Dynamic Behavior of the Nanostructure of Load-bearing Biological Materials
Typical load-bearing biological materials like bone,
mineralized tendon and shell, are biocomposites made from both
organic (collagen) and inorganic (biomineral) materials. This
amazing class of materials with intrinsic internally designed
hierarchical structures show superior mechanical properties with
regard to their weak components from which they are formed.
Extensive investigations concentrating on static loading conditions
have been done to study the biological materials failure. However,
most of the damage and failure mechanisms in load-bearing
biological materials will occur whenever their structures are exposed
to dynamic loading conditions. The main question needed to be
answered here is: What is the relation between the layout and
architecture of the load-bearing biological materials and their
dynamic behavior? In this work, a staggered model has been
developed based on the structure of natural materials at nanoscale and
Finite Element Analysis (FEA) has been used to study the dynamic
behavior of the structure of load-bearing biological materials to
answer why the staggered arrangement has been selected by nature to
make the nanocomposite structure of most of the biological materials.
The results showed that the staggered structures will efficiently
attenuate the stress wave rather than the layered structure.
Furthermore, such staggered architecture is effectively in charge of
utilizing the capacity of the biostructure to resist both normal and
shear loads. In this work, the geometrical parameters of the model
like the thickness and aspect ratio of the mineral inclusions selected
from the typical range of the experimentally observed feature sizes
and layout dimensions of the biological materials such as bone and
mineralized tendon. Furthermore, the numerical results validated with
existing theoretical solutions. Findings of the present work emphasize
on the significant effects of dynamic behavior on the natural
evolution of load-bearing biological materials and can help scientists
to design bioinspired materials in the laboratories.
[1] J. Y. Rho, L. Kuhn Spearing, and P. Zioupos, "Mechanical properties
and the hierarchical structure of bone," Medical engineering & physics,
vol. 20, pp. 92-102, 1998.
[2] M. A. Meyers, P. Y. Chen, A. Y. M. Lin, and Y. Seki, "Biological
materials: structure and mechanical properties," Progress in Materials
Science, vol. 53, pp. 1-206, 2008.
[3] S. Weiner and H. D. Wagner, "The material bone: structure-mechanical
function relations," Annual Review of Materials Science, vol. 28, pp.
271-298, 1998.
[4] R. Puxkandl, I. Zizak, O. Paris, J. Keckes, W. Tesch, S. Bernstorff, et
al., "Viscoelastic properties of collagen: synchrotron radiation
investigations and structural model," Philosophical Transactions of the
Royal Society of London. Series B: Biological Sciences, vol. 357, pp.
191-197, 2002.
[5] R. Menig, M. Meyers, M. Meyers, and K. Vecchio, "Quasi-static and
dynamic mechanical response of Strombus gigas (conch) shells,"
Materials Science and Engineering: A, vol. 297, pp. 203-211, 2001.
[6] J. D. Currey, The mechanical adaptations of bones. Princeton: Princeton
University Press, 1984.
[7] P. D. Delmas, R. P. Tracy, B. L. Riggs, and K. G. Mann, "Identification
of the noncollagenous proteins of bovine bone by two-dimensional gel
electrophoresis," Calcified tissue international, vol. 36, pp. 308-316,
1984.
[8] P. Fratzl and R. Weinkamer, "Nature’s hierarchical materials," Progress
in Materials Science, vol. 52, pp. 1263-1334, 2007.
[9] H. D. Espinosa, J. E. Rim, F. Barthelat, and M. J. Buehler, "Merger of
structure and material in nacre and bone perspectives on de novo
biomimetic materials," Progress in Materials Science, vol. 54, pp. 1059-
1100, 2009.
[10] R. O. Ritchie, "The conflicts between strength and toughness," Nature
Materials, vol. 10, pp. 817-822, 2011.
[11] Y. Shao, H.-P. Zhao, and X.-Q. Feng, "On flaw tolerance of nacre: a
theoretical study," Journal of The Royal Society Interface, vol. 11, p.
20131016, 2014.
[12] H. Gao, B. Ji, I. L. Jäger, E. Arzt, and P. Fratzl, "Materials become
insensitive to flaws at nanoscale: lessons from nature," Proceedings of
the national Academy of Sciences, vol. 100, pp. 5597-5600, 2003.
