3. Strain

Question 1

What is the definition of engineering strain?

Answer 1

e = (L-L₀)/L₀

Where L is the final length of the line, and L₀ is the starting length. It may be positive or negative depending upon whether the line had increased or decreased in length

Question 2

What is the definition of logarithmic strain?

Answer 2

natural strain

Question 3

What is the definition of angular shear and engineering shear strain?

Answer 3

The change in angle between two lines that were originally perpendicular ψ

positive for an anticlockwise rotation

Engineering shear strain: γ = tanψ

Question 4

Explain the distinction between the terms ‘deformation’, ‘displacement, and ‘strain’

Answer 4

Displacement: change in position of a given particle

Strain: relative change in position of particles within the feature - change in distances between particles: small = infinitesimal, large(measurable) = finite

Deformation: displacement (may or may not involve strain)

Question 5

What are the four basic types of displacement? Which of these produce strain?

Answer 5

Rigid body translation: every particle in the body moves in the same direction and by the same distance

Rigid body rotation: uniform physical rotation of the body; the displacement vectors of the particles are not all the same but the distance between particles remains unchanged

Distortion(shape change): movement of particles so that they change position relative to each other; the displacement vectors are not all the same (STRAIN)

Dilation: change in volume but not change in shape (STRAIN)

Question 6

What is a strain ellipse?

Given a strain ellipse, make sure that you can use it to work out engineering strain and angular shear (and hence logarithmic strain and engineering shear strain) in a specified direction. Given a strain ellipse, show the direction of the principal strains, e₁ and e₂

Answer 6

• represents the deformed shape of an initially circular marker, and illustrates how linear strain and angular shear vary with direction
• principal strains are the major and minor axes of the ellipse

_{Make sure that you can spell ‘principal’; it is NOT ‘principle’ - S. J. Covey-Crump}

Question 7

Draw a diagram illustrating the difference between pure shear and simple shear

Answer 7

Simple shear: rotational and non-coaxial

Pure shear: irrotational and co-axial

Question 8

Define ‘plane strain, and ‘axially symmetric strain’

Answer 8

Plane strain: no stretching or shortening in one principal direction (Y direction); in such cases, the strain can be regarded as two- dimensional

Axially symmetric extension or compression: an irrotational deformation in which the length changes along two principal directions (Y and Z or X and Y respectively) are equal

Question 9

Using the X, Y, Z nomenclature, define a prolate and an oblate strain ellipsoid

Answer 9

Prolate(cigar): X>>Y≥Z

Oblate(pancake): X≥Y>>Z

Question 10

In the X, Y, Z nomenclature, what direction is a stretching lineation, and what plane is cleavage?

Answer 10

Cleavage in deformed rocks is generally assumed to represent the XY plane (principal flattening plane)

_{cleavage formed as shear bands and crenulation cleavage do not directly relate to the strain ellipsoid}

_{if the orientations of X, Y and Z can be determined, you should specify the orientation of each of these as a plunge/plunge direction}