guided-discovery activities for teaching stress and strain ann bykerk-kauffman california state university, chico abykerk-kauffman@csu

Guided-Discovery Activities for Teaching Stress and Strain
Ann Bykerk-Kauffman
California State University, Chico
[email protected]
Type of Activity : Pencil-and-paper guided-discovery worksheet
Brief description: Helping students discover and come to understand
essential and useful aspects of stress and strain theory without
asking them to derive the theory.
Context
Type and level of course in which I use this activity or assignment:
undergraduate required structural geology course for majors
Skills and concepts that students must have mastered before beginning
the activity: Students should have seen enough examples of patterns of
structures in various tectonic settings (e.g. thrust faults tend to
have gentle dips but strike-slip faults tend to be steep) so that they
begin to wonder why these patterns exist and thus can see the
usefulness of studying stress and strain theory.
How the activity is situated in my course: This activity is one of
many combined homework assignments/in-class activities that students
do over the course of the semester.
Goals of the Activity or Assignment
Content/concepts goals for this activity: Introduction to stress and
strain (exploration of the stress equations, Mohr circle, Coulomb
fracture criterion, Anderson’s theory of faulting, pure vs. simple
shear); exploration of these concepts, discovering some of their
properties and usefulness.
Higher order thinking skills goals for this activity: moving from xyz
3-dimensional space to n/s space and back again, applying theory to
a real situation.
Other skills goals for this activity: peer teaching, oral
communication of ideas.
Description
To prepare for each activity, students listen to a brief lecture on
the basics of stress and strain theory. Short summaries of these
lectures are included in the course packet. In class, students answer
guided-discovery questions on worksheets. They perform simple
calculations, make graphs, draw sketches and write summaries of their
discoveries. The students are divided into groups. Each group is
assigned a different portion of the worksheet to present to the class,
using overhead transparencies that they prepare. These activities
guide students to discover essential and useful aspects of stress and
strain theory. For example, students discover that (1) the Mohr circle
is simply a graph of all possible solutions to the stress equations
(thus it is not a picture of something physical) and (2) in pure
shear, material lines rotate in two directions but in simple shear,
material lines rotate in only one direction.
Evaluation
I check each team to make sure that they have understood their
assigned concepts before they have a chance to teach other students
about them.
Documentation
The following pages contain excerpts from the stress/strain portion of
the course packet as described below:
Everything you Never Wanted to Know About Stress: A one-page summary
of basic stress theory.
In-Class Exercise on Stress Theory: Students do this activity on the
first day they encounter stress theory. They complete the assignment
at home and present their results at the beginning of the following
class session.
In-Class Exercise on Stress Theory—Answers: Suggested answers to
questions on the Stress worksheet
Everything You Need to Know About Strain: A brief summary of basic
strain theory.
In-Class Assignment: Pure and Simple-Shear Strain Eggs: Students do
this activity on the first day the encounter strain theory. They
complete the assignment at home and present their results at the
beginning of the following class session.
In-Class Assignment: Pure and Simple-Shear Strain Eggs —Answers:
Suggested answers to questions on the Strain worksheet
Instructor’s notes for running the in-class assignments
*
Class begins with a brief lecture on theory, based on the
handouts.
*
I divide the class into several teams, each is assigned different
specific plug-and-chug calculations to complete. As teams complete
the basic calculations, they fill in their answers on a copy of
the data table displayed on the overhead projector. These basic
calculations help students ease into the subject matter.
*
After students have completed the basic calculations, they begin
analyzing the results of those calculations, using higher-order
thinking skills.
*
A 50- minute class usually ends before students complete either of
the worksheets. I assign the remainder of each worksheet as
homework for the following class period.
*
At the beginning of the following class period, I assign each team
to prepare a presentation on a portion of the worksheet. I give
each team an overhead transparency, including any graphics that
appear in their part of the worksheet.
*
After a few minutes of preparation time, each team presents its
results to the class.