[13] B. Ji and H. Gao, "Mechanical properties of nanostructure of biological
materials," Journal of the Mechanics and Physics of Solids, vol. 52, pp.
1963-1990, 2004.
[14] B. Ji and H. Gao, "A study of fracture mechanisms in biological nanocomposites
via the virtual internal bond model," Materials Science and
Engineering: A, vol. 366, pp. 96-103, 2004.
[15] B. Ji, H. Gao, and K. Jimmy Hsia, "How do slender mineral crystals
resist buckling in biological materials?," Philosophical Magazine
Letters, vol. 84, pp. 631-641, 2004.
[16] B. Ji, H. Gao, and T. Wang, "Flow stress of biomorphous metal–matrix
composites," Materials Science and Engineering: A, vol. 386, pp. 435-
441, 2004.
[17] B. Ji and H. Gao, "Elastic properties of nanocomposite structure of
bone," Composites science and technology, vol. 66, pp. 1212-1218,
2006.
[18] R. A. Robinson, "An electron-microscopic study of the crystalline
inorganic component of bone and its relationship to the organic matrix,"
The Journal of Bone & Joint Surgery, vol. 34, pp. 389-476, 1952.
[19] R. A. Robinson and M. L. Watson, "Collagen‐crystal relationships in
bone as seen in the electron microscope," The anatomical record, vol.
114, pp. 383-409, 1952.
[20] R. A. Robinson and M. L. Watson, "Crystal-collagen relationships in
bone as observed in the electron microscope. III. Crystal and collagen
morphology as a function of age," Annals of the New York Academy of
Sciences, vol. 60, pp. 596-630, 1955.
[21] Z. Molnar, "Additional observations on bone crystal dimensions," Clin.
Orthop, vol. 17, pp. 38-42, 1960.
[22] A. S. Posner, "Crystal chemistry of bone mineral," Physiological
reviews, vol. 49, pp. 760-792, 1969.
[23] J. Moradian-Oldak, S. Weiner, L. Addadi, W. Landis, and W. Traub,
"Electron imaging and diffraction study of individual crystals of bone,
mineralized tendon and synthetic carbonate apatite," Connective tissue
research, vol. 25, pp. 219-228, 1991.
[24] W. Landis, M. Song, A. Leith, L. McEwen, and B. McEwen, "Mineral
and organic matrix interaction in normally calcifying tendon visualized
in three dimensions by high-voltage electron microscopic tomography
and graphic image reconstruction," Journal of structural biology, vol.
110, pp. 39-54, 1993.
[25] V. Ziv and S. Weiner, "Bone crystal sizes: a comparison of transmission
electron microscopic and X-ray diffraction line width broadening
techniques," Connective tissue research, vol. 30, pp. 165-175, 1994.
[26] W. Landis, "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, vol. 16, pp. 533-544, 1995.
[27] M. A. Rubin, I. Jasiuk, J. Taylor, J. Rubin, T. Ganey, and R. P.
Apkarian, "TEM analysis of the nanostructure of normal and
osteoporotic human trabecular bone," Bone, vol. 33, pp. 270-282, 2003.
[28] T. Hassenkam, G. E. Fantner, J. A. Cutroni, J. C. Weaver, D. E. Morse,
and P. K. Hansma, "High-resolution AFM imaging of intact and
fractured trabecular bone," Bone, vol. 35, pp. 4-10, 2004.
[29] H. Gao, "Application of fracture mechanics concepts to hierarchical
biomechanics of bone and bone-like materials," International Journal of
Fracture, vol. 138, pp. 101-137, 2006.
[30] Z. Zhang, Y. W. Zhang, and H. Gao, "On optimal hierarchy of loadbearing
biological materials," Proceedings of the Royal Society B:
Biological Sciences, vol. 278, pp. 519-525, 2011.
[31] B. Borah, G. J. Gross, T. E. Dufresne, T. S. Smith, M. D. Cockman, P.
