Editing Young's modulus (section)

===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.