Biological materials in nature serve as a valuable source of inspiration for developing novel synthetic materials with extraordinary properties or functions. Much effort to date has been directed toward fabricating and understanding bio-inspired nanocomposites with internal architectures mimicking those of nacre and collagen fibril. Here we establish simple and explicit analytical solutions for both upper and lower bounds of the elastic properties of biocomposites in terms of various physical and geometrical parameters including volume fraction and moduli of constituents, and aspect ratio and alignment pattern of stiff reinforcements. Numerical analyses based on the finite element method are performed to validate the derived elastic bounds.

References

References
1.
Currey
,
J. D.
,
1977
, “
Mechanical Properties of Mother of Pearl in Tension
,”
Proc. R. Soc. London, Ser. B
,
196
, pp.
443
463
.10.1098/rspb.1977.0050
2.
Landis
,
W. J.
,
1995
, “
The Strength of a Calcified Tissue Depends in Part on the Molecular Structure and Organization of Its Constituent Mineral Crystals in Their Organic Matrix
,”
Bone
,
16
, pp.
533
544
.10.1016/8756-3282(95)00076-P
3.
Landis
,
W. J.
,
Hodgens
,
K. J.
,
Song
,
M. J.
,
Arena
,
J.
,
Kiyonaga
,
S.
,
Marko
,
M.
,
Owen
,
C.
, and
McEwen
,
B. F.
,
1996
, “
Mineralization of Collagen May Occur on Fibril Surfaces: Evidence From Conventional and High-Voltage Electron Microscopy and Three-Dimensional Imaging
,”
J. Struct. Biol.
,
117
, pp.
24
35
.10.1006/jsbi.1996.0066
4.
Rho
,
J.-Y.
,
Kuhn-Spearing
,
L.
, and
Zioupos
,
P.
,
1998
, “
Mechanical Properties and the Hierarchical Structure of Bone
,”
Med. Eng. Phys.
,
20
, pp.
92
102
.10.1016/S1350-4533(98)00007-1
5.
Weiner
,
S.
, and
Wagner
,
H. D.
,
1998
, “
The Material Bone: Structure-Mechanical Function Relations
,”
Ann. Rev. Mater. Sci.
,
28
, pp.
271
298
.10.1146/annurev.matsci.28.1.271
6.
Jackson
,
A. P.
,
Vincent
,
J. F. V.
, and
Turner
,
R. M.
,
1988
, “
The Mechanical Design of Nacre
,”
Proc. R. Soc. London, Ser. B
,
234
, pp.
415
440
.10.1098/rspb.1988.0056
7.
Jager
, I
.
, and
Fratzl
,
P.
,
2000
, “
Mineralized Collagen Fibrils: A Mechanical Model With a Staggered Arrangement of Mineral Particles
,”
Biophys. J.
,
79
, pp.
1737
1746
.10.1016/S0006-3495(00)76426-5
8.
Ji
,
B.
, and
Gao
,
H.
,
2004
, “
Mechanical Properties of Nanostructure of Biological Materials
,”
J. Mech. Phys. Solids
,
52
, pp.
1963
1990
.10.1016/j.jmps.2004.03.006
9.
Tang
,
Z. Y.
,
Kotov
,
N. A.
,
Magonov
,
S.
, and
Ozturk
,
B.
,
2003
, “
Nanostructured Artificial Nacre
,”
Nat. Mater.
,
2
, pp.
413
418
.10.1038/nmat906
10.
Podsiadlo
,
P.
,
Kaushik
,
A. K.
,
Arruda
,
E. M.
,
Waas
,
A. M.
,
Shim
,
B. S.
,
Xu
,
J.
,
Nandivada
,
H.
,
Pumplin
,
B. G.
,
Lahann
,
J.
,
Ramamoorthy
,
A.
, and
Kotov
,
N. A.
,
2007
, “
Ultrastrong and Stiff Layered Polymer Nanocomposites
,”
Science
,
318
, pp.
