Tong 215
Cathodic Arc Deposition of Films,
I
an G. Brown 243
The Material Bone: Structure--Mechanical Function Relations, S. Weiner,
H
. D. Wa
g
ner 271
Science and Technology of High-Temperature Superconducting Films, D.
P. Norton 299
IN SITU STUDIES OF THE PROPERTIES OF MATERIALS UNDER
HIGH-PRESSURE AND TEMPERATURE CONDITIONS USING
MULTI-ANVIL APPARATUS AND SYNCHROTRON X-RAYS, J. B.
Parise, D. J. Weidner, J. Chen, R. C. Liebermann, G. Chen
349
STUDIES OF MULTICOMPONENT OXIDE FILMS AND LAYERED
HETEROSTRUCTURE GROWTH PROCESSES VIA IN SITU, TIME-
OF-FLIGHT ION SCATTERING AND DIRECT RECOIL
SPECTROSCOPY, Orlando Auciello, Alan R. Krauss, Jaemo Im, J.
A
lbert Schultz
375
Perovskite Thin Films for High-Frequency Capacitor Applications, D.
D
imos, C. H. Mueller 397
RECENT DEVELOPMENTS IN CONDUCTOR PROCESSING OF
HIGH IRREVERSIBILITY FIELD SUPERCONDUCTORS, J. L.
M
acManus-Driscoll 421
Point Defect Chemistry of Metal Oxide Heterostructures, Sanjeev
Agg
arwal, R. Ramesh 463
Processing Technologies for Ferroelectric Thin Films and
Heterostructures, Orlando Auciello, Chris M. Foster, Rammamoorthy
R
amesh 501
The Role of Metastable States in Polymer Phase Transitions: Concepts,
Principles, and Experimental Observations, Stephen Z. D. Cheng, Andrew
K
elle
r
533
Processing and Characterization of Piezoelectric Materials and Integration
into Microelectromechanical Systems, Dennis L. Polla, Lorraine F.
F
rancis 563
Recent Advances in the Development of Processable High-Temperature
Pol
y
mers,
M
ichael A. Meador 599
High-Pressure Synthesis, Characterization, and Tuning of Solid State
Materials,
J
. V. Baddin
g
631
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