This document discusses stresses, strains, and mechanical properties of materials as they relate to biomechanics and bone behavior. It contains the following key points: 1. Stresses are defined as forces per unit area and strains are defined as deformations or changes in length. Normal stresses act perpendicular to a plane, while shear stresses act parallel. 2. Materials experience different types of stresses and strains including compression, tension, bending, torsion, and shear. Stress-strain curves are used to characterize elastic behavior, yield points, and failure properties. 3. Bone is a non-homogeneous, anisotropic, viscoelastic composite material that can withstand different loading rates and stresses in longitudinal and transverse directions. Its

1.  Stresses = local force intensities
(Dimensions = Force per unit area, N/m2 or
Pa).
δ=F/A
 Strains = Local deformations
(Dimensions = length per length).
ε = ∆L/L.

2.  Normal stress =
Force per unit area
acting
perpendicular to a
given plane (MPa).
 Shear stress =
Force per unit area
acting parallel to a
given plane (MPa).

3.  Strain caused by
compressive stresses.
• Strain caused by
shear stresses.

5.  Equal and opposite
loads are applied
outwards from the
surface of the
structure.
 The structure will be in
form of lengthening
and narrowing.
 The forces are co-
planar (same plane)
and colinear,

6.  equal and opposite two
forces applied toward the
surface of the segment
causing strain in the form
of shortening and
widening.
 In pure compression these
forces are co-planar (same
plane) and colinear,

7.  Both tension and compression are normal
stresses because they are perpendicular to
the cross section and directed either away
from or towards the centre of the segment.
 When tensile stresses are applied to the
segment the resistance between the
molecules of this segment (intermolecular
resistance) decrease more than if it is
compared with application of the compressive
stresses.

8.  There is two types of bending
are generally referred to as
pure bending (four point) and
three point bending.
 produce a convex surface on
one side of the beam and a
concave surface on the other
side.
 The material on the concave
side of the beam will be
subjected to compressive
strains, while the material on
the convex side will be
subjected to tensile strains.

9.  The material on the surface of the beam
experiences the highest stresses.
 If the bending force is increased until the bar
begins to fracture, fracture will be initiated at
the surface of the beam, where the stresses
are highest.

10. Biomechanical Behavior of Bone (e)
Two types of bending tests: A. Three-point
bending and B. Four-point bending

11.  Combined compressive
and bending loads.
 High compressive
stresses will be created
on one side of the bar
while the other side of
the bar will experience
either lower tensile
stresses.

12.  Torsion load tend to twisted the
bar about its axis.
 it can be demonstrated that
significant tensile and
compressive stresses are
present on oblique planes
through the bar.
 If a bar is subjected to torsional
loading and fracture a long an
oblique or spiral plane, then it
can be assumed that failure
occurred primarily because of
high tensile stresses on this
plane.

13.  Shear strain on any transverse section
through the bar.
 The shear strains are associated with shear
stresses in a transverse and axial direction.
The magnitude of the shear stresses and
strains varies linearly with the distance from
the central axis of the bar such that the
material on the surface of the bar experiences
the greatest shear stresses.

14.  The relationship between the applied
force (F) and the increase in the length of
the bar (∆ L) can be demonstrated on a
force- deformation curve.
 The initial portion of the force-
deformation curve is essentially linear.
This linear portion of the curve
represents the elastic behavior of the
structure.
 If load is applied in the elastic region of
the curve and is then released, the bar
will return to its original length. If
sufficient force is applied, however,
internal damage will created in the
structure and the bar will begin to yield.
Yield occurs at point Y on the force-
deformation curve.

15.  Further loading beyond the yield point will
result in marking deformation until total
fracture occurs, point U .
 The total energy absorbed by the bar during
the fracture process is represented by the
area under the force- deformation curve.

16.  Mechanical properties are
best described by strength
and stiffness.
 Strength is often described
as the load at the yield
point, while stiffness (k) is
the slope of the
load/deformation curve…

17.  The first part of the curve (linear part)
indicates “elastic behavior” or “reversible
behavior”.
 The bone has a viscoelastic property when it
is subjected to loading and unloading cycles.
 Energy is stored during loading then released
completely during unloading.
 The linear part of the curve obeys Hook’s law
which states that “Stress is directly
proportional to the strain in the elastic region
of the stress-strain curve”.

18. 9.6 Common Characteristics of Biological Tissues


• Living tissues are very difficult to determine material properties.
• Composite materials
• Nonhomogeneous and anisotropic
• Collagen : to withstand axial tension
• Elastin: elastic
 Biological Tissues
1 2

19. 9.7 Biomechanics of Bone
• Primary structural element of the human body.
9.7.1 Composition of bone
• Composite material
• Cortical or compact bone
• Cancelleous, trabecular or spongy bone
• Periosteum

20. 9.7 Biomechanics of Bone (continued)
9.7.2 Mechanical properties of bone
• Nonhomogeneous because of various cells and organic and inorganic substances
• Anisotropic
• Can resist rapidly applied loads better than slowly applied loads. (Stiffer and stronger at higher strain rates)
• Viscoelastic
(MPa)

2
10


0
150
100
50
1 2 3
Y

GPa
17
1 
E
GPa
9
.
0
2 
E
u

026
.
0
with
MPa
128
MPa
110






u
Y
1
s
05
.
0 




21. • Fast loading vs. Slow loading


Fast loading
slow loading
)
(high ε

)
(low ε

• Longitudinal loading vs. Transverse loading


Longitudinal
loading
Transverse
loading
Longitudinal Transverse
tension compression shear tension compression
Ultimate strength (MPa) 133 193 68 51 133
Elastic modulus (GPa) 17.0 11.5
Shear modulus (GPa) 3.3

22. Shape of articulating surface
Stress distribution in the femoral neck subjected to bending
Gluteus medius
muscle

23. Biomechanical Behavior of Bone (i)
Theory of muscle fatigue as a cause of stress fracture in lower
extremity skeletal components