a visual basic 6 program that facilitates learning

ABSTRACT

Visualizing Strain, a Visual Basic 6 program withGraphical User Interface, was developed to allowstudents a means of discovery through experimentation.The program allows students to conduct simple and pureshear experiments. Both of these strain types areproduced when the area (or in 3D, the volume) of anobject does not change during a distorting event.

The mathematical background necessary forstudents to fruitfully use Visualizing Strain is typicallygained in a high school algebra class. Hence, VisualizingStrain is appropriate for both introductory geology andstructural geology courses.

Using Visualizing Strain, students can producesophisticated strain models that simulate the distortionsof the circular cross sectional area of a crinoid columnal.

Keywords: Education – geoscience; education –structural geology; education – computer science;education – visualization.

INTRODUCTION

Strain, a fundamental concept that all geologists areintroduced to in under graduate structural geology, isalso covered to varying degrees in nearly all introductorygeology textbooks. In 14 structural geology textbookspublished since 1970, coverage of the topic varies frommodest to very thorough (Dennis, 1972; Billings, 1972;Hills, 1972; Means, 1976; Spencer, 1977; Ramsay andHuber, 1983; Suppe, 1985; Marshak and Mitra, 1988;Ragan, 1985; Park, 1989; Twiss and Moores, 1992; Davisand Reynolds, 1996; Hatcher, 1996; van der Pluijm andMarshak, 1997). Nevertheless, one of the majorshortcomings of all existing treatments is that studentsare not provided a means of discovering throughexperimentation the critical aspects of strain. Hencestudents commonly develop little intuition about strain.

In an attempt to mitigate the above, as well as otherproblems commonly encountered in teaching theprinciples of strain, we developed a Visual Basic 6program called Visualizing Strain. The program is free todownload at http://www.geology.sdsu.edu/visual-

structure, and will run on Windows 98, Windows NT 4.0,Windows 2000, and Windows XP operating systems. ForMacintosh users a Java applet called Strain Machine isprovided at the above URL.

Below a brief description of the algorithms, graphicaluser interface (GUI), and other important characteristicsof Visualizing Strain are provided. We then concludewith an example of an experiment conducted within theVisualizing Strain environment.

GENERAL BACKGROUND INFORMATION

When we casually speak of strain, we are commonlyreferring to the quality of some distortion that an objecthas undergone. For example, we might say that thecircular cross-sectional area of the crinoid columnalshown in Figure 1A is not strained while that in Figure 1Bis highly strained. Such qualitative observationscommonly lead to more direct questions like how muchwas the cross-sectional area of the crinoid columnalshortened in some specified direction or how much wasit elongated in another? In order to address these andother questions, we need to establish prior to distortion aset of reference points or lines on the object that we canmeasure after deformation has run its course (e.g.,Ramsay and Huber, 1983).

Any object can be thought of as a series of pointsconnected by lines. In fact, that is how many computerprograms draw complicated three-dimensional objects.For the purposes of this discussion, we define materiallines as imaginary lines that connect two material pointsin a rock body (van der Pluijm and Marshak, 1997). Forexample, line R in Figure 1 is a material line connectingthe center of the circular cross-sectional area of thecrinoid columnal to some point along its circumference.

If material lines that were parallel before a distortionremain parallel after the distortion, then we say thatstrain is homogeneous; otherwise it is heterogeneous.However, any heterogeneously strained object can besubdivided into small areas that exhibit thecharacteristics of homogeneous strain. Changes in thelengths and orientations of material lines represent animportant characterization of the distortion or strain thata body has undergone (Means, 1976; Ramsay and Huber,1983). Below we discuss four important parameters thatare useful for such characterizations.

Girty et al. - Learning the Characteristics of Simple Shear Through Experimentation 559

A VISUAL BASIC 6 PROGRAM THAT FACILITATES LEARNING THE

CHARACTERISTICS OF SIMPLE AND PURE SHEAR THROUGH

EXPERIMENTATION

Gary H. Girty Department of Geological Sciences, San Diego State University,San Diego, California 92182-1020

Nathaniel ReishPatricia BaroekBrett HeitmanKesler RandallDaniel R. LillyChristopher Lynch

The dimension-less quantity elongation (e), isexpressed as

e = �l / lo = (l - lo) / lo (1)

where l is the strained length, and lo is the original lengthof some measurable material line. Positive values ofelongation represent an increase in length while negativevalues represent a decrease.

