Mechanical properties of
Cortical and Cancellous Bone
Schematic drawing showing microstructure of cortical and cancellous bone.
From Nordin & Frankel.
1a
Anisotropy of bone
Example: the femoral shaft (From Nordin & Frankel)
1b
1
Anisotropy of bone specimens is determined by local variations in
trabecular shape, density and orientation, as well as by mineral
density variation, which are constituted, according to Wolff s law,
by the internal stress fields.
From Kosmahl.
1c
Ultimate stress for human adult cortical bone specimens.
Shaded area indicates ultimate stress for trabecular bone.
From Nordin & Frankel.
1d
Illustration of a bone test specimen and a stress-strain
curve resulting from a tensile test
2a
2
Two types of bending tests can be taken: A. Three-point bending
and B. Four-point bending.
From Nordin & Frankel.
2b
Maximal stress at the surface of bone for bending or torsion can be
estimated for bone with circular shape using the following relations.
2c
Loading modes for bone specimens
From Nordin & Frankel.
2d
3
Behavior of bone in uniaxial tension compared
to other common materials
3
Illustration of the strain-rate sensitivity of cortical bone
(from a canine tibia). As the strain-rate increases, the
stiffness and ultimate stress increases.
From Nordin & Frankel.
4
Illustration of the different types of loading that can be impos ed on bone.
Bones can be subjected to axial compression, axial tension, torsion,
shear, bending, or any combination of these.
5
4
Because bones can resist more
compression than tension, they typically
fail in tension.
For this reason, we theorize that
osteoporotic fractures of the femoral
neck happen by virtue failure at the
superior aspect of the femoral neck
(where tension develops as a result of
weight-bearing during locomotion).
From Kosmahl.
6a
Illustration of the effect
that muscle forces can
have on bone stresses
6b
Effect of Aging:
Vertebral cross-sections from autopsy specimens of
young (A) and old (B) bone show a marked reduction in
trabecular bone in the later. Bone reduction with aging
(C) is schematically depicted
7
5
Effect of Aging: Stress-strain curves for samples of adult
human tibia of two widely differing ages tested in tension
8
Illustration of an Injury Threshold dependent on the magnitude of the load and the
number of times the load is applied. The curve indicates that the bone can withstand
n1 cycles of stress σ 1 and n 2 cycles of the lower stress σ 2.
9
Viscoelasticity of bone: strain-rate dependency.
10
6
Creep and recovery.
Stress σ and strain ε vs. time t.
From Lakes.
11
Stress relaxation in a viscoelastic material
12
This animation shows creep of a rod (60
cm long, 3 mm diameter) of polymethyl
methacrylate
(PMMA)
in
cantilever
bending at room temperature, ~20 deg. C.
Images of the free rod end were captured
after ~1, 10, 100, 1,000, 104, 105 seconds,
106 seconds (about 11 days), 107 seconds
(almost four months).
From Lakes.
13
7
Regions of creep behavior.
Strain e vs. time t, for different load levels.
14
Stress and strain vs. time t (in arbitrary units) in
dynamic loading of a viscoelastic material. From Lakes.
15
Stress vs. strain for linearly viscoelastic material under
oscillatory load history. From Lakes.
8
16
MOTOR
BONE VISCOELASTICITY
Torsion of a bone specimen:
-Specimen with circular cross-section
-Loaded with cyclic sinusoidal torsion
-Shear developing due to torsion
-Constant compression for fixing the specimen
|G*|= dynamic shear modulus
Torque-meter
|G*|2 =(G ) 2 +(G ) 2
Strain
G = storage modulus
G = loss modulus
Time
δ=tan-1 (G / G )
Or, phase between sinusoidal load and measured moment
17
Setup for torsion
experiments to
determine the
viscoelasticity of
a bone specimen
From Lakes., J. Biomech. Eng.
18
Viscoelastic behavior of bone under torsion:
Shear modulus vs. time and the loss angle δδ vs. the loading frequency. From
Lakes.
9
19
Viscoelastic behavior of bone: stiffness versus damping for
bone and synthetic materials. From Lakes.
20
Viscoelastic behavior of bone:
loss angle δ versus the loading frequency. From Lakes.
21
From Lakes., J. Biomech. Eng.
10
22
Motion of cement lines between osteons as a cause for
viscoelastic behavior of bone:
Cement lines are compliant (Katz, 1980). Viscous-like cement line
motion gives rise to a portion of the viscoelasticity in bone,
particularly at long times (Lakes and Saha, 1979).
23
11
From Lakes., J. Biomech. Eng.
24
From Lakes., J. Biomech. Eng.
25
From Lakes., J. Biomech. Eng.
26
From Lakes., J. Biomech. Eng.
27
Nanoindentation
technique for bone
tissue elastic modulus
measurements.
From Cowin.
12
28
29
30
31
13
Microtesting techniques for measuring mechanical
properties of cancellous bone tissue. From Cowin.
32
Modulus results for different cortical specimen preparation and testing
conditions using nanoindentation. The subscripts a,b, and c denote the
initial, immediate repeat, and delayed repeat indentation at 500 nm. The
error bars show standard deviations. The moduli of dry specimens are
significantly greater than the wet, and wet and embedded specimens.
From Cowin.
33
Elastic moduli measured by the nanoindentation technique in five
microstructures in eight individual femurs (Dia Ost: Diaphyseal
Osteons; Dia Int: Diaphyseal Interstitial; Neck Ost: Neck Osteons; Neck
Int: Neck Interstitial; Neck Tra: Neck Trabeculae). The error bars indicate
the standard deviation.
From Cowin.
14
34
Estimation of elastic
modulus of cancellous
bone tissue using large
scale
micro-imaging
based finite element
methods
From Cowin.
35
Tissue modulus measured from
4-point-bending microtesting for
cancellous (A) and cortical (B)
bone specimens from human
vertebral bodies of various age
groups. Cortical tissue (2.44 GPa)
is 14% stiffer than cancellous
tissue (2.11 GPa). In addition, the
tissue from the younger age
group (20-40) is stiffer than the
older age groups (55-65 and 7585).
From Cowin.
36
37
15