Anisotropy is an essential attribute exhibited by most biological materials. Based on the recent work on anisotropy of a wide range of crystals and polycrystals, we propose an appropriate measure (A) to quantify the extent of elastic anisotropy in biomaterials by accounting the tensorial nature (both stiffness-based and compliance-based) of their elastic properties. Next, we derive a relationship between A and an empirically defined existing measure. Also, the preceding measure is used to quantify the extent of anisotropy in select biological materials that include bone, dentitional tissues, and a variety of woods. Our results indicate that woods are an order of magnitude more anisotropic than hard tissues and apatites. Finally, based on the available data, it is found that the anisotropy in human femur increases by over 40% when measured between 30% and 70% of the total femur length.

References

References
1.
Li
,
Y.
, and
Zeng
,
Z.
, 2009,
“New Potential Super-Incompressible Phase of ReN2,”
Chem. Phys. Lett.
,
474
, pp.
93
96
.
2.
Zhang
,
X.-D.
,
Jiang
,
Z.-Y.
,
Hou
,
Y.-Q.
, and
Li
,
L.-S.
, 2009,
“Elastic Properties of NaXH4 (X = B, Al)
,
J. Phys.: Condens. Matter
,
21
, p.
275401
.
3.
Berryman
,
J. G.
, 2010,
“Poroelastic Measurement Schemes Resulting in Complete Data Sets for Granular and Other Anisotropic Porous Media,”
Int. J. Eng. Sci.
,
48
, pp.
446
459
.
4.
Ranganathan
,
S. I.
, and
Ostoja-Starzewski
,
M.
, 2008a,
“Universal Elastic Anisotropy Index,”
Phys. Rev. Lett.
,
101
, p.
055504
.
5.
Ranganathan
,
S. I.
, and
Ostoja-Starzewski
,
M.
, 2008b,
“Scaling Function, Anisotropy and the Size of RVE in Elastic Random Polycrystals,”
J. Mech. Phys. Solids
,
56
, pp.
2773
2791
.
6.
Ranganathan
,
S. I.
, and
Ostoja-Starzewski
,
M.
, 2009,
“Towards Scaling Laws in Random Polycrystals,”
Int. J. Eng. Sci.
,
47
, pp.
1322
1330
.
7.
Chung
,
D. H.
, and
Buessem
,
W. R.
, 1968,
Anisotropy in Single Crystal Refractory Compounds
,
F. W.
Vahldiek
and
S. A.
Mersol
, eds.,
Plenum
,
New York
, Vol.
2
, p.
217
.
8.
Katz
,
J. L.
, and
Meunier
,
A.
, 1987,
“The Elastic Anisotropy of Bone,”
J. Biomech.
,
20
, pp.
1063
1070
.
9.
Katz
,
J. L.
, and
Meunier
,
A.
, 1990,
“A Generalized Method for Characterizing Elastic Anisotropy in Solid Living Tissues,”
J. Mater. Sci.: Mater. Med.
,
1
, pp.
1
8
.
10.
Katz
,
J. L.
,
Kinney
,
J. H.
,
Spencer
,
P.
,
Wang
,
Y.
,
Fricke
,
B.
,
Walker
,
M. P.
, and
Friis
,
E. A.
, 2005,
“Elastic Anisotropy of Bone and Dentitional Tissues,”
J. Mater. Sci.: Mater. Med.
,
16
, pp.
803
806
.
11.
Katz
,
J. L.
,
Spencer
,
P.
,
Wang
,
Y.
,
Misra
,
A.
,
Marangos
,
O.
, and
Friis
,
L.
, 2008,
“On the Anisotropic Elastic Properties of Woods,”
J. Mater. Sci.
,
43
, pp.
139
145
.
12.
Rapoff
,
A. J.
, 2006,
“Orthotropic Index for Bone,”
J. Mater. Sci.: Mater. Med.
,
17
, pp.
803
805
.
13.
Ferrari
,
M.
, 1991,
“Asymmetry and the High Concentration Limit of the Mori-Tanaka Effective Medium Theory,”
Mech. Mater.
,
11
, pp.
251
256
.
14.
Walpole
,
L. J.
, 1969,
“On the Overall Elastic Moduli of Composite Materials,”
J. Mech. Phys. Solids
,
17
, pp.
235
251
.
15.
van Buskirk
,
W. C.
and
Ashman
,
R. B.
, 1981, “The Elastic Moduli of Bone,”
Mechanical Properties of Bone
,
S.
Cowin
, ed.,
ASME
,
New York
, pp.
131
143
.
You do not currently have access to this content.