Stretch (s) is the ratio between (l) and (lo); i.e.,

s = l / lo (2)

where, l and lo are as defined in the previous paragraph.Stretch also can be expressed as

s = e + 1. (3)

Values of stretch greater than 1.0 represent elongations whilevalues less than 1.0 represent shortening.

Quadratic elongation (�, lambda) is simply

� = (s)2� ��

Shear strain (�, gamma), is expressed mathematically as

� = tan � (5)

where the angular shear strain (�, psi), is defined inFigure 1. As � increases from 0 to 90, tan(�) increasesfrom 0 to infinity. In other words, large values of � reflectgreater amounts of shear strain and rotation than dosmaller values (Figure 1).

STRAIN TRANSFORMATION EQUATIONS

The strain transformation equations used in thedevelopment of Visualizing Strain

are for simple shear

x’ 1 y x= *

y’ 0 1 y , (6)

and for pure shear

x’ (e + 1) 0 x= *

y’ 0 1/(e + 1) y (7)

All parameters are as defined previously.The first author has developed a set of Macromedia

Flash 5 movies that are useful for presenting thederivations of these equations within in a smartclassroom setting. These and eight other Flash 5 moviesthat can be used in the development of strain conceptswith in a classroom setting are freely downloadable atthe URL provided earlier in this paper.

VISUALIZING STRAIN

The main components of the Graphical User Interface(GUI) used in Visualizing Strain are shown in Figure 2.The first step in any strain experiment is to select one ofthe three different types of circles described in Figure 2A.Before making a selection of the type of circle to plot, theuser can specify from a properties page, the radius of thecircle, the size of the symbols to be plotted at each point,and font size (Figure 3). In addition, from within theproperties page, the parameters � and (e+1) can bechanged from their default values of 0.2 and 1.1

560 Journal of Geoscience Education, v. 50, n. 5, November, 2002, p. 559-565

Figure 1. Circular cross-sectional area of a crinoid columnal. (A) Unstrained. (B) Strained by simple shear.

respectively, and the dimensions of the strain grid can bemodified. The algorithm used in Visualizing Strain uses �

for simple shear and (e + 1) for pure sheartransformations. Once a circle has been plotted, the userthen selects either to conduct a simple or pure shearexperiment by clicking on one of two radio buttonsvisible within the plotting area (Figure 2B). If thecoordinates of each point are needed during theexperiment, then the user selects the “show table of data”button from the menu strip near the top of the screen(Figure 2A).

In a typical experiment conducted withinVisualizing Strain the next step is to distort the circle oneincrement by selecting the button labeled “I” (Figure 2A).Selection of this button applies the selected straintransformation equation to all points in the circle,resulting in the generation of an ellipse. The ellipse canbe strained further by reselection of button “I”. Print outs

of each step of applied strain can be made by selectingthe Print Graph or Print Table functions that areavailable under the File menu at the top of the screen(Figure 2A).

While in a strained condition, placing the cursor overany end point of a ray emanating from the origin resultsin the values of the key finite strain parameters (i.e.,stretch, elongation, �, and �) for that ray being displayedin the upper left corner of the plotting window. Valuesassociated with the incremental strain are displayed inthe status bar at the bottom of the screen. Both finite andincremental values also can be calculated by insertingcoordinates displayed in the table of data into one ofthree calculators that are accessed through the mainmenu at the top of the screen (Figure 2C). Selecting thebutton labeled “M” plays a movie of the experiment(Figure 2A). If the movie plays to fast, then set theSeconds to Pause value in the properties page (Figure 3)to some value between 0 and 0.5 seconds. Beforeconducting a new experiment the user must first clear the


Figure 2. Screen captures of the graphical user

interface available in Visualizing Strain. (A) The 8

functions that are utilized during any given strain

experiment. (B) The two radio buttons that allow the

user to select either a simple or pure shear

experiment. (C) The three calculators available in

Visualizing Strain.