A. Chmielewski, et al., "Three-dimensional microimaging (MRμI and
μCT), finite element modeling, and rapid prototyping provide unique
insights into bone architecture in osteoporosis," The anatomical record,
vol. 265, pp. 101-110, 2001.
[32] H. Gong, M. Zhang, L. Qin, and Y. Hou, "Regional variations in the
apparent and tissue-level mechanical parameters of vertebral trabecular
bone with aging using micro-finite element analysis," Annals of
biomedical engineering, vol. 35, pp. 1622-1631, 2007.
[33] X. N. Dong, T. Guda, H. R. Millwater, and X. Wang, "Probabilistic
failure analysis of bone using a finite element model of mineral–collagen
composites," Journal of biomechanics, vol. 42, pp. 202-209, 2009.
[34] Q. Luo, R. Nakade, X. Dong, Q. Rong, and X. Wang, "Effect of
mineral–collagen interfacial behavior on the microdamage progression
in bone using a probabilistic cohesive finite element model," Journal of
the mechanical behavior of biomedical materials, vol. 4, pp. 943-952,
2011.
[35] F. Yuan, S. R. Stock, D. R. Haeffner, J. D. Almer, D. C. Dunand, and L.
C. Brinson, "A new model to simulate the elastic properties of
mineralized collagen fibril," Biomechanics and Modeling in
Mechanobiology, vol. 10, pp. 147-160, 2011.
[36] T. J. Vaughan, C. T. McCarthy, and L. M. McNamara, "A three-scale
finite element investigation into the effects of tissue mineralisation and
lamellar organisation in human cortical and trabecular bone," Journal of
the Mechanical Behavior of Biomedical Materials, vol. 12, pp. 50-62,
2012.
[37] A. Barkaoui and R. Hambli, "Nanomechanical properties of mineralised
collagen microfibrils based on finite elements method: biomechanical
role of cross-links," Computer methods in biomechanics and biomedical
engineering, vol. 17, pp. 1590-1601, 2014.
[38] A. Barkaoui and R. Hambli, "Finite element 3D modeling of mechanical
behavior of mineralized collagen microfibrils," Journal of Applied
Biomaterials and Biomechanics, vol. 9, pp. 199-205, 2011.
[39] C. C. Chen and R. Clifton, "Asymptotic solutions for wave propagation
in elastic and viscoelastic bilaminates," in Midwestern Mechanics
Conference, 14 th, Norman, Okla, 1975, pp. 399-417. [40] Y. Oved, G. E. Luttwak, and Z. Rosenberg, "Shock wave propagation in
layered composites," Journal of Composite Materials, vol. 12, pp. 84-96,
1978.
[41] N. Chandra, C. Xianglei, and A. Rajendran, "The effect of material
heterogeneity on the shock response of layered systems in plate impact
tests," Journal of composites technology & research, vol. 24, pp. 232-
238, 2002.
[42] S. Zhuang, G. Ravichandran, and D. E. Grady, "An experimental
investigation of shock wave propagation in periodically layered
composites," Journal of the Mechanics and Physics of Solids, vol. 51,
pp. 245-265, 2003.
[43] X. Chen and N. Chandra, "The effect of heterogeneity on plane wave
propagation through layered composites," Composites science and
technology, vol. 64, pp. 1477-1493, 2004.
[44] X. Chen, N. Chandra, and A. Rajendran, "Analytical solution to the plate
impact problem of layered heterogeneous material systems,"
International Journal of Solids and Structures, vol. 41, pp. 4635-4659,
2004.
[45] I. Jäger and P. Fratzl, "Mineralized collagen fibrils: a mechanical model
with a staggered arrangement of mineral particles," Biophysical Journal,
vol. 79, pp. 1737-1746, 2000.
[46] H. A. Lowenstam and S. Weiner, On biomineralization. Oxford: Oxford
University Press, 1989.
[47] S. J. Eppell, W. Tong, J. L. Katz, L. Kuhn, and M. J. Glimcher, "Shape
and size of isolated bone mineralites measured using atomic force
microscopy," Journal of orthopaedic research, vol. 19, pp. 1027-1034,
2001.
[1] J. Y. Rho, L. Kuhn Spearing, and P. Zioupos, "Mechanical properties
and the hierarchical structure of bone," Medical engineering & physics,
vol. 20, pp. 92-102, 1998.
