# Basics of Stress and Strain

## Contents

# Basics of Stress and Strain#

Deformation, in relation to the Earth’s crust, is the process of physical change within the rock body by the action of applied forces, namely gravity and tectonics. The physical change - strain, is caused by an applied stress

## Stress#

Stresses are pressures or tension exerted on a material body. These stresses can be either Normal or Shear, with respect to the direction in which they occur. Stresses are defined as a force acting over an area - \(\text{Stress}=\frac{F}{A}\). The units for stress are \(Nm^{-2}\), Pa, or Bars.

**Normal Stresses** act perpendicular to the body’s surface. These could be compressional or tensional.
**Shear Stresses** act paralllel to the area to which it is applied.

If there is no overall acceleration on a body where the sum of the forces actiing on the body is equal to zero, 3 mutually perpendicular planes of zero shear stress can always be found.

The **Principle Stress Axes** are axes of normal compressive stresses perpendicular to the planes of zero shear stresses mentioned above. These are denoted by \(\omega_1,\,\omega_2,\,\text{and}\,\omega_3\), and are called the maximum, intermediate, and minimum principle stress axes. \(\omega_1>\omega_2>\omega_3\).

Stress can lead to changes in volume, size, and/or orientation. This is an example of **strain**, which is what stresses results in.

## Strain#

Strain is the magnitude of a deformation, equal to the change in the dimension of a deformed object divided by its original dimension.

These can either be homogeneous, or heterogeneous.

**Homogeneous** strain produces the same distortion everywhere. As a result the strain is uniform throughout the body, and straight lines are kept straight. Homogeneous strain can be:

**Pure**: Where the strain axes remain the same as the original body.**Simple**: Where the strain results in a rotation of the original body.

For homogeneous strain, pure and simple strain components are enough to define a body.

**Heterogeneous** strain is the opposite of this, where strain is no longer uniform throughout the body.

Strain can be defined as below:

**Linear Strain**, \(e = \frac{(L - L_0)}{L_0}\), where \(e\) is the linear strain, \(L_0\) is the length of the body before deformation, and, \(L\) being the new length post deformation