Young's modulus

Young's modulus (or Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise.

Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material.

The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years.

Young's modulus is commonly measured in the International System of Units (SI) in multiples of the pascal (Pa) and common values are in the range of gigapascals (GPa).

Examples: A solid material undergoes elastic deformation when a small load is applied to it in compression or extension.

Elastic deformation is reversible, meaning that the material returns to its original shape after the load is removed.

Conversely, a very soft material (such as a fluid) would deform without force, and would have zero Young's modulus.

Material stiffness is a distinct property from the following: 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.

Any two of these parameters are sufficient to fully describe elasticity in an isotropic material.

For example, calculating physical properties of cancerous skin tissue, has been measured and found to be a Poisson’s ratio of 0.43±0.12 and an average Young’s modulus of 52 KPa.

[3] For homogeneous isotropic materials simple relations exist between elastic constants that allow calculating them all as long as two are known: Young's modulus represents the factor of proportionality in Hooke's law, which 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.

Otherwise (if the typical stress one would apply is outside the linear range), the material is said to be non-linear.

In solid mechanics, the slope of the stress–strain curve at any point is called the tangent modulus.

It can be experimentally determined from the slope of a stress–strain curve created during tensile tests conducted on a sample of the material.

Most metals and ceramics, along with many other materials, are isotropic, and their mechanical properties are the same in all orientations.

These materials then become anisotropic, and Young's modulus will change depending on the direction of the force vector.

Although classically, this change is predicted through fitting and without a clear underlying mechanism (for example, the Watchman's formula), the Rahemi-Li model[5] demonstrates how the change in the electron work function leads to change in the Young's modulus of metals and predicts this variation with calculable parameters, using the generalization of the Lennard-Jones potential to solids.

In general, as the temperature increases, the Young's modulus decreases via

is a calculable material property which is dependent on the crystal structure (for example, BCC, FCC).

Young's modulus is calculated by dividing the tensile stress,

where Young's modulus of a material can be used to calculate the force it exerts under specific strain.

Hooke's law for a stretched wire can be derived from this formula: where it comes in saturation Note that the elasticity of coiled springs comes from shear modulus, not Young's modulus.

When a spring is stretched, its wire's length doesn't change, but its shape does.

This is why only the shear modulus of elasticity is involved in the stretching of a spring.

In a nonlinear elastic material the Young's modulus is a function of the strain, so the second equivalence no longer holds, and the elastic energy is not a quadratic function of the strain: Young's modulus can vary somewhat due to differences in sample composition and test method.

The rate of deformation has the greatest impact on the data collected, especially in polymers.