Kinematic analysis and strain

1
Kinematic analysis and strain

• (Chapter 2, also page 25)

2

• Geologic structures are formed by material
  movement in all scales
• Kinematic analysis attempts to reconstruct the
  stages of progressive movement of geological
  structures
• Geological structures do not have built-in stress
  gauges (no point worrying about the stresses
  causing the movement)

3

• Total displacement field (page 39) can be divided
  into
• Bulk translation (Displacement of the center of
  mass)
• General deformation
• General deformation can be further divided into
• Rigid rotation (about a point in the mass)
• Pure strain (or deformation)
• Pure strain can have two components
• Dilation (change in size)
• Distortion (change in shape)

4
Strain (page 51-61)

• Strain dilation and /or distortion
• Can be homogeneous or heterogeneous
• Homogeneous strain
• Straight lines remain straight
• Parallel lines remain parallel
• Can be described mathematically
• Heterogeneous strain can be divided into zones of
  homogeneous strain for analysis

5
Strain ellipse (or ellipsoid) page 54

• Under homogeneous strain, a circle (or sphere)
  deforms to a perfect ellipse (or ellipsoid)
• A convenient way of looking at strain
• Forms when an undeformed circle (or sphere) is
  homogeneously deformed

6
Stretch and extension pages 55-68

• Stretch (S)
• Extension (e) S-1
• Quadratic elongation (?) S2 (1e)2

7

• Strain Can be
• Instantaneous (each increment of deformation.
  More on this later)
• Finite (the final deformed shape after adding up
  all the instantaneous strain)
• Line with maximum finite stretch after
  deformation The long axis of the finite strain
  ellipse
• Line with minimum finite stretch (maximum
  shortening) after deformation The short axis of
  the finite strain ellipse (page 66)

8

• Angular shear (?) (pages 61-63) Measures change
  in angles between lines
• Find two lines that were initially perpendicular
  to each other
• Measure the angle between them after deformation
• Subtract that angle from 90 (departure from its
  perpendicular position)
• Sign of ? indicates which direction the line has
  rotated (page 61)
• Shear strain ? tan ? (page 64)

9
Fundamental properties of homogeneous strain in
2-D (page 70)

• The finite (or principal) strain axes are
  mutually perpendicular (directions of zero
  angular shear)
• Principal strain axes Directions of maximum and
  minimum stretch Directions of zero shear strain
• The strain ellipse Always contain
• two lines that do not change length (stretch0)
• two directions with maximum shear strain
• Stretch and shear strain values change
  systematically

10

• In reality, strain is ALWAYS three dimensional
  (S1gtS2gtS3, pages 78-79)
• When S1xS2xS3?1, Strain is accompanied by change
  in overall volume (pages 81-83)
• Important Ramsays strain field diagram (page
  83, Fig. 2.58)
• Special case scenario Plane strain
• When S1gtS21gtS3 (No finite strain along
  intermediate strain axis)
• Implies no volume change

11

• Plane strain can be expressed in 2-D
• Two end member cases (pages 84-85)
• Pure shear
• Simple shear
• Pure shear
• Principal strain axes do not rotate in space (no
  external rotation)
• Lines within the strain ellipse rotate with
  respect to the principal strain axes (internal
  rotation present)
• This is an example of coaxial strain (pages
  83-84), not synonymous with it

12

• Simple shear
• Principal strain axes rotate in space (external
  rotation present)
• All lines except ONE rotate with respect to the
  principal strain axes (internal rotation present)
• This is an example of noncoaxial strain (pages
  83-84), not synonymous with it
• General shear (a combination of pure and simple
  shear) is also noncoaxial