Figure 3. The Properties Page is accessed through the

Edit menu. Within the Properties Page the user can

modify key strain parameters as well as graphical

attributes.


Figure 4. Shown in the right-hand column is a circular

cross-sectional area of a crinoid columnal that was

digitally strained in three increments by simple shear with

� equal to 15o

(� = 0.268). Shown in the left-hard column is

the output from a Visualizing Strain experiment

conducted under the same conditions. While in

Visualizing Strain, when the user places the cursor over

any of the boxes marking the end points of the strained

lines radiating from the center of the plot, the values of �,

stretch, �, and elongation for that line are revealed in a box

displayed in the upper left corner of the users screen.

Figure 5. Shown in the right-hand column is a crinoid

columnal that was digitally strained in three increments by

pure shear with (e + 1) = 1.27. Shown in the left-hard column

is the output from a Visualizing Strain experiment

conducted under the same condition. While in Visualizing

Strain, when the user places the cursor over any of the

boxes marking the end points of the strained lines radiating

from the center of the plot, the values of stretch and

elongation for that line are revealed in a box displayed in

the upper left corner of the users screen.

strain grid by selecting the button labeled “C” (Figure2A).

EXPERIMENTING IN VISUALIZING STRAIN

It is important for students to learn strain conceptsthrough the process of discovery rather than throughrote memorization or laborious tasks involving numbercrunching. Hence, we have developed an experimentthat uses Visualizing Strain to guide students throughthe act of discovering the key components of pure andsimple shear.

To begin an experiment in Visualizing Strain weprovide each student an image of a plan view of a crinoidcolumnal like that in Figure 4A. Note that the plan viewof the crinoid columnal displays a series of raised ridgesthat resemble rays radiating from its center. Students areasked to express mathematically the form of the circularcross-sectional area of the crinoid columnal within an XYcoordinate system, and to calculate its area. They thenopen Visualizing Strain and plot a circle with raysemanating from its center. The radius of the plotted circleis adjusted through the properties page (Figure 3) until itclosely resembles the undistorted cross-sectional area ofthe crinoid columnal. At this point the students haveproduced a computerized 2D model of the circular crosssectional area of the crinoid columnal.

After developing a 2D model of the cross-sectionalarea of a crinoid columnal, students are then providedimages of a columnal distorted by simple and pure shear(Figures 4 and 5). They are told that the original circular

cross section was distorted in 3 steps to form the imagesportrayed in Figures 4B - 4D and 5B – 5D. For simpleshear � was 0.268 (� = 15o), and for pure shear (e + 1) was1.27. Students are then asked to use Visualizing Strain todevelop a model and movie depicting how each point onthe circumference of the circular cross-section of thecrinoid columnal behaved during the transformationfrom undistorted to final distorted state. They are told toprint out copies of their results for each step of theirexperiment (see Figures 4 and 5, column labeledVisualizing Strain). By laying a copy of the original circle(Figures 4A and 5A) over printed copies of ellipsesrepresentative of each strain step (Figures 4B – 4D and5B-5D) students are asked to produce a vector-displacement map by tracing out the paths that particleson the circumference of the original circle took in goingfrom the undistorted to final strain state (e.g., Figure 6).


Figure 6. Vector-displacement maps. (A) Pure shear.

(B) Simple shear.

Figure 7. Positions of lines of no finite longitudinal

strain during the three-step experiment with pure

and simple shear. (A) Pure shear. (B) Simple shear.

Lines of no finite longitudinal strain are those that

have the same length as the radius of the initial

circle. In (B) note how the X and Z principal strain

axes have rotated toward the shearing direction

indicated by the arrows.

Using these data they are asked to address the followingquestions.

For simple shear:

(1)The principal strain axes X and Y are parallel to themajor and minor axes of the strain ellipse. What are thelengths and orientations of these axes during each stepof your simple shear experiment? Are thesemeasurements reflective of incremental or finitestrains? How would you characterize the incrementalstrain ellipse? How would you characterize the finitestrain ellipse?

