Biomedical Engineering Reference
In-Depth Information
Fig. 5.16  Deformation in all three directions of an elastic material subjected to a force in ten-
sion along the x -axis. The initial body shape expands in the x- direction but contracts in the y- and
z- directions
Deformation in all three directions caused by an axial force load is referred to as
the Poisson effect and for isotropic materials, the Poisson's ratio, ν is
ε
lateral strain
axial strain
ε
y
(5.28)
z
v
=
=
=
ε
ε
x
x
which measures the change in shape in the lateral direction in relation to the change
in shape in the axial direction.
5.3.2
Plane Stress
Stresses occurring on arterial walls can be assumed as a plane stress, where we
assume the walls are subjected to parallel blood shear forces. By using this assump-
tion the stress analysis is simplified considerably into a 2D analysis (Fig. 5.17 ).
The stress-strain relations are given here without its derivation (a full description
can be found in Hutton 2000) as,
σ
1
v
0
10
ε
x
x
E
(5.29)
σ
=
v
ε
y
y
2
1
v
00 1
2
v
τ
γ
xy
xy
which can be rewritten as
{ }
{ }
σ = D
[]
ε
where σ is a column matrix of stress components, D is the elastic material property
matrix for plane stress, and ε is the column matrix of strain components. The strain
energy per unit volume, u e , becomes
 
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