Young's Modulus And Hookes Law

To a greater or lesser extent, most solid materials exhibit elastic behaviour, but there is a l imit to the magnitude of the force and the accompanying deformation within which

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In a simple tension test, the elastic response of materials such as steel
and bone is typified by a linear relationship between the **tensile stress **(tension or stretching force
per unit area of cross section of the material), σ, and the **extension ratio** (difference between extended
and initial lengths divided by the initial length), e. In other words, σ is proportional to e; this is
expressed σ = Ee, where E, the constant of proportionality, is called **Young’s modulus**.

The value of E depends on the material; the ratio of its values for steel and rubber is about 100,000. The equation σ = Ee is known as**Hooke’s law** and is an example of a **constitutive law**.

It expresses, in terms of macroscopic quantities, something about the nature (or constitution) of the material.**Hooke’s law applies essentially to one-dimensional deformations**, but it can be extended to more general
(three-dimensional) deformations by the introduction of linearly related stresses and strains
(generalizations of σ and e) that account for shearing, twisting, and volume changes.
The resulting
generalized Hooke’s law, upon which the linear theory of elasticity is based, provides a good
description of the elastic properties of all materials, provided that the deformations correspond
to extensions not exceeding about 5 percent. This theory is commonly applied in the analysis of
engineering structures and of seismic disturbances
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The value of E depends on the material; the ratio of its values for steel and rubber is about 100,000. The equation σ = Ee is known as

It expresses, in terms of macroscopic quantities, something about the nature (or constitution) of the material.