Biomedical Engineering Reference
In-Depth Information
The strain,
ε
, is the ratio of the change of length to the original length of an
object:
ε ¼
Δ
L
L
i
¼
j
L
f
L
i
j
;
(7.2)
L
i
where
L
i
and
L
f
mean initial and final length and
L
, the change in the length which
can be positive or negative, depending on whether the applied force is tension or
compression, and it is always used in modulus, with a positive sign. Note that strain
is a dimensionless quantity, related to the deformation.
For very small stresses,
Δ
σ
is proportional to the strain,
ε
. The constant of
proportionality is called the elasticity modulus and is given by:
Elasticity modulus
¼
stress
=
strain
¼ σ=ε:
(7.3)
The unit of the elasticity modulus is the same as the stress, i.e., pascal (Pa),
because the strain is dimensionless.
7.4 Modulus of Elasticity
The elastic properties of solids are always described in terms of the modulus of
elasticity that varies from material to material, but does not depend on the size of
the object. Here we will treat two elasticity moduli of interest to us:
(a) Young's modulus that measures the resistance of solids relative to the change in
their length.
(b) Shear modulus that measures the resistance to the sliding motion of different
plane layers of a solid.
7.4.1 Young's Modulus Y
In this case,
T
A
ΔL
¼
σ
Y
ε
¼
L
i
;
(7.4)
T
is the tension applied along the cylinder as shown in Fig.
7.1
and
A
is the cross-
sectional area of the cylinder. The larger is Young's modulus, the smaller is the
elasticity of the material regarding the change in the length by tension or by
compression, or in other words, it is more difficult to change its length.