1. A rock is under stress, where 1 = 1.5 kbars and 3 = 0.8 kbars. We
are interested in the normal and shear stresses experienced by seven
planes within the rock. Each of these planes is parallel to 2 (and
therefore unaffected by 2), so we only have to worry about 1 and3.
The orientation of each plane is defined by its  angle (the angle
between the 1 axis and the pole to the plane).
a. Using the stress equations, calculate normal stress (n) and shear
stress (S) for planes B through N; write your answers in the
appropriate boxes of the table below.
Plane
 angle
n
s
A
+10°
1.48
0.12
B
-10°
C
+25°
D
-25°
E
+35°
F
-35°
G
+50°
H
-50°
I
+70°
J
-70°
K
+80°
L
-80°
M

N
90°
b. Plot all 14 points on the graph paper below.

c. What pattern is formed by the data?
d. What is special about planes M and N with regard to normal, shear
and principle stresses? Why?
2. The states of stress for two mutually perpendicular planes are
measured as follows:
Plane
n
S
 angle
1
3
1
1.2 kbar
-0.6 kbar
2
0.6 kbar
0.6 kbar
Assuming that both planes are parallel to 2(and, therefore, neither
plane “feels” 2),
a. Plot the (n, S) points for the two planes on the graph on the
next page. Use a drawing compass to construct a Mohr circle that goes
through both points and whose center is on the n axis.
b. Using this Mohr circle, determine 1 and 3. Write your answers in
the appropriate boxes in the table above.
c. Determine the  angle for each plane. Write your answers in the
appropriate boxes above.
d. In the spaces provided on the next page, draw the orientations of
the planes and their poles.
Note: location doesn't matter; orientation does.
e. If 1 is vertical, what kinds of faults will form when the rock
breaks along the two planes? Explain how you arrived at your answer.
f. Imagine that, when looking at the diagrams of Plane 1 and Plane 2
on the next page, you are looking north, with west on the left and
east on the right. In other words, 2 is north-south, 3 is east-west,
and 1 is vertical. What are the strikes and dips of planes 1 and 2?

I. Basic Definitions
A. Definition of Strain: Distortion (change in shape) and/or dilation
(change in size).
Note: Translation (change in location relative to the outside world)
and rotation (change in orientation relative to the outside world) are
specifically excluded from this definition. A tomato thrown at a
professor does not undergo any strain (even if it spins) until it
actually hits the professor and squishes all over her. The resulting
strain does not take into account the spinning or the flight path,
just the change in shape of the tomato itself.
B. Assumptions: Deformation is homogeneous (if we look at a small
enough area, this is true).
(1) Lines that were straight before deformation remain straight after
deformation.
(2) Pairs of lines that were parallel before deformation remain
parallel after deformation.
See Figure 15.1 (p. 293) in Twiss and Moores for an illustration of
the difference between homogeneous strain and inhomogeneous strain.
C. Material Objects: When we talk about strain, we talk about the
changes of size and shape that happen to geometric objects made of
actual material. These are called material objects. A bedding plane,
for example, is a material object because no matter how it moves and
deforms, it is always defined by the same set of material particles.
Some examples of material objects include ripple marks (lines),
contacts (planes), and oolites (spheres when undeformed; “egg-shaped”
ellipsoids when deformed)
D. Imaginary Objects: In order to talk about strain, we also need to
use imaginary objects such as coordinate axes, shear planes, axes of
maximum stretch, etc. These imaginary lines and planes can rotate with
respect to material particles.
E. Describing the Change in the Length of a Material Line
If lf = final length, li = initial length, the stretch (s) =
F. Describing the Change in Angle Between Material Lines
See Figure 15.2 (p. 298) in Twiss and Moores for illustrations of the
concepts below.
1. Angular Shear () is defined as the degree to which two originally
perpendicular lines are deflected from 90°.
2. Shear Strain ()1:  = tan 
Sign Convention: For a line initially aligned with the positive Y-axis
of a coordinate system, angular shear and shear strain are measured
with respect to a perpendicular line aligned with the positive X-axis
of the same coordinate system. A decrease in the angle between these
two lines is positive; an increase in the angle between them is
negative.
Note: When we talk about the strain enjoyed by a rock, we measure all
changes in orientations of lines relative to other lines in the same
rock body. In other words, if the rock body rotated rigidly as a
whole, we would not call the changes in orientations of the lines
shear strain. We only talk about shear strain when the size or shape
of the rock body has been changed, resulting in changes in the
orientations of lines relative to each other.
II. The Strain Ellipsoid (the infamous strain egg - drawing from
Davis, 1984; p. 124).
A . Definition: Imagine a perfect sphere (radius=1) embedded in
an undeformed rock. After homogeneous deformation, that material
sphere becomes an ellips­oid. The imaginary ellipsoid with the same
shape is called the strain ellipsoid.
B. Principal Axes of the Strain Ellipsoid:
s1 = line of greatest stretch (usually s1 > l)
s3 = line of least stretch (usually s3 < l)
s2 = line perpendicular to both s1 and s3.
• The principal axes of the strain ellipsoid are mutually
perpendicular.
• The material lines parallel to the principal axes of the strain
ellipsoid are the only set of 3 line orientations that were
perpendicular before and after deformation (they may or may not have
remained perpendicular during the deformation process).
C. Possible Shapes of the Strain Ellipsoid (See diagram below; see
also Fig. 15.19, p. 311)
s2 > l • Flattening Strain Field
s1 = s2 Special (extreme) case = oblate ellipsoid (pancake)
s2 < l • Constriction Strain Field
s2 = s3 Special (extreme) case = prolate ellipsoid (cigar)
s2 = l • Plane Strain Field (no deformation in the s2 direction)

