Deformation, stress and strain - Introducing Tectonics, Rock Structures and Mountain Belts - page 23

Z

Z

X

4

Y

X

Y

Y

B distortion

A dilation

X

22 23

B uniaxial extension:

X>Y=Z

Z

A principal strain

axes, X, Y, Z

rotation

original length
new length

Z

Z

X

X

D extension

C shear strain

Figure 4.4 Types of strain. A. Dilation = volume change; B. Distortion = shape change; C.
Shear strain: the distortional strain produced by a shear couple; D. Strain in one dimension:
the extension = the change in length (pink) divided by the original length (yellow).

Y

Y

C uniaxial flattening:

X=Y>Z

D plane strain:
X>Y=1>Z

either an increase or decrease, is dif-
ficult to measure in rocks, although we
know that volume decreases are associ-
ated with large increases in lithostatic
pressure by, for example, reducing pore
space, expelling fluids and replacing
low-density minerals by their high-
density equivalents. Changes in shape,
on the other hand, lead to character-
istic fabrics (rock textures arising from
deformation) that are obvious and
potentially measurable ( see Chapter
7). Such changes can consist either of
a distortion - that is, a shape change
(Figure 4.4B), or a rotation, or some
combination of both. Distortional strain
in response to a shear stress involves
rotation of elements of the original
unstrained body, and is termed shear
strain or rotational strain (Figure 4.4C).

Thus a body can be said to have
been shortened, say, by one-tenth, or
10%. In other words, a strain is just
a number, with no attached units.
In three dimensions, the strain in a
body whose original shape is known
can in theory be measured by the
amounts by which the lengths of meas-
ured lines in the body have changed.
Although the strained body may have
been any shape prior to the deforma-
tion, it is more convenient in practice
to describe the strain as if the original
body was equidimensional. The strain
can then be described with reference
to three mutually perpendicular axes
through the centre of the strained body,
parallel respectively to the maximum,
intermediate and minimum extensions.
These axes are termed the principal
strain axes (Figure 4.5A-D). It is usual
to describe the strain as if the original
body was a sphere, and the strained
body an ellipsoid. Depending on the
ratio of the principal strain axes to each
other, the strain ellipsoid may be either
prolate , shaped like a rugby ball (Figure
4.5B), oblate or pancake-shaped (Figure

X

X

Z Z

E progressive shear strain

Figure 4.5 A-D. Co-axial strain in three
dimensions affecting an initial sphere: A. The
three principal strain axes X, Y, and Z. B. Uniaxial
extension: the maximum strain axis (X) is greater
than the intermediate (Y) and minimum (Z)
axes, which are equal; C. Uniaxial flattening:
the minimum strain axis (Z) is smaller than the
intermediate (Y) and maximum (X) axes, which
are equal; D. Plane strain: the intermediate
strain axis (Y) is unchanged, and all the strain
is in the plane of X and Z. E. Progressive shear
strain: in the XZ plane, the strain axes X and Z
progressively rotate with increasing strain.

4.5C), or what is termed plane strain ,
where the intermediate strain axis is
unchanged (Figure 4.5D); or indeed any
intermediate shape between these end-
member types. Prolate ellipsoids cor-
respond to extensional deformation ,
where the maximum principal strain is
appreciably greater than the other two
strain axes, which are approximately
equal. Oblate ellipsoids correspond
to flattening deformation , where the

The description of strain
In one dimension, the amount of
strain is measured as an extension,
which can be either positive or nega-
tive and is the proportionate amount
by which the length of the original
body has been changed (Figure 4.4D).