Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 86

or anticlockwise. This last measurement depends on the
observation point. Imagine looking at a spinning wheel
from one end of the rotational axis; if this movement is
clockwise, when we turn to the other side of the wheel and
look at it, the rotational movement will be anticlockwise.
To avoid such indetermination it is generally agreed that
the observer will look at the axis in the sense of plunge,
that is, looking down the axis. In the case of a horizontal
rotation axis, the position of the observer has to be
specified.

depicting two mutually perpendicular black lines and an
inner circle as decoration, is represented. In (b) the square
has been deformed by flattening (pure shear), in (c) by
shearing (simple shear), and in (d) by volume loss or
dilation. Note that (b), (c), and (d) have suffered a homo-
geneous strain, as the original straight parallel lines remain
parallel and straight after deformation and also the circle
has been transformed into a perfect ellipse, whereas (e)
and (f) suffered an inhomogeneous strain as the original
straight lines became curved as in (e) or originally parallel
lines converge or diverge in the deformed state as in (f).
Note also that the circle has not become an ellipse but
shows an irregular shape in (e) and (f). A good example of
inhomogeneous strain is the generation of folds
(Section 4.16) as the originally straight lines of rock layers
become curved. In Nature when tectonic deformation
takes place, nonhomogeneous deformations are most
likely to occur and strain analysis cannot be used to predict
deformation following simple mathematical rules.
Nonetheless, inhomogeneous deformed terrains can be
analyzed separately by dividing them into discrete homo-
geneous domains. Then, the whole deformation can be
evaluated and strain gradients assessed.
In homogeneous strain different parameters are used to
state the differences in the length of lines and angular
changes between lines. To determine changes in length of
straight lines, two of the most commonly used parameters

3.14.3 Nonrigid deformation

The evaluation of changes in shape and volume of objects
or rock bodies is called strain analysis . This technique is a
useful tool in kinematics and can be used if the original
shape and size of objects in the rock are known. Distortion
is a nonrigid deformation (Figs 3.77e) which causes the
objects or rocks to change shape, preserving the original
volume. Displacement vectors can have various orienta-
tions and magnitudes. Dilation is a displacement which
produces a change in volume (Fig. 3.77d). The object can
be enlarged or contracted so that the original regularly
spaced points in the object are separated or get closer but
they still preserve the original proportions so that no
change in the shape of the object is produced. The dis-
placement vectors converge or diverge radially from a
point in a regular way.

(a)

(b)

3.14.4 Homogeneous strain analysis

Strain (generically represented as ) can be homogeneous or

inhomogeneous (Fig. 3.80) and, as with stresses, can be
analyzed in 2D or 3D. Homogeneous strain is constant
along the whole object. This means that all small portions
of the deformed body have the same deformation propor-
tions as the whole body. Homogeneous strain satisfies two
conditions: (i) originally straight lines in the unstrained
object remain straight after deformation, which applies
also in 3D, where originally plane surfaces remain plane
after deformation; and (ii) parallel lines or surfaces in the
original object remain parallel after deformation. A conse-
quence is that in 2D any circular object is transformed into
a perfect ellipse and in 3D any sphere is converted into a
perfect ellipsoid. Deformation is inhomogeneous when
there are variable gradients of displacement through the
object and so straight lines are changed into curved lines
and originally parallel lines converge or diverge after being
strained. In Fig. 3.80 a nondeformed square object,

(c)

(d)

(e)

(f )

Fig. 3.80 Homogeneous and inhomogeneous strain. (a) is the object
before deformation; (b), (c), and (d) show homogeneous strain; and
(e) and (f ) inhomogeneous strain.