Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 13

Fig. 1.7 Schematic diagram
showing the conceptual
model of the leg used to
predict the runner's
performance on a compliant
track. Descending commands
from the cortex, brain stem,
and spinal centers (acting to
crank the rack and pinion) are
assumed to be separate from
the mechanical properties of
the muscles plus local reflexes
( parallel spring and dashpot ).
From McMahon and
Greene ( 1979 )

experiment that Darcy did is shown in Fig. 1.8 . A layer of sand of thickness L is
supported on a stiff wire mesh with mesh openings larger than the size of the typical
fluid passages through the sand layer. On top of the layer of sand is a reservoir of
water maintained at a constant height h. The constancy of this head is maintained by
providing a continuous supply of water to the reservoir and providing an over flow
run-off passage. The domain at the bottom of the sand layer is open to the air again
as is the upper surface of the water reservoir; the air pressure is p o . Thus the
decrease in water pressure across the sand layer is from p + p o where p

gh ,
to p o . The pressure gradient across the layer is then p / L , where L is the layer
thickness. The volume flux of water, that is to say, the volume of water coming
out of the sand layer per unit area per unit time, is denoted by q . If the cross-
sectional area of the sand layer is denoted by A o , then the volume per unit time is
A o (d w /d t ) where d w /d t is the rate at which the surface of the water in the catchment
basin of cross-sectional area A o below the sand layer is filling with water. The
volume flux q through the layer is then given by q

¼ r

(dw/d t ).
Darcy found that the volume flux q through the sand layer was proportional to the
pressure gradient across the sand layer, p / L . The constant of proportionality

¼ (1/ A o ) A o (d w /d t ) ¼

is
called the permeability and it is calculated in the experiment described by the
formula

k

k ¼ qL / p . Replacing p / L by the gradient, ( p / L ), Darcy's law is written

∂ ∂