Stress and Strain

Deformation

Refers to any change in shape, volume, position, or orientation of a body under stress. Has 4 components: rotation, translation, distortion, and dilation.

Rotation, translation, distortion, and dilation

4 components of deformation

Stress

A force that acts on rock to change its shape or volume. Pair of equal and opposite forces acting on a unit area of a body.

Sigma

Stress that is perpendicular to the surface.

Tau

Stress that is parallel to the surface.

Principal stress planes

3 mutually perpendicular planes on where the shear stress is 0.

Principal stress axes

Normal stresses across principal stress planes.

Sigma 1

Maximum compressive stress, minimum tensional stress.

Sigma 2

Intermediate compressive stress.

Sigma 3

Minimum compressional stress, maximum tensional stress.

Hydrostatic stress

A state of stress at a point where the normal stress is the same in all directions. Principal stress all equal. Results in volume change. Lithostatic stress. Equal to the sum of 3 sigmas.

Deviatoric stress

Unequal pressure in different directions. Difference between the mean stress and the total stress. Controls the extent of shape change or distortion.

Dilation

Change in size; volume change.

Distortion

Change in shape.

Continuous homogenous and continuous heterogenous

2 natures of continuous strain.

Continuous homogenous strain

When any 2 portions of the body that were similar in form and orientation before are similar in form and orientation after strain.

Continuous heterogenous strain

When any 2 portions of the body that were similar in form and orientation before are different in shape in form and shape after distortion.

Discontinuous strain

When 2 portions of a body that was once similar were broken into pieces / displaced after deformation.

Continuous deformation

Forms folds. Also called distributed deformation.

Discontinuous deformation

Forms faults. Also called discrete deformation.

Shear strain

The amount of deformation perpendicular to a given line rather than parallel to it. Deformation / Original Length = Tan A

Simple shear

Rock is sheared like a deck of cards. Square to parallelogram. Non-coaxial deformation. One direction remains constant and everything else rotates relative to it.

Pure shear

Rock is shortened in one direction and extended in the perpendicular direction. Square to rectangle. Coaxial deformation