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Kinematic analysis and strain

Kinematic analysis and strain . (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

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Kinematic analysis and strain

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  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 (λ) = S2 =(1+e)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 (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)

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

  10. In reality, strain is ALWAYS three dimensional (S1>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

  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

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