Homogeneous Strain

Lectures: Monday, April 12 and Wednesday, April 14

Text: pages 292-313

Monday, April 12

MondayÌs lecture followed to text pretty closely, so I will not go into

much detail.

Definition The strain of a body is the change in size and shape that the

body experiences during deformation. Homogeous strain is when the changes

in size and shape are proportionately identical for each small part of the

body and for the body as a whole.

Deformation is compsoed of 1) translation, 2) rotation, 3)distortion (or

strain).

We went through a quantitative description of strain and defined the following:

Box 15.1

strain tensor as the sum of infinitesimal strain and infinitesimal rotation.

The tensor is symmentric when the off-diagonal terms of the matrix are

equal, and antisymmentric when the off-diagonoal elements are equal in

magnitude but opposite in sign.

Finite strain tensor (non-infinitesimal)

Dilatation (volumetiric extension ev = sv -1), with volumetirc strestch sv

Equations for infinitesimal stress and strain parallel each other. This is

not true for finite stress and strain.

There is a linear relationship between stress and the strain rate.

Strain Ellipsoid - This is covered in the text. One note is that the axes

of the ellipsoid are actually stretch s

strain e = s - 1

where s = deformed radius l/ undeformed radius L

Wednesday, April 14

Questions:

Crenulation foliations vs. S-C mylonites

Crenulation foliation formed by harmonic folds that develop in a prexisting

foliation, so the new foliation cuts across the old one. If the

crenulations are symmetic, both limbs defines the cleavage. If they are

asymmetric, then only one of the limbs defines the new foliation. (p266-7)

S-C mylonites are formed by only one deformation event and are always

asymmetric.

Pressure Solution

Dissolution occurs at grain boundaries and can re-precipitate next to the

grain (stress shadow).

Original State from Strained State

Fossils are good indicators for inferring the amount of strain because they

can have a known symmetric or radial shape. Some examples are trilobites,

brachiopods, and ammonites.

Otherwise, it is not possible to find a direct relationship for stress and

strain. Genearlly, the stress diraction is parallel to the incremental

strain or strain rate. However, large stress will produce large deviations

from its orientation.

We looked at strain progression diagrams for simple and pure shear. In

pure shear, the orientation of the ellips remains the same. For simple

shear, the ellpse can rotate and over-rotae while shortening, so the end

product does not indicate what past strain has occurse.