[2] M. A. Meyers, P. Y. Chen, A. Y. M. Lin, and Y. Seki, "Biological
materials: structure and mechanical properties," Progress in Materials
Science, vol. 53, pp. 1-206, 2008.
[3] S. Weiner and H. D. Wagner, "The material bone: structure-mechanical
function relations," Annual Review of Materials Science, vol. 28, pp.
271-298, 1998.
[4] R. Puxkandl, I. Zizak, O. Paris, J. Keckes, W. Tesch, S. Bernstorff, et
al., "Viscoelastic properties of collagen: synchrotron radiation
investigations and structural model," Philosophical Transactions of the
Royal Society of London. Series B: Biological Sciences, vol. 357, pp.
191-197, 2002.
[5] R. Menig, M. Meyers, M. Meyers, and K. Vecchio, "Quasi-static and
dynamic mechanical response of Strombus gigas (conch) shells,"
Materials Science and Engineering: A, vol. 297, pp. 203-211, 2001.
[6] J. D. Currey, The mechanical adaptations of bones. Princeton: Princeton
University Press, 1984.
[7] P. D. Delmas, R. P. Tracy, B. L. Riggs, and K. G. Mann, "Identification
of the noncollagenous proteins of bovine bone by two-dimensional gel
electrophoresis," Calcified tissue international, vol. 36, pp. 308-316,
1984.
[8] P. Fratzl and R. Weinkamer, "Nature’s hierarchical materials," Progress
in Materials Science, vol. 52, pp. 1263-1334, 2007.
[9] H. D. Espinosa, J. E. Rim, F. Barthelat, and M. J. Buehler, "Merger of
structure and material in nacre and bone perspectives on de novo
biomimetic materials," Progress in Materials Science, vol. 54, pp. 1059-
1100, 2009.
[10] R. O. Ritchie, "The conflicts between strength and toughness," Nature
Materials, vol. 10, pp. 817-822, 2011.
[11] Y. Shao, H.-P. Zhao, and X.-Q. Feng, "On flaw tolerance of nacre: a
theoretical study," Journal of The Royal Society Interface, vol. 11, p.
20131016, 2014.
[12] H. Gao, B. Ji, I. L. Jäger, E. Arzt, and P. Fratzl, "Materials become
insensitive to flaws at nanoscale: lessons from nature," Proceedings of
the national Academy of Sciences, vol. 100, pp. 5597-5600, 2003.
[13] B. Ji and H. Gao, "Mechanical properties of nanostructure of biological
materials," Journal of the Mechanics and Physics of Solids, vol. 52, pp.
1963-1990, 2004.
[14] B. Ji and H. Gao, "A study of fracture mechanisms in biological nanocomposites
via the virtual internal bond model," Materials Science and
Engineering: A, vol. 366, pp. 96-103, 2004.
[15] B. Ji, H. Gao, and K. Jimmy Hsia, "How do slender mineral crystals
resist buckling in biological materials?," Philosophical Magazine
Letters, vol. 84, pp. 631-641, 2004.
[16] B. Ji, H. Gao, and T. Wang, "Flow stress of biomorphous metal–matrix
composites," Materials Science and Engineering: A, vol. 386, pp. 435-
441, 2004.
[17] B. Ji and H. Gao, "Elastic properties of nanocomposite structure of
bone," Composites science and technology, vol. 66, pp. 1212-1218,
2006.
[18] R. A. Robinson, "An electron-microscopic study of the crystalline
inorganic component of bone and its relationship to the organic matrix,"
The Journal of Bone & Joint Surgery, vol. 34, pp. 389-476, 1952.
[19] R. A. Robinson and M. L. Watson, "Collagen‐crystal relationships in
bone as seen in the electron microscope," The anatomical record, vol.
114, pp. 383-409, 1952.
[20] R. A. Robinson and M. L. Watson, "Crystal-collagen relationships in
bone as observed in the electron microscope. III. Crystal and collagen
morphology as a function of age," Annals of the New York Academy of
Sciences, vol. 60, pp. 596-630, 1955.
