Geoscience Reference
In-Depth Information
Fig. 5.3
Strain modes and rotation, and their measures: upper graphs, extension and contraction;
lower graphs, shear and rotation. Note that shear and rotation are drawn for positive signs
Example 5.2.
Simple shear is given by
o
d
x
o
y
6
¼ 0
, with other displacement derivatives equal
to zero. Then the xy shear strain is
2
o
d
x
2
o
d
x
and the rotation around z-axis is
.Inpure
o
y
o
y
o
y
¼
o
d
y
shear, we have
o
d
x
o
x
6
¼ 0
, with other displacement derivatives equal to zero. Then the
xy shear strain is
o
d
x
o
y
and the rotation is zero. In both cases the spherical strain is zero
(tr
= 0).
Velocity equals the rate of displacement, and consequently the strain-rate and the
rotation rate or the vorticity are obtained from the velocity gradient just as strain and
rotation were obtained from the displacement gradient.
ʵ
5.1.3 Rheological Models
The basic models are linear elastic or Hooke
'
s medium, linear viscous or Newton
'
s
medium, and ideal plastic or St. Venant
'
s medium (e.g., Mase 1970; Hunter 1976). One-
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