Elastic modulus

The Modulus of Elasticity (also known as the elastic modulus, the tensile modulus, or Young's modulus) is a number that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form:

where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some length parameter caused by the deformation to the original value of the length parameter. If stress is measured in pascals, then since strain is a dimensionless quantity, the units of λ will be pascals as well.

Since the strain equals unity for an object whose length has doubled, the elastic modulus equals the stress induced in the material by a doubling of length. While this scenario is not generally realistic because most materials will fail before reaching it, it gives heuristic guidance, because small fractions of the defining load will operate in exactly the same ratio. Thus, for steel with a Young's modulus of 30 million psi, a 30 thousand psi load will elongate a 1 inch bar by one thousandth of an inch; similarly, for metric units, a load of one-thousandth of the modulus (now measured in gigapascal) will change the length of a one-meter rod by a millimetre.

In a general description, since both stress and strain are described by second-rank tensors, including both stretch and shear components, the elasticity tensor is a fourth-rank tensor with up to 21 independent constants.

Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:

Three other elastic moduli are Poisson's ratio, Lamé's first parameter, and P-wave modulus.

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