80
83
.10.1126/science.1143176
11.
Bonderer
,
L. J.
,
Studart
,
A. R.
, and
Gauckler
,
L. J.
,
2008
, “
Bioinspired Design and Assembly of Platelet Reinforced Polymer Films
,”
Science
,
319
, pp.
1069
1073
.10.1126/science.1148726
12.
Munch
,
E.
,
Launey
,
M. E.
,
Alsem
,
D. H.
,
Saiz
,
E.
,
Tomsia
,
A. P.
, and
Ritchie
,
R. O.
,
2008
, “
Tough, Bio-Inspired Hybrid Materials
,”
Science
,
322
, pp.
1516
1520
.10.1126/science.1164865
13.
Ryu
,
S.
,
Lee
,
Y.
,
Hwang
,
J.-W.
,
Hong
,
S.
,
Kim
,
C.
,
Park
,
T. G.
,
Lee
,
H.
, and
Hong
,
S. H.
,
2011
, “
High-Strength Carbon Nanotube Fibers Fabricated by Infiltration and Curing of Mussel-Inspired Catecholamine Polymer
,”
Adv. Mater.
,
23
, pp.
1971
1975
.10.1002/adma.201004228
14.
Stankovich
,
S.
,
Dikin
,
D. A.
,
Dommett
,
G. H. B.
,
Kohlhaas
,
K. M.
,
Zimney
,
E. J.
,
Stach
,
E. A.
,
Piner
,
R. D.
,
Nguyen
,
S. T.
, and
Ruoff
,
R. S.
,
2006
, “
Graphene-Based Composite Materials
,”
Nature
,
442
, pp.
282
286
.10.1038/nature04969
15.
Foroughi
,
J.
,
Spinks
,
G. M.
,
Wallace
,
G. G.
,
Oh
,
J.
,
Kozlov
,
M. E.
,
Fang
,
S.
,
Mirfakhrai
,
T.
,
Madden
,
J. D. W.
,
Shin
,
M. K.
,
Kim
,
S. J.
, and
Baughman
,
R. H.
,
2011
, “
Torsional Carbon Nanotube Artificial Muscles
,”
Science
,
334
, pp.
494
497
.10.1126/science.1211220
16.
Gao
,
H.
,
Ji
,
B.
,
Jager
, I
. L.
,
Arzt
,
E.
, and
Fratzl
,
P.
,
2003
, “
Materials Become Insensitive to Flaws at Nanoscale: Lessons From Nature
,”
Proc. Natl. Acad. Sci. U. S. A.
,
100
, pp.
5597
5600
.10.1073/pnas.0631609100
17.
Liu
,
B.
,
Zhang
,
L.
, and
Gao
,
H.
,
2006
, “
Poisson Ratio Can Play a Crucial Role in Mechanical Properties of Biocomposites
,”
Mech. Mater.
,
38
, pp.
1128
1142
.10.1016/j.mechmat.2006.02.002
18.
Laraia
, V
. J.
, and
Heuer
,
A. H.
,
1989
, “
Novel Composite Microstructure and Mechanical Behavior of Mollusk Shell
,”
J. Am. Ceram. Soc.
,
72
, pp.
2177
2179
.10.1111/j.1151-2916.1989.tb06053.x
19.
Anup
,
S.
,
Sivakumar
,
S. M.
, and
Suraishkumar
,
G. K.
,
2007
, “
Structural Arrangement Effects of Mineral Platelets on the Nature of Stress Distribution in Bio-Composites
,”
Comput. Model. Eng. Sci.
,
18
, pp.
145
153
.10.3970/cmes.2007.018.145
20.
Nukala
,
P.
, and
Simunovic
,
S.
,
2005
, “
Statistical Physics Models for Nacre Fracture Simulation
,”
Phys. Rev. E
,
72
, p.
041919
.10.1103/PhysRevE.72.041919
21.
Kamat
,
S.
,
Su
,
X.
