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

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

Deformation vs. Strain

Deformation is a reaction to differential stress. It can involve:

a) Translation — movement of rocks

b) Rotation

c) Distortion — change in shape and/or size. Distortion = Strain

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

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

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

Strain in 2-D

Strain ellipse: Ellipse formed by subjecting a circle to homogeneous strain

Undeformed Deformed

The strain ellipse2 principal axes — maximum and minimum

diameters of the ellipse.

If volume is constant, average value of axes = diameter of undeformed circle

=

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

S1

S2

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.

S1

S2

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

FlatteningS1 = S2 > S3

Plane strainS1 > S2 > S3

ConstrictionS1 > S2 = S3

Three end-member strain ellipsoids

We can plot 3-D strain graphically on a Flinn

diagram

Use the strain ratios — S1/S2 and S2/S3

Flinn Diagram

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

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

Strain rate (ė)

Elongation per second, so

ė = e/t and units are s-1

Calculate strain rate for your three putty types

Natural strain markers

Sand grains, pebbles, cobbles, breccia clasts, and fossils

Must have same viscosity as rest of rock