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In solid mechanics, Young's modulus or modulus of elasticity (and also elastic modulus) is a measure of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. This can be experimentally determined from the slope of a stress-strain curve created during tensile test s conducted on a sample of the material.
The SI unit of modulus of elasticity is the Pascal.
The modulus of elasticity can also be measured in other units of pressure, for example pounds per square inch (psi).
The Young's modulus allows engineers and other scientists to calculate the behavior of a material under load. For instance, it can be used to predict the amount a wire will extend under tension, or to predict the load at which a thin column will buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus , density or Poisson's ratio.
For many materials, Young's modulus is a 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. RubberThis article is about the material rubber, for other uses see Rubber (disambiguation Rubber is an elastic hydrocarbon polymer which occurs as a milky emulsion (known as latex) in the sap of a number of plants but can also be produced synthetically. The ma is a non-linear material.
The modulus of elasticity, λ, can be calculated by dividing the stress by the strain, i.e.
where
λ is the modulus of elasticity, measured in pascals
F is the force, measured in newtonThis article is about the SI unit of force. For other uses see Newton (disambiguation In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was adopted by the Generals
A is the cross-sectional area through which the force is applied, measured in square metreA square metre ( US spelling: square meter is by definition the area enclosed by a square with sides each 1 metre long. It is the SI unit of area. A square metre is equal to: 0. 000001 square kilometre 10000 square centimetres 0. 01 ares 1. 196 square yars
x is the extension, measured in metreFor other uses of "metre" and "meter", see Metre (disambiguation). The metre is the basic unit of length in the International System of Units (SI: Systeme International d'Unites). It is defined as the length of the path travelled by light in absolute vacus
l is the natural length, measured in metreFor other uses of "metre" and "meter", see Metre (disambiguation). The metre is the basic unit of length in the International System of Units (SI: Systeme International d'Unites). It is defined as the length of the path travelled by light in absolute vacus
The modulus of elasticity of a material can be used to calculate the tension force it exerts under a specific extension.
where
T is the tension, measured in newtonThis article is about the SI unit of force. For other uses see Newton (disambiguation In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was adopted by the Generals
The elastic potential energy stored is given by the integral of this expression with respect to x, i.e. energy stored E is given by:
where
E is the elastic potential energy, measured in joules
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