Week 3
Kinematic Analysis II. Read pages 66-85 and
93-97 in Chapter 2: Kinematic Analysis.
You are expected to read all the
sections listed below. Information from the sections in italics
will be discussed in class. You are expected to read the other
sections and you may be called on in class to answer questions
based on that material.
- Strain (continued) p.66-85
- The Issue of Strain Compatibility p.93-97
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You should become familiar with the
following terms during this weeks lectures and readings:
| coaxial strain |
finite stretching axes |
internal rotation |
maximum finite stretch |
| minimum finite stretch |
non-coaxial strain |
plane strain |
principal strain axes |
| quadratic elongation |
reciprocal quadratic elongation |
strain field diagram |
zero angular shear |
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You should be able to answer the questions
below following this week:
- How does angular shear change for line AC in Figure 2.39
as deformation progresses from figure A to E?
- Determine the orientation (relative to S1) and
angular shear of a line that underwent no finite stretch
in the ellipse pictured in Figure 2.46.
- Use a copy of Fig. 2.48B to determine the stretch and
angular shear for lines oriented at 20, 45, and 75
degrees to S1.
- Where would the ellipses pictured in Figure 2.57 plot in
the strain field diagram of Figure 2.58?
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Kinematic Analysis II
Finite Strain Ellipse
- graphic representation of strain in rocks
- greatest elongation parallel to the long axis of the
ellipse (S1)
- greatest shortening parallel to the short axis of the
ellipse (S3)
- angular shear and shear strain zero parallel to S1 and S3
Determining line length changes for Skolithus burrow (Fig.
2.34)
- area of original circle vs. area of ellipse
- determine original radius of circle (r = 1.2)
- use r to determine strain (extension and stretch)
parallel to S1 and S3
- we can determine strain for any line within the strain
ellipse, either graphically or by using the strain
equations: introduce lines L1 and L2
Use fundamental strain equations to determine changes in
lengths of lines
- introduce lambda, quadratic elongation = stretch squared
- introduce reciprocal quadratic elongation = reciprocal
stretch squared
- determine both quadratic elongation and reciprocal
quadratic elongation for S1 and S3
- introduce fundamental strain equations
- determine the lengths of two arbitrary lines (L1, L2)
using the strain equations
Mohr Strain diagram
- graphical representation of the strain equations
- X axis = reciprocal quadratic elongation
- Y axis = shear strain/quadratic elongation
- center of circle = first term in strain equations
- radius of circle = first part of second term in strain
equations
- reciprocal quadratic elongation = second term in strain
equations
- Mohr strain diagram can be used to determine reciprocal
quadratic elongation (and hence stretch) and shear strain
(and hence angular shear) for any line
- to use the Mohr strain diagram we need to know, the
orientation of the line relative to S1, and reciprocal
quadratic elongations for S1 and S3
Rotation of a line during deformation
- theta = original position of line relative to S1 in
undeformed state
- thetad = position of line relative to S1 in deformed
state
- tan(thetad) = tan theta (S3/S1) or (S1tan thetad)/S3 =
tan theta
- determine original position of lines L1 and L2 in
undeformed circle
Finite Strain Ellipsoid
- three-dimensional volume strains
- plane strain when there is no length change parallel to
S2 axis of ellipsoid
Dilation
- increase in volume by opening of cracks (S1S3 >1.0)
- volume decrease by dissolution (S1S3 < 1.0) possible
changes represesented by strain field diagram
Pure Shear vs. Simple Shear
- both types of plane strain
- pure shear = coaxial deformation (orientation of strain
axes remains uniform before and after deformation)
- simple shear = principal strain axes rotate during
deformation (noncoaxial deformation)
Structural compatibility
all observations and interpretations of deformation should be
compatible
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