[21] Z. Molnar, "Additional observations on bone crystal dimensions," Clin.
Orthop, vol. 17, pp. 38-42, 1960.
[22] A. S. Posner, "Crystal chemistry of bone mineral," Physiological
reviews, vol. 49, pp. 760-792, 1969.
[23] J. Moradian-Oldak, S. Weiner, L. Addadi, W. Landis, and W. Traub,
"Electron imaging and diffraction study of individual crystals of bone,
mineralized tendon and synthetic carbonate apatite," Connective tissue
research, vol. 25, pp. 219-228, 1991.
[24] W. Landis, M. Song, A. Leith, L. McEwen, and B. McEwen, "Mineral
and organic matrix interaction in normally calcifying tendon visualized
in three dimensions by high-voltage electron microscopic tomography
and graphic image reconstruction," Journal of structural biology, vol.
110, pp. 39-54, 1993.
[25] V. Ziv and S. Weiner, "Bone crystal sizes: a comparison of transmission
electron microscopic and X-ray diffraction line width broadening
techniques," Connective tissue research, vol. 30, pp. 165-175, 1994.
[26] W. Landis, "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, vol. 16, pp. 533-544, 1995.
[27] M. A. Rubin, I. Jasiuk, J. Taylor, J. Rubin, T. Ganey, and R. P.
Apkarian, "TEM analysis of the nanostructure of normal and
osteoporotic human trabecular bone," Bone, vol. 33, pp. 270-282, 2003.
[28] T. Hassenkam, G. E. Fantner, J. A. Cutroni, J. C. Weaver, D. E. Morse,
and P. K. Hansma, "High-resolution AFM imaging of intact and
fractured trabecular bone," Bone, vol. 35, pp. 4-10, 2004.
[29] H. Gao, "Application of fracture mechanics concepts to hierarchical
biomechanics of bone and bone-like materials," International Journal of
Fracture, vol. 138, pp. 101-137, 2006.
[30] Z. Zhang, Y. W. Zhang, and H. Gao, "On optimal hierarchy of loadbearing
biological materials," Proceedings of the Royal Society B:
Biological Sciences, vol. 278, pp. 519-525, 2011.
[31] B. Borah, G. J. Gross, T. E. Dufresne, T. S. Smith, M. D. Cockman, P.
A. Chmielewski, et al., "Three-dimensional microimaging (MRμI and
μCT), finite element modeling, and rapid prototyping provide unique
insights into bone architecture in osteoporosis," The anatomical record,
vol. 265, pp. 101-110, 2001.
[32] H. Gong, M. Zhang, L. Qin, and Y. Hou, "Regional variations in the
apparent and tissue-level mechanical parameters of vertebral trabecular
bone with aging using micro-finite element analysis," Annals of
biomedical engineering, vol. 35, pp. 1622-1631, 2007.
[33] X. N. Dong, T. Guda, H. R. Millwater, and X. Wang, "Probabilistic
failure analysis of bone using a finite element model of mineral–collagen
composites," Journal of biomechanics, vol. 42, pp. 202-209, 2009.
[34] Q. Luo, R. Nakade, X. Dong, Q. Rong, and X. Wang, "Effect of
mineral–collagen interfacial behavior on the microdamage progression
in bone using a probabilistic cohesive finite element model," Journal of
the mechanical behavior of biomedical materials, vol. 4, pp. 943-952,
2011.
[35] F. Yuan, S. R. Stock, D. R. Haeffner, J. D. Almer, D. C. Dunand, and L.
C. Brinson, "A new model to simulate the elastic properties of
mineralized collagen fibril," Biomechanics and Modeling in
Mechanobiology, vol. 10, pp. 147-160, 2011.
[36] T. J. Vaughan, C. T. McCarthy, and L. M. McNamara, "A three-scale
finite element investigation into the effects of tissue mineralisation and
lamellar organisation in human cortical and trabecular bone," Journal of
the Mechanical Behavior of Biomedical Materials, vol. 12, pp. 50-62,
2012.
[37] A. Barkaoui and R. Hambli, "Nanomechanical properties of mineralised
collagen microfibrils based on finite elements method: biomechanical
role of cross-links," Computer methods in biomechanics and biomedical
engineering, vol. 17, pp. 1590-1601, 2014.
