Elasticity is a general property of all bodies. When an external force is applied to a body, the body becomes deformed. However, the body often regains its shape as soon as the force is removed, and this property is known as Elasticity. The deformation produced in a body is