Note: k =
This diagram assumes that the volume of the rock did not change during
deformation
Diagram modified from: Ramsay and Huber (1983) The Techniques of
Modern Structural Geology, V. 1: Strain Analysis (Fig. 10.8, p. 172).
III. Types of Strain
====================
A. Dilation: Changes in volume (an increase is a positive dilation; a
decrease is a negative dilation).
• Figures 16.16 and 16.17 (p. 333) in Twiss show examples of negative
dilation. Negative dilation is usually caused by a process called
pressure solution in which part of the rock dissolves and is carried
away by fluids.
• A dike swarm, or a series of veins are examples of positive
dilation. Positive dilation is usually caused by the opening and
filling of cracks.
B. Coaxial Strain vs. Noncoaxial Strain: In coaxial strain, the
principal axes of the strain ellipsoid do not rotate through the rock
with time; in noncoaxial strain they do.
C. The Special Case of Plane Strain with no Dilation (What we actually
consider “normal”)
1. The Strain Ellipse: In plane strain, nothing happens in the s2
direction so we can ignore it and collapse the 3-D strain ellipsoid
into a 2-D ellipse, greatly simplifying the math and the graphics
(whew!). The axes of the strain ellipse are s1 and s3.
2. Pure Shear vs. Simple Shear: See Fig's. 15.14 & 15.15 (p. 306–307)
in Twiss and Moores
Pure Shear (Fig. 15.14, p. 306): Coaxial deformation; like squeezing a
rock in a vise.
• The axes of the strain ellipsoid do not rotate but all other
material lines do.
• Typical of the deep interiors of orogenic belts.
Simple Shear (Fig. 15.15, p. 307): Noncoaxial deformation; like
shearing a deck of cards.
• Shear Plane: analogous to the surfaces between the cards.
• There is no shortening in the direction perpendicular to the shear
plane (but individual planes do get distorted)
• There is no distortion of planes parallel to the shear plane (but
they do get moved).
• Simple shear typically happens within shear zones, which are like
faults except the shearing is distributed over a thick zone instead of
being along one discrete surface.
D. Shortening Field vs. Stretching Field of the Strain Ellipse (See
Fig. 15.11, p. 304):
A strain ellipse can be divided into two types of fields:
• Shortening Field: all lines within this field have been shortened (s
< 1).
• Lengthening Field: all lines within this field have been lengthened
(s > 1).
• Lines of no finite extension (s=1): separate the ellipse into the
two types of fields.
E. Finite, Infinitesimal, and Incremental Strain
------------------------------------------------
• All of the ellipses (and ellipsoids) we've been talking about so far
are finite strain ellipses (and ellipsoids); they show the sum total
of all deformation from the undeformed state to the final deformed
state.
• The incremental strain ellipse depicts the tiny increment of strain
that happens within a small period of time during the deformation
process. In incremental strain, the ellipsoid is “reset” to a sphere
after each increment of deformation occurs.
• The infinitesimal strain ellipse is like the incremental strain
ellipse except that it depicts the in­stan­tan­eous strain that occurs
within an infinitesimally small instant of time (think calculus).
IV. A Final Note About Ellipsoids and Mohr Circles
I have emphasized strain ellipsoids and stress Mohr circles because
they are used frequently. You may have noticed in the readings that
there are such things as stress ellipsoids and strain Mohr circles.
These things are, in practice, virtually never used, so you don't need
to understand them for this class.
Reading: On the CD Introduction to Structural Methods by Burger &
Harms, read the following sections of Chapter 12:
1) Introduction (Frames 1239–1266
2) The Strain Ellipse (Frames 1267–1317)
3) Three-Dimensional Strain (Frames 1385–1392)
4) Strain Paths (Frames 1438–1461)
Introduction
Page Lecture–75 shows two identical circles and the resulting ellipses
that form after deformation. One of the ellipses was formed by pure
shear of the circle; the other ellipse was formed by simple shear of
the circle.
The Circles: The two circles are identical in every way. They both
have diameters of 3 inches.
The Ellipses: Both ellipses have the same area as the original
circles. The two ellipses are exactly the same shape and have exactly
the same orientation as given in the table below.
Length of Long Axis
Length of Short Axis
Angle Between Long Axis and Horizontal Reference Line
4.85 inches
1.85 inches
32°
The Lines: There are eight lines (four pairs of two initially
perpendicular lines) in each original circle. These lines are
identical in the two original circles. But, during deformation, these
lines behave very differently during the two different deformat­ional
events. The tables below summarize the lengths of the lines and the
angles between the lines before and after deformation (some boxes are
intentionally left blank--you will calculate them and fill them in).
Deformation #1
#1
#2
#3
#4
#5
#6
#7
#8
Initial Length (li)
3 in
3 in
3 in
3 in
3 in
3 in
3 in
3 in
Final Length (lf)
1.85 in
4.85 in
2.71 in
4.44 in
4.64 in
2.35 in
3 in
4.30 in
Stretch (s)
0.62
1.62
1.55
0.78
Final angle between line and originally perpendicular line
90°
90°
48°
132°
56°
124°
135°
45°
Angular Shear ()