(2)Recall that the area of a circle is r2 while that of anellipse is ab, where a is the length of the semimajoraxis and b is the length of the semiminor axis. Is strainisochoric during each step of applied simple shear?

(3)What does the vector-displacement map tell youabout displacements associated with simple shear?

(4)Material lines that have not undergone a net change inlength are said to be lines of no finite longitudinalstrain (i.e., stretch = 1.0) (e.g., Ragan, 1985). For eachstep of imposed simple shear how many material linesexhibit no finite longitudinal strain? What are theorientations of the X and Z principal strain axesrelative to the lines of no finite longitudinal strain?

(5)The set of lines of no finite longitudinal strainsubdivide the strain ellipse into four wedge orpie-shaped segments. During the experiment whathappens to the set of material lines that are containedwithin each of these four segments?

For pure shear:

(1)What are the lengths and orientations of the principalstrain axes during each step of applied pure shear?

(2)Is strain during each step of pure shear isochoric?(3)What does a vector-displacement map tell you about

displacements during pure shear?(4)Are there lines of no finite longitudinal strain

produced during the three steps of applied pure shear?If so, then what are the orientations of the X and Zprincipal strain axes relative to these lines?

(5)What happens to material lines lying in the fourwedge or pie-shaped segments bounded by the lines ofno finite longitudinal strain?

(6)What happens to material lines that are parallel to theprincipal strain axes X and Z?

Finally, students are asked if there is only one way(i.e., one unique strain path) that the distorted crosssectional areas of the crinoid columnal shown in Figures4D and 5D could have been produced? They are thenasked to discuss what their answer implies aboutdetermining the strains developed during an ancient

orogenic event in a large region like that of the SierraNevada, California.

CONCLUSIONS

From the above experiment students should be able todiscover the following key components of strain.

(1) Both simple and pure shear are two simplifiedsubsets of plane strain, and are therefore constantarea (or volume) distortions that can be describedmathematically by a transformation equation. Undersuch conditions r

2= ab.

(2) For pure shear and a given stretch, and for simpleshear and a given �, applying the transformationequation to a set of coordinates defining a circleproduces an ellipse (Figures 4 and 5). In both casesthe major and minor axes of the resulting ellipsedefine the principal strain axes X and Z fortwo-dimensional strain.

(3) Vector displacement maps reveal that duringprogressive pure shear, all particles, with theexception of those oriented parallel to the principalstrain axes, follow complex curved paths (Figure6A). In contrast, particles located along X follow alinear path moving outward away from the origin,while those located on Z follow a linear path movinginward toward the origin. Hence, it is not surprisingthat material lines that are oriented parallel to the Zprincipal strain axis are shortened, while thoseoriented parallel to the X principal strain axis areextended (Figures 5B – 5D. But what about materiallines that are not oriented parallel to X and Z?Surprisingly, material lines not oriented parallel tothe principal strain axes undergo complexdistortions, sometimes shortening early in the strainhistory and then lengthening later on. For example,rays bounded by points 7, 11, 25, and 29 in Figure 5have the following stretch values following each ofthe three steps of applied pure shear: 0.86 (after step1), 0.80 (after step 2), and 0.84 (after step 3) (Figures5B – 5D).

(4) Vector-displacement maps for progressive simpleshear reveal that all particles follow simple linearpaths that are parallel to the shear direction (Figure6B). Both the X and Z principal strain axes, alongwith material lines not parallel to the shear direction,rotate toward the direction of shear (Figures 4B –4D). Depending upon their initial orientation somematerial lines will initially shorten and then passthrough an orientation where their stretch values are1.0. Subsequent shearing will result in these lineselongating. For example, rays bounded by the points11 and 29 have the following stretches followingeach of the three applied steps of simple shear: 0.94,0.95, and 1.03 (Figures 4B – 4D). Though not shownin Figure 4, between steps 2 and 3 this ray must passthrough a stretch value of 1.0. The orientations and


lengths of material lines that are oriented parallel tothe direction of shear do not change duringprogressive simple shear (see rays bounded bypoints 16 and 36, Figure 4).

