Biomedical Engineering Reference
In-Depth Information
Fig. 8.1 Cartoon of the total loading for a cube of material (only a cross-section is visible)
representing a mechanically loaded portion of a saturated anisotropic compressible poroelastic
medium. The pores in this porous material are represented by ellipsoids which appear as ellipses in
the cross-section; however pore shape and pore connectivity is unrestricted. The pressure on the
walls of the ellipse is indicated by the arrows perpendicular to the walls, t ¼pn on O p , where O p
represents the boundaries of the pores. The tractions on the exterior boundary, t ¼ T n on O o ,
where O o represents the outer boundary of the porous medium, are indicated by the arrows slanted
with respect to the lines forming the boundary of the square and acting on that boundary
where O o and O p represent the outer boundary of the porous medium and the pore
boundary, respectively. This loading is illustrated for a cube of material (only a
cross-section is visible) in Fig. 8.1 . The pores in this porous material are represented
by ellipsoids which appear as ellipses in the cross-section of Fig. 8.1 . The pressure
on the walls of the ellipse is indicated by the arrows perpendicular to the walls,
pn on O p .
The tractions on the exterior boundary, t
n on O o , are indicated by the
arrows slanted with respect to the lines forming the boundary of the square and
acting on that boundary.
The first key to this proof is to treat the loading ( 8.9 ) as the superposition of two
separate loadings:
¼
T
t
¼
pn on O o ;
t
¼
p n on O p ;
loading
ð
8
:
10
Þ
(8.10)
and
t
¼
T
n
þ
pn on O o ;
t
¼
0onO p ;
loading
ð
8
:
11
Þ:
(8.11)
The loading ( 8.10 ) is illustrated in Fig. 8.2a ; this loading creates a uniform
hydrostatic pressure p in the matrix material and, consequently, a uniform strain if
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