# Kinematic analysis and strain - PowerPoint PPT Presentation

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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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## 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

• 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:

• 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 (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 (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 pages 55-68

• Stretch (S) =

• Extension (e) = = S-1

• Quadratic elongation (λ) = S2 =(1+e)2

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)

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 (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

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

• 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