Biomedical Engineering Reference
In-Depth Information
Fig. 6.1
Stress-strain diagram of a typical human cortical bone with strain percentage along the
horizontal axis and stress in Mega Pascal along the vertical axis. When forces are exerted in the
longitudinal direction instead of the transverse, the material can withstand more stress before it
reaches the point of failure, characterized by the longer dotted graph. Also apparent is the toughness
of the cortical bone material during compression when compared to tension. Inspired by Ref. [
8
]
shear
strain. Normal strain occurs when the displacement happens along the material
fibers and is formally written as:
l
1
−
=
Δ
l
0
l
l
0
=
l
0
where
l
is the displacement in length and
l
0
is the initial length before any
deformation occurred. A negative outcome represents a compressive strain, while
a positive outcome represents a tensile strain. For shear strains, denoted
Δ
ʳ
, deforma-
ʳ
tions made by shear forces are measured.
represents the tangent between relative
displacements of shear forces.
Studying the relationship between stress and strain provides insight into the intrin-
sic behavior of an object under different load conditions. Figure
6.1
shows a typical
stress-strain diagram of the human cortical bone.
When an object experiences tensile or compressive forces in one direction it can
contract or expand in other directions that lie orthogonal to the direction of the
applied forces. This characteristic is known as the
Poisson effect
. This effect can be
measured by taking the ratio between the change in normal strain with the change in
shear strain and is referred to as
Poisson's ratio
, denoted
ʽ
. Formally it is written as:
