Young's Modulus

Young's modulus (E) is a measure of the stiffness of a material. It is also known as the Young modulus, modulus of elasticity, elastic modulus (though the Young's modulus is actually one of several elastic moduli such as the bulk modulu and the shear modulus) or tensile modulus. It is defined as the ratio of stres over strain in the region in which Hooke's Law is obeyed for the material. This can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material.
Young's modulus is named after Thomas Young, the 18th century British scientist.

Units
Young's modulus is the ratio of stress, which has units of pressure, to strain, which is dimensionless; therefore Young's modulus itself has units of pressure.
The SI unit of modulus of elasticity (E, or less commonly Y) is the pascal.

Usage
The Young's modulus allows the behavior of a material under load to be calculated. For instance, it can be used to predict the amount a wire will extend under tension or buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson's ratio.
Linear vs non-linear
For many materials, Young's modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials include steel, carbon fiber, and glass. Rubber and soils (except at very small strains) are non-linear materials.
Directional materials
Most metals and ceramics, along with many other materials, are isotropic: their mechanical properties are the same in all directions. However metals and ceramics can be treated with certain impurities to give them a “grain”. The grain of these, and other composites of two or more ingredients, is a mechanical structure of various orientations and sizes, which makes the material anisotropic. This means that Young's modulus will change depending on which direction the force is applied from. As a result, these anisotropic materials have different mechanical properties when load is applied in different directions. For example, carbon fiber is much stiffer (higher Young's modulus) when loaded parallel to the fibers (along the grain), and is an example of a material with transverse isotropy. Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating various structures in our environment.
Copper as an excellent electrical conductor is used to transmit electricity over long distance cables, however although copper has a relatively high value for Young's modulus at 130 GPa, it has a very low value for yield strength, and thus easily deforms in tension. When the copper cable is co-wound with hardened steel wire the stretching can largely be prevented, as the steel (with a higher value of Young's modulus in tension and much higher yield strength) takes up the tension that the copper would otherwise experience.
Calculation
Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain:
where

E is the Young's modulus (modulus of elasticity)
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ΔL is the amount by which the length of the object changes;
L0 is the original length of the object.

Example:


Pressure in a fluid:
Fluid pressure is the pressure at some point within a fluid, such as water or air.
Fluid pressure occurs in one of two situations:
1. an open condition, such as the ocean, a swimming pool, or the atmosphere; or
2. a closed condition, such as a water line or a gas line.
Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.
Closed bodies of fluid are either "static," when the fluid is not moving, or "dynamic," when the fluid can move as in either a pipe or by compressing and air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.
The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli.