### Young's modulus - Wikipedia

We know that the Young's modulus of an object is defined as the ratio We also know that Hooke's law, which can be applied to any linear. is Young's modulus. We may say that Young's modulus is the Hooke's-law spring constant for the spring made from a specifically cut section of the solid material. Young's modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain Young's modulus represents the factor of proportionality in Hooke's law, which .

Usage[ edit ] The Young's modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression. The Young's modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions.

Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports. Other elastic calculations usually require the use of one additional elastic property, such as the shear modulusbulk modulus or Poisson's ratio.

### Elasticity: Young's modulus & Hooke's Law - SchoolWorkHelper

Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. Linear versus non-linear[ edit ] Young's modulus represents the factor of proportionality in Hooke's lawwhich relates the stress and the strain.

However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear.

## What is Hooke's Law?

Otherwise if the typical stress one would apply is outside the linear range the material is said to be non-linear. Steelcarbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. In the horizontal x axis, the interatomic separation is r. In both perpendicular directions, the separation is y, as shown in this sketch.

## Elasticity: Young’s modulus & Hooke’s Law

Young's modulus Y for a material is defined as the ratio of tensile stress to tensile strain. However, the repulsive term is simply a convenient, differentiable function that gives a very strong repulsion. So, we have related Young's modulus to individual atomic forces and energies: To relate Hooke's law to Young's modulus in the experiment above, it would be necessary to consider bending of the wire. In bending, one side of an object is stretched and the other compressed.

This also requires considering the geometry of the spring. Although the length of the spring may change by many percent, nowhere is the steel compressed or stretched more than one percent.

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Polymers and entropic forces Many polymeric materials, such as rubber, have much lower values of Young's modulus than other solids. The stretching mechanism here is different, because to a large extent stretching straightens polymer molecules, rather than changing the average distance between them.

A completely straightened polymer molecule has only one possible configuration. A bent and therefore shorter molecule has at least one kink in it. The kinks can occur at many different locations, so usually there are many possible configurations corresponding to a particular shortened length.

**Hooke's law and Young's modulus of elasticity - Strength of Material in Hindi lecture 3**

Consequently, the entropy of the contracted state is higher than that of the straightened state. More on thermal properties: As a consequence, polymers often contract as the temperature rises, rather than expand, as explained for 'normal' solids above.

See Fig 4 in Wolfe, J.