ability of a deformed
material body to return to its original shape and size when the forces causing the
deformation are removed. A body with this ability is said to behave (or respond)
Elastically
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
elastic recovery
is possible for any given material. This limit, called the
elastic limit, is the maximum stress or
force per unit area within a solid material that can arise before the onset of permanent deformation.
Stresses beyond the elastic limit cause a material to yield or flow. For such materials the elastic
limit marks the end of elastic behaviour and the beginning of plastic behaviour. For most brittle
materials, stresses beyond the elastic limit result in fracture with almost no
plastic deformation.
The
elastic limit depends markedly on the type of solid considered; for example,
a
steel bar or wire can be extended elastically only about 1 percent of its original length,
while for strips of certain
rubberlike materials, elastic extensions of up to 1,000 percent
can be achieved.
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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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