[38] A. Barkaoui and R. Hambli, "Finite element 3D modeling of mechanical
behavior of mineralized collagen microfibrils," Journal of Applied
Biomaterials and Biomechanics, vol. 9, pp. 199-205, 2011.
[39] C. C. Chen and R. Clifton, "Asymptotic solutions for wave propagation
in elastic and viscoelastic bilaminates," in Midwestern Mechanics
Conference, 14 th, Norman, Okla, 1975, pp. 399-417. [40] Y. Oved, G. E. Luttwak, and Z. Rosenberg, "Shock wave propagation in
layered composites," Journal of Composite Materials, vol. 12, pp. 84-96,
1978.
[41] N. Chandra, C. Xianglei, and A. Rajendran, "The effect of material
heterogeneity on the shock response of layered systems in plate impact
tests," Journal of composites technology & research, vol. 24, pp. 232-
238, 2002.
[42] S. Zhuang, G. Ravichandran, and D. E. Grady, "An experimental
investigation of shock wave propagation in periodically layered
composites," Journal of the Mechanics and Physics of Solids, vol. 51,
pp. 245-265, 2003.
[43] X. Chen and N. Chandra, "The effect of heterogeneity on plane wave
propagation through layered composites," Composites science and
technology, vol. 64, pp. 1477-1493, 2004.
[44] X. Chen, N. Chandra, and A. Rajendran, "Analytical solution to the plate
impact problem of layered heterogeneous material systems,"
International Journal of Solids and Structures, vol. 41, pp. 4635-4659,
2004.
[45] I. Jäger and P. Fratzl, "Mineralized collagen fibrils: a mechanical model
with a staggered arrangement of mineral particles," Biophysical Journal,
vol. 79, pp. 1737-1746, 2000.
[46] H. A. Lowenstam and S. Weiner, On biomineralization. Oxford: Oxford
University Press, 1989.
[47] S. J. Eppell, W. Tong, J. L. Katz, L. Kuhn, and M. J. Glimcher, "Shape
and size of isolated bone mineralites measured using atomic force
microscopy," Journal of orthopaedic research, vol. 19, pp. 1027-1034,
2001.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70599", author = "M. Qwamizadeh and K. Zhou and Z. Zhang and YW. Zhang", title = "Dynamic Behavior of the Nanostructure of Load-bearing Biological Materials", abstract = "Typical load-bearing biological materials like bone,
mineralized tendon and shell, are biocomposites made from both
organic (collagen) and inorganic (biomineral) materials. This
amazing class of materials with intrinsic internally designed
hierarchical structures show superior mechanical properties with
regard to their weak components from which they are formed.
Extensive investigations concentrating on static loading conditions
have been done to study the biological materials failure. However,
most of the damage and failure mechanisms in load-bearing
biological materials will occur whenever their structures are exposed
to dynamic loading conditions. The main question needed to be
answered here is: What is the relation between the layout and
architecture of the load-bearing biological materials and their
dynamic behavior? In this work, a staggered model has been
developed based on the structure of natural materials at nanoscale and
Finite Element Analysis (FEA) has been used to study the dynamic
behavior of the structure of load-bearing biological materials to
answer why the staggered arrangement has been selected by nature to
make the nanocomposite structure of most of the biological materials.
The results showed that the staggered structures will efficiently
attenuate the stress wave rather than the layered structure.
Furthermore, such staggered architecture is effectively in charge of
utilizing the capacity of the biostructure to resist both normal and
shear loads. In this work, the geometrical parameters of the model
like the thickness and aspect ratio of the mineral inclusions selected
from the typical range of the experimentally observed feature sizes
and layout dimensions of the biological materials such as bone and
mineralized tendon. Furthermore, the numerical results validated with
existing theoretical solutions. Findings of the present work emphasize
on the significant effects of dynamic behavior on the natural
evolution of load-bearing biological materials and can help scientists
to design bioinspired materials in the laboratories.", keywords = "Load-bearing biological materials, nanostructure,
staggered structure, stress wave decay.", volume = "9", number = "9", pages = "1589-8", }