,
Ballarini
,
R.
, and
Heuer
,
A. H.
,
2000
, “
Structural Basis for the Fracture Toughness of the Shell of the Conch Strombus Gigas
,”
Nature
,
405
, pp.
1036
1040
.10.1038/35016535
22.
He
,
L. H.
, and
Swain
,
M. V.
,
2008
, “
Understanding the Mechanical Behaviour of Human Enamel From Its Structural and Compositional Characteristics
,”
J. Mech. Behav. Biomed. Mater.
,
1
, pp.
18
29
.10.1016/j.jmbbm.2007.05.001
23.
Gupta
,
H. S.
,
Seto
,
J.
,
Wagermaier
,
W.
,
Zaslansky
,
P.
,
Boesecke
,
P.
, and
Fratzl
,
P.
,
2006
, “
Cooperative Deformation of Mineral and Collagen in Bone at the Nanoscale
,”
Proc. Natl. Acad. Sci. U. S. A.
,
103
, pp.
17741
17746
.10.1073/pnas.0604237103
24.
Gao
,
H. J.
,
2006
, “
Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-Like Materials
,”
Int. J. Fract.
,
138
, pp.
101
137
.10.1007/s10704-006-7156-4
25.
Zhang
,
Z.
,
Zhang
,
Y.-W.
, and
Gao
,
H.
,
2011
, “
On Optimal Hierarchy of Load-Bearing Biological Materials
,”
Proc. R. Soc. B
,
278
, pp.
519
525
.10.1098/rspb.2010.1093
26.
Zhang
,
Z. Q.
,
Zhong
,
Y.
,
Liu
,
B.
,
Fang
,
D. N.
, and
Hwang
,
K. C.
,
2008
, “
Mechanical Properties of Staggered-Alignment Biomimetic Composites
,”
Advances in Heterogeneous Material Mechanics 2008
,
J. H.
Fan
and
H. B.
Chen
, eds.,
DEStech Publications
,
Lancaster, UK
, pp.
606
609
.
27.
Barthelat
,
F.
,
Tang
,
H.
,
Zavattieri
,
P. D.
,
Li
,
C. M.
, and
Espinosa
,
H. D.
,
2007
, “
On the Mechanics of Mother-of-Pearl: A Key Feature in the Material Hierarchical Structure
,”
J. Mech. Phys. Solids
,
55
, pp.
306
337
.10.1016/j.jmps.2006.07.007
28.
Kotha
,
S. P.
,
Li
,
Y.
, and
Guzelsu
,
N.
,
2001
, “
Micromechanical Model of Nacre Tested in Tension
,”
J. Mater. Sci.
,
36
, pp.
2001
2007
.10.1023/A:1017526830874
29.
Zhang
,
Z. Q.
,
Liu
,
B.
,
Huang
,
Y.
,
Hwang
,
K. C.
, and
Gao
,
H.
,
2010
, “
Mechanical Properties of Unidirectional Nanocomposites With Non-Uniformly or Randomly Staggered Platelet Distribution
,”
J. Mech. Phys. Solids
,
58
, pp.
1646
1660
.10.1016/j.jmps.2010.07.004
30.
Lei
,
H. F.
,
Zhang
,
Z. Q.
, and
Liu
,
B.
,
2012
, “
Effect of Fiber Arrangement on Mechanical Properties of Short Fiber Reinforced Composites
,”
Compos. Sci. Technol.
,
72
, pp.
506
514
.10.1016/j.compscitech.2011.12.011
31.
Mori
,
T.
, and
Tanaka
,
K.
,
1973
, “
Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,”
Acta Metall.
,
21
, pp.
571
574
.10.1016/0001-6160(73)90064-3
32.
Zhao
,
Y. H.
, and
Weng
,
G. J.
,
1990
, “
Effective Elastic Moduli of Ribbon-Reinforced Composites
,”
J. Appl. Mech.
,
57
, pp.
158
167
.10.1115/1.2888297
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