1. Strain: Making ordinary rocks look cool for over 4 billion years

2. Goals: To understand homogeneous, nonrecoverable strain, some useful quantities for describing it, and how we might measure strain in naturally deformed rocks.

3. Deformation vs. Strain
Deformation is a reaction to differential stress. It can involve:
Translation — movement of rocks
Rotation
Distortion — change in shape and/or size. Distortion = Strain

4. Folded single layer can serve as an example of deformation that involves translation, rotation, and distortion.

5. Recoverable vs. nonrecoverable strain
Recoverable strain: Distortion that goes away once stress is removed
Example: stretching a rubber band
Nonrecoverable strain: Permanent distortion, remains even after stress is removed
Example: squashing silly putty

6. Strain in 2-D Elongation (e) change in length of a line
e = (L - L0)/ L0
L = deformed length L0 = original length
Elongation often expressed as percent of the absolute value, so we would say 30% shortening or 40% extension

7. Strain in 2-D
Strain ellipse: Ellipse formed by subjecting a circle to homogeneous strain
Undeformed
Deformed

8. The strain ellipse
2 principal axes — maximum and minimum diameters of the ellipse.
If volume is constant, average value of axes = diameter of undeformed circle =

9. Stretch (S): Relates elongation to the strain ellipse
S = 1 + e = 1 + [(L - L0)/ L0]
Maximum and minimum principal stretches (S1 and S2) define the strain ellipse
S1 = 1 + e1 and S2 = 1 + e2 S2 S1

10. The strain ratio is defined as S1/S2
Magnitude of shape change recorded by strain ellipse.
Because it is dimensionless, the strain ratio can be measured directly without knowing L0. S2 S1

11. Strain in 3-D
For 3-D strain, add a third axis to the strain ellipse, making it the strain ellipsoid
The axes of the strain ellipsoid are S1, S2, and S3
S1, S2, and S3 = Maximum, intermediate, and minimum principal stretches

12. Three end-member strain ellipsoids
Constriction
S1 > S2 = S3
Plane strain
S1 > S2 > S3
Flattening
S1 = S2 > S3

13. We can plot 3-D strain graphically on a Flinn diagram
Use the strain ratios — S1/S2 and S2/S3

15. Flinn Diagram

16. We can also describe the shape of the finite strain ellipsoid using Flinn’s parameter (k)
k = 0 for flattening strain
k = 1 for plane strain
k = ∞ for constrictional strain

17. Activity
As a group, measure S1/S2 and S2/S3 of the flattened Silly Putty, Sparkle Putty, and Fluorescent Putty balls from Monday
Plot these results individually on a Flinn diagram. Use different symbol for each putty type
Calculate Flinn’s parameter for the Silly Putty

18. Strain rate (ė) ė = e/t and units are s-1 Elongation per second, so
Calculate strain rate for your three putty types

19. Natural strain markers
Sand grains, pebbles, cobbles, breccia clasts, and fossils
Must have same viscosity as rest of rock