8. Deformation and Strain

Deformation

A transformation from an initial to a final geometry by means of rigid body translation, rigid body rotation, strain (distortion) and/or volume change

Strain

Any change in shape with or without change in volume, is referred to as strain, and implies that particles in a rock have changed positions relative to each other

Stress

Stress on a surface is the force over the area on which it is applied to cause the deformation

Coordinate Axes

Arbitrary axes in space that we use to describe the motion and length/shape change

Translation

The body is moved horizontally and/or vertically from its original location

Rotation

The body is rotated about its original location against a point

Simple Shear

Non coaxial deformation where the material lines rotate after deformation

Pure Shear

Coaxial deformation where material lines before and after deformation remain parallel

Strain Ellipse

The deformed shape of a circle, can measure deformation lines in accordance to original circle of unit radius

Homogeneous Deformation

Strain (change in shape and/or size) for each small part of the body are geometrically similar to that of the whole body

Heterogeneous Deformation

Strain where a rock body changes shape, size, or orientation unevenly, so different parts deform differently

e

Extension, e = (l – l0) / l0

s

Stretch, s = l / l0, s = 1+ e

l0

Original length of line

l

Finite (end) length of line

Principal Axes

Major/minor axes of strain ellipse

3D General/Triaxial Strain

Strain where X > Y > Z (plane strain ellipsoid)

2D Planar Strain

Strain where X > 1 > Z

1D Simple Shortening/Volume Change

Strain where 1 > Z

3D Axially Symmetric Shortening

Z-axis oblate strain where X = Y > Z

3D Axially Symmetric Extension

X-axis prolate strain where X > Y = Z

Flinn Diagram

A graphical representation of the full range of three-dimensional strain states in deformed rocks, with or without a change in their volume

Deformation

A transformation from an initial to a final geometry by means of rigid body translation, rigid body rotation, strain (distortion) and/or volume change