Editing Young's modulus (section)

==Definition==
Young's modulus, <math>E</math>, quantifies the relationship between tensile or compressive [[stress (mechanics)|stress]] <math>\sigma</math> (force per unit area) and axial [[strain (mechanics)|strain]] <math>\varepsilon</math> (proportional deformation) in the [[linear elasticity|linear elastic]] region of a material:<ref>{{cite book |last=Jastrzebski |first=D. |title=Nature and Properties of Engineering Materials |publisher=[[John Wiley & Sons, Inc]] |year=1959 |edition=Wiley International}}</ref>
<math display="block">E = \frac{\sigma}{\varepsilon}</math>

Young's modulus is commonly measured in the [[International System of Units]] (SI) in multiples of the [[Pascal (unit)|pascal]] (Pa) and common values are in the range of [[gigapascal]]s (GPa).

Examples:
* [[Rubber]] (increasing pressure: ''large length increase, meaning low <math>E</math>'')
* [[Aluminium]] (increasing pressure: ''small length increase, meaning high <math>E</math>'')

===Linear elasticity===
{{Main|Linear elasticity}}
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.

At near-zero stress and strain, the stress–strain curve is [[linear]], and the relationship between stress and strain is described by [[Hooke's law]] that states stress is proportional to strain. The coefficient of proportionality is Young's modulus. The higher the modulus, the more stress is needed to create the same amount of strain; an idealized [[rigid body]] would have an infinite Young's modulus. Conversely, a very soft material (such as a fluid) would deform without force, and would have zero Young's modulus.

===Related but distinct properties===
Material stiffness is a distinct property from the following:
* [[Strength of materials|Strength]]: maximum amount of stress that material can withstand while staying in the elastic (reversible) deformation regime;
* Geometric stiffness: a global characteristic of the body that depends on its shape, and not only on the local properties of the material; for instance, an [[I beam|I-beam]] has a higher bending stiffness than a rod of the same material for a given mass per length;
* [[Hardness]]: relative resistance of the material's surface to penetration by a harder body;
* [[Toughness]]: amount of energy that a material can absorb before fracture.
*The point E is the elastic limit or the yield point of the material within which the stress is proportional to strain and the material regains its original shape after removal of the external force.