42°
-42°
-45°
45°
Rotation Direction of Line (cw or ccw)
Deformation #2
#1
#2
#3
#4
#5
#6
#7
#8
Initial Length (li)
3 in
3 in
3 in
3 in
3 in
3 in
3 in
3 in
Final Length (lf)
4.44 in
2.7 in
1.85 in
4.85 in
3.68 in
3.68 in
4.60 in
3 in
Stretch (s)
1.48
0.9
1.23
1.23
Final angle between line and originally perpendicular line
132°
48°
90°
90°
42°
138°
140°
40°
Angular Shear ()


-50°
50°
Rotation Direction of Line (cw or ccw)
ccw
cw
Questions
1. Do the appropriate calculations and complete the tables.
2. Study the diagrams and tables. Compare and contrast the behavior of
the lines in Deformation #1 vs. Deformation #2. Which way do the
various lines rotate (as measured relative to the horizontal reference
line—rotation is different from angular shear)? Do all lines rotate in
the same direction? By the same amount?
3. Are there any lines that didn't rotate at all? Why not?
4. Which ellipse resulted from pure shear deformation? from simple
shear? How do you know?
5. Find the long and short axes of the two ellipses. Why are there
different numbered lines aligned with these axes in the two different
ellipses?
6. Notice that some lines got longer and some lines got shorter. What
are the implications of this fact for real rocks? For example, if the
circles and ellipses were map views of the deformation, what different
types of structures (folds, normal faults, thrusts, etc.) would form
parallel and perpendicular to the various lines?

To Watch the Deformation Happen Before Your Eyes…
1. Get onto one of the computers in Rm. 208 and open the StrainSim
program (obtained from Dr. Rick Allmendinger, Cornell University).
2. Under the File menu, choose New Objects. A dialog box appears
entitled Input Objects to Deform. Highlight the circles next to Box,
Circle, and Line. You may deform up to four lines at a time. To watch
lines 1 through 6 rotate, shrink and stretch, type in the angles as
listed below:
Line
Initial Angle for Pure Shear*
Initial Angle for Simple Shear
Line 1 (Black)
-64°
-32°
Line 2 (Black)
26°
58°
Line 3 (Gray)
90°
-58°
Line 4 (Gray)

