{"cells": [{"cell_type": "markdown", "metadata": {"tags": ["module-dte"]}, "source": ["# Basics of Stress and Strain\n", "[Deforming the Earth](module-dte) \n", "\n", "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\n", "\n", "## Stress\n", "```{Index} Stress\n", "```\n", "\n", "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.\n", "\n", "**Normal Stresses** act perpendicular to the body's surface. These could be compressional or tensional.\n", "**Shear Stresses** act paralllel to the area to which it is applied.\n", "\n", "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. \n", "\n", "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. $\\omega_1>\\omega_2>\\omega_3$.\n", "\n", "Stress can lead to changes in volume, size, and/or orientation. This is an example of **strain**, which is what stresses results in.\n", "\n", "\n", "## Strain\n", "```{Index} Strain\n", "```\n", "Strain is the magnitude of a deformation, equal to the change in the dimension of a deformed object divided by its original dimension.\n", "\n", "These can either be homogeneous, or heterogeneous.\n", "\n", "**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:\n", "\n", "* **Pure**: Where the strain axes remain the same as the original body.\n", "* **Simple**: Where the strain results in a rotation of the original body.\n", "\n", "For homogeneous strain, pure and simple strain components are enough to define a body.\n", "\n", "**Heterogeneous** strain is the opposite of this, where strain is no longer uniform throughout the body.\n", "\n", "Strain can be defined as below:\n", "\n", "**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\n"]}], "metadata": {"celltoolbar": "Tags", "kernelspec": {"display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.8"}}, "nbformat": 4, "nbformat_minor": 4}