Editing Young's modulus (section)

==Usage==
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#Statically determinate|statically determinate]] [[beam (structure)|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 modulus]] <math>G</math>, [[bulk modulus]] <math>K</math>, and [[Poisson's ratio]] <math>\nu</math>. 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. Defining the elastic properties of skin may become the first step in turning elasticity into a clinical tool.<ref>{{Cite journal |last1=Tilleman |first1=Tamara Raveh |last2=Tilleman |first2=Michael M. |last3=Neumann |first3=Martino H.A. |date=December 2004 |title=The Elastic Properties of Cancerous Skin: Poisson's Ratio and Young's Modulus |url=https://www.ima.org.il/FilesUploadPublic/IMAJ/0/52/26480.pdf |journal=Israel Medical Association Journal |volume=6 |issue=12 |pages=753–755|pmid=15609889 }}</ref> For homogeneous isotropic materials [[Elastic modulus|simple relations]] exist between elastic constants that allow calculating them all as long as two are known:
:<math>E = 2G(1+\nu) = 3K(1-2\nu).</math>

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

[[Steel]], [[carbon (fiber)|carbon fiber]] and [[glass]] among others are usually considered linear materials, while other materials such as [[rubber]] and [[soils]] are non-linear. However, this is not an absolute classification: if very small stresses or strains are applied to a non-linear material, the response will be linear, but if very high stress or strain is applied to a linear material, the linear theory will not be enough. For example, as the linear theory implies [[Reversible process (thermodynamics)|reversibility]], it would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.

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 test]]s conducted on a sample of the material.

===Directional materials===
Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are [[isotropy|isotropic]], and their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become [[anisotropy|anisotropic]], and Young's modulus will change depending on the direction of the force vector.<ref>{{Cite journal| last1=Gorodtsov |first1=V.A. |last2=Lisovenko |first2=D.S. |date=2019 |title=Extreme values of Young's modulus and Poisson's ratio of hexagonal crystals|journal=Mechanics of Materials |language=en |volume=134 |pages=1–8 |doi=10.1016/j.mechmat.2019.03.017 |bibcode=2019MechM.134....1G |s2cid=140493258 }}</ref> Anisotropy can be seen in many composites as well. For example, [[carbon (fiber)|carbon fiber]] has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain).  Other such materials include [[wood]] and [[reinforced concrete]]. Engineers can use this directional phenomenon to their advantage in creating structures.