32°
Line 5 (Dashed)
45°
77°
Line 6 (Dashed)
-45°
-13°
Line 7 (Dotted)
32°

Line 8 (Dotted)
-58°
90°
*These angles are different from those in the table on page Lecture–73
because the program can only “squash” things horizontally or
vertically, not diagonally. Turn your head to the right to see the
diagram as it looks on page Lecture–75.
3. Click Okay. A dialog box appears telling you to drag the mouse to
define the box.
4. Click Okay and draw the box. You can draw the box any size you
like. I suggest placing the box near the center of the screen and
making it about three inches across (if you make it too big or put it
too close to the edge, the deformed box won't fit on the screen).
5. Choose Animate from the Strain menu. A dialog box will appear.
6. Highlight the circle next to the type of deformation you want to
see (Pure Shear or Simple Shear).
7. Fill in the Increment and # of Steps boxes as listed below.
Pure Shear: In the Increment box, type .01, in the # of Steps box,
type 62
Simple Shear: In the Increment box, type .5, in the # of Steps box,
type 90
8. Click Okay and watch the box, circle and lines deform.
9. To start over with a new undeformed object, choose Input Objects…
from the File menu. The Input Objects to Deform dialog box appears and
you are back at step 2.
10. Repeat as often as you like. Play with the parameters and watch
how they affect the deformation (you may wish to draw in lines
parallel to the expected strikes of synthetic and antithetic
strike-slip faults, normal faults and thrusts and watch them rotate).
If you input too many increments (over 150 or so), the program will
crash. Don't worry, just start it up again.
11. To save any of your plots, choose Save Plot from the File menu.
1. A rock is under stress, where 1 = 1.5 kbars and 3 = 0.8 kbars. We
are interested in the normal and shear stresses experienced by seven
planes within the rock. Each of these planes is parallel to 2 (and
therefore unaffected by 2), so we only have to worry about 1 and3.
The orientation of each plane is defined by its  angle (the angle
between the 1 axis and the pole to the plane).
a. Using the stress equations, calculate normal stress (n) and shear
stress (S) for planes B through N; write your answers in the
appropriate boxes of the table below.
Plane
 angle
n
s
A
+10°
1.48
0.12
B
-10°
1.48
-0.12
C
+25°
1.37
0.27
D
-25°
1.37
-0.27
E
+35°
1.27
0.33
F
-35°
1.27
-0.33
G
+50°
1.09
0.34
H
-50°
1.09
-0.34
I
+70°
0.88
0.22
J
-70°
0.88
-0.22
K
+80°
0.82
0.12
L
-80°
0.82
-0.12
M

1.5
0
N
90°
0.8
0
b. Plot all 14 points on the graph paper below.

c. What pattern is formed by the data?
A circle; specifically, the Mohr circle.
d. What is special about planes M and N with regard to normal, shear
and principle stresses? Why?
PlaneM and N have zero shear stress; their normal stresses are equal
to the principal stresses. Plane M is perpendicular to 1; thus its
normal stress is exactly equal to 1. Plane N is perpendicular to 3;
thus its normal stress is exactly equal to 3.
2. The states of stress for two mutually perpendicular planes are
measured as follows:
Plane
n
S
 angle
1
3
1
1.2 kbar
-0.6 kbar
-31.5°
1.57 kbar
0.23 kbar
2
0.6 kbar
0.6 kbar
58.5°
Assuming that both planes are parallel to 2(and, therefore, neither
plane “feels” 2),
a. Plot the (n, S) points for the two planes on the graph on the
next page. Use a drawing compass to construct a Mohr circle that goes
through both points and whose center is on the n axis.
b. Using this Mohr circle, determine 1 and 3. Write your answers in
the appropriate boxes in the table above.
c. Determine the  angle for each plane. Write your answers in the
appropriate boxes above.
d. In the spaces provided on the next page, draw the orientations of
the planes and their poles.
Note: location doesn't matter; orientation does.
e. If 1 is vertical, what kinds of faults will form when the rock
breaks along the two planes? Explain how you arrived at your answer.
Normal faults. You can tell by the signs of the shear stresses (+ or
-) and by the way that 1 will tend to cause the two sides of each
fault to move.
f. Imagine that, when looking at the diagrams of Plane 1 and Plane 2
on the next page, you are looking north, with west on the left and
east on the right. In other words, 2 is north-south, 3 is east-west,
and 1 is vertical. What are the strikes and dips of planes 1 and 2?
Plane 1: 000, 31.5° E
Plane 2: 000, 58.5° W

