Lab 10 Strain Analysis Pure and Simple Shear

Lab 10: Strain Analysis

Pure and Simple Shear • in simple shear, the finite stretching axes (S 1 and S 3) rotate during deformation • in pure shear, the finite stretching axes (S 1 and S 3) do not rotate, but shorten in one direction and lengthen in the other direction

Angular Shear and Shear Strain • angular shear (ψ) describes the change in angle between two lines that were originally perpendicular to each other • shear strain (γ) is another way to describe this change in angular relationship as the horizontal translation of a line

The Strain Ellipse • the strain ellipse allows us to describe the amount of deformation that has occurred in an originally circular body • S 1 = the direction and magnitude of maximum finite stretch (long axis, e 1) • S 3 = the direction and magnitude of minimum finite stretch (short axis, e 3)

Stretch and Elongation e = elongation lo = original length lf = deformed length S = stretch

Wellmann Strain Analysis • uses bilaterally symmetric objects, such as brachiopod fossils to determine a strain ellipse for a sample

Wellman Strain Analysis 1. number each fossil 2. draw arbitrary reference line 3. draw reference line/pts. on tracing paper 4. draw hinge and median lines at each reference point for each fossil 5. make a point for line intersections 6. draw best fit ellipse through points

Strain in Shear Zones shear zone defined by elongated (and rotated) quartz, feldspar, and biotite grains 1. 2. 3. define the shear zone boundaries define the fabric developed by shearing measure as many θ' angles as possible across the shear zone

Strain in Shear Zones γ = 2/tan 2θ' 1. calculate shear strain (γ) for each angle you measured in the shear zone 2. plot shear strain vs. distance 3. determine the displacement (D) across the shear zone by numerical or graphical integration (i. e. , determine the area under the curve)

Regional Strain rotation during distortion: θd = angle between the line of interest and S 2 in the deformed state • can retrodeform a region to determine the original area and strike of bedding θ = angle between line of interest and S 2 in the undeformed state