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Kinematic analysis and strain PowerPoint Presentation

Kinematic analysis and strain

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### Kinematic analysis and strain

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

(Chapter 2, also page 25)

- 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)

Total displacement field (page 39) can be divided into: scales

- 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)

Strain scales (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

Strain ellipse scales (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

Stretch and extension scales pages 55-68

- Stretch (S) =
- Extension (e) = = S-1
- Quadratic elongation (λ) = S2 =(1+e)2

Strain Can be scales

- 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)

Angular shear (ψ) (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 ψ indicates which direction the line has rotated (page 61)

Shear strain γ = tan ψ (page 64)

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 (stretch=0)
- two directions with maximum shear strain
Stretch and shear strain values change systematically

In reality, strain is ALWAYS three dimensional (S 70)1>S2>S3, pages 78-79)

When S1xS2xS3≠1, Strain is accompanied by change in overall volume (pages 81-83)

Important: Ramsay’s strain field diagram (page 83, Fig. 2.58)

Special case scenario: Plane strain

When S1>S2=1>S3 (No finite strain along intermediate strain axis)

Implies no volume change

Plane strain can be expressed in 2-D 70)

Two end member cases (pages 84-85)

- Pure shear
- Simple shear
Pure shear

Simple shear 70)

- 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

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