(5) Following any step of pure or simple shear, two linesof no finite longitudinal strain can be identified. InVisualizing Strain this relationship is best seen bydistorting circles defined by 360 points (Figure 7).Lines of no finite longitudinal strain have stretchvalues of 1.0, and divide the strain ellipse into fourwedge or pie-shaped segments. The principal strainaxes X and Z bisect the two lines of no finitelongitudinal strain (Figure 7).

(6) Progressive simple and pure shear are a series ofstrain events, each event being an addition to agrowing distortion. Such a process can be modeledfor n steps, by first applying the transformationequation to the coordinates of a circle to produce anellipse (Figures 4A and 5A). This ellipse isrepresentative of the applied strain transformationequation, and is referred to as the incremental strainellipse. Applying the transformation equation to thecoordinates of the first through nth ellipses producesthe second through nth steps (Figures 4B – 4D and 5B– 5D). Thus, after completion of the first step what isdisplayed in Visualizing Strain is the finite and notthe incremental strain. Though incremental strainwas kept constant during the above experiment, it isimportant to realize that this does not need to be thecase.

(7) Point (6) implies that strain histories can be verycomplicated, and that finite strains can be arrived atthrough more than one path.

Though the current analysis does not includethree-dimensional strain, all students should understandthat the Y principal strain axis is oriented perpendicularto the XZ plane, and that during experimentation theorientations and dimensions of material lines parallel toit are assumed to not change.

We are currently working on additions toVisualizing Strain that will include 3D procedures, and amenu for developing bivariate plots of various strainparameters (e.g., Ramsay and Huber, 1983; Ragan, 1985).If you would like us to add some additional routine orprocedure to Visualizing Strain, then please contact thefirst author. As an act of synergism, he will attempt toaddress your needs.

In conclusion, we believe that Visualizing Strainadds a new dimension to learning the basic concepts ofstrain theory. We encourage our colleagues to give it atry. From our experience students will like “playing” and“experimenting” with the program, and in so doing willbe gaining intuition about this core concept of structuralgeology.

ACKNOWLEDGMENTS

We thank Carl Jacobson, Mary Hubbard, and CinviaCervato for their timely and constructive criticisms ofour work.

REFERENCES CITED

Billings, M.P., 1972, Structural Geology: EnglewoodCliffs, New Jersey, Prentice-Hall, 606 p.

Davis, G.H. and Reynolds, S., 1996, Structural Geology ofRocks and Region: New York, John Wiley & Sons,776 p.

Dennis, J.G., 1972, Structural Geology: New York,Ronald Press Co., 532 p.

Hatcher, R.D., Jr., 1996, Structural Geology, Principles,Concepts, and Problems: Englewood Cliffs, NewJersey, Prentice Hall, 525 p.

Hills, E.S., 1972, Elements of Structural Geology:London, Chapman and Hall, 502 p.

Marshak, S. and Mitra, G., 1988, Basic Methods ofStructural Geology: Englewood Cliffs, New Jersey,Prentice-Hall, 446 p.

Means, W.D., 1976, Stress and Strain: New York,Springer-Verlag, 339 p.

Park, R.G., 1989, Foundations of Structural Geology:New York, Chapman and Hall, 140 p.

Ragan, D.M., 1985, Structural Geology: An Introductionto Geometrical Techniques: New York, Wiley, 393 p.

Ramsay, J.G. and Huber, M.L, 1983, The Techniques ofModern Structural Geology v.1; Strain Analysis:New York, Academic Press, 307 p.

Spencer, E.W., 1977, Introduction to the Structure of theEarth: New York, McGraw-Hill, 640 p.

Suppe, J., 1985, Principles of Structural Geology:Prentice-Hall, New Jersey, 537 p.

Twiss, R.J., and Moores, E.M., 1992, Structural Geology:New York, Freeman, 532 p.

Van der Pluijm, B.A., and Marshak, S., 1997, EarthStructure: An Introduction to Structural Geologyand Tectonics: New York, McGraw-Hill, 495 p.


a visual basic 6 program that facilitates learning

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