Introduction
Page Lecture–75 shows two identical circles and the resulting ellipses
that form after deformation. One of the ellipses was formed by pure
shear of the circle; the other ellipse was formed by simple shear of
the circle.
The Circles: The two circles are identical in every way. They both
have diameters of 3 inches.
The Ellipses: Both ellipses have the same area as the original
circles. The two ellipses are exactly the same shape and have exactly
the same orientation as given in the table below.
Length of Long Axis
Length of Short Axis
Angle Between Long Axis and Horizontal Reference Line
4.85 inches
1.85 inches
32°
The Lines: There are eight lines (four pairs of two initially
perpendicular lines) in each original circle. These lines are
identical in the two original circles. But, during deformation, these
lines behave very differently during the two different deformational
events. The tables below summarize the lengths of the lines and the
angles between the lines before and after deformation (some boxes are
intentionally left blank--you will calculate them and fill them in).
Deformation #1
#1
#2
#3
#4
#5
#6
#7
#8
Initial Length (li)
3 in
3 in
3 in
3 in
3 in
3 in
3 in
3 in
Final Length (lf)
1.85 in
4.85 in
2.71 in
4.44 in
4.64 in
2.35 in
3 in
4.30 in
Stretch (s)
0.62
1.62
0.91
1.48
1.55
0.78
1
1.43
Final angle between line and originally perpendicular line
90°
90°
48°
132°
56°
124°
135°
45°
Angular Shear ()


42°
-42°
34°
-34°
-45°
45°
Rotation Direction of Line (cw or ccw)
cw
cw
cw
cw
cw
cw
---
cw
Deformation #2
#1
#2
#3
#4
#5
#6
#7
#8
Initial Length (li)
3 in
3 in
3 in
3 in
3 in
3 in
3 in
3 in
Final Length (lf)
4.44 in
2.7 in
1.85 in
4.85 in
3.68 in
3.68 in
4.6 in
3 in
Stretch (s)
1.48
0.9
0.62
1.62
1.23
1.23
1.53
1
Final angle between line and originally perpendicular line
132°
48°
90°
90°
42°
138°
140°
40°
Angular Shear ()
-42°
42°


48°
-48°
-50°
50°
Rotation Direction of Line (cw or ccw)
ccw
cw
---
---
cw
ccw
ccw
cw
Questions
1. Do the appropriate calculations and complete the tables.
2. Study the diagrams and tables. Compare and contrast the behavior of
the lines in Deformation #1 vs. Deformation #2. Which way do the
various lines rotate (as measured relative to the horizontal reference
line—rotation is different from angular shear)? Do all lines rotate in
the same direction? By the same amount?
In deformation #1, all lines rotate clockwise, except for line #7,
which doesn’t rotate at all. Some lines rotate a lot, others just a
little.
In deformation #2, lines 3 and 4 do not rotate at all. Half of the
remaining lines rotate clockwise and the other half rotate
counterclockwise. Again, some lines rotate a lot, some just a little.
3. Are there any lines that didn't rotate at all? Why not?
Deformation #1: line #7 didn’t rotate. It was parallel to the shear
plane in a simple shear deformation.
Deformation #2: lines 3 and 4 didn’t rotate. They were parallel to the
s1 and s3 axes of the strain ellipse in a pure shear deformation.
4. Which ellipse resulted from pure shear deformation? from simple
shear? How do you know?
Deformation #1: simple shear. All lines but one rotated clockwise. One
line maintained its original length and orientation.
Deformation #2: pure shear. Half the lines rotated clockwise; half
rotated counterclockwise. Two lines maintained their original
orientation but one of these got shorter and the other longer. No
lines maintained both their original orientation and their original
length (line #8 maintained its original length but it rotated).
5. Find the long and short axes of the two ellipses. Why are there
different numbered lines aligned with these axes in the two different
ellipses?
For deformation #1, lines 1 and 2 rotated into a position parallel to
the long and short axes of the strain ellipse. In the next increment
of deformation, they will no longer be in that position.
For deformation #2, lines 3 and 4 start out parallel to the long and
short axes of the strain ellipse. They stay in those orientations
throughout the deformation; they don’t rotate.
6. Notice that some lines got longer and some lines got shorter. What
are the implications of this fact for real rocks? For example, if the
circles and ellipses were map views of the deformation, what different
types of structures (folds, normal faults, thrusts, etc.) would form
parallel and perpendicular to the various lines?
We would expect to see fold axes and thrust faults perpendicular to
lines that got shorter.
We would expect to see normal faults and dikes perpendicular to lines
that got longer.
1This is the “engineering shear strain” of Twiss and Moores. To avoid
confusion, we will not use the other definition of shear strain also
used in the book (the “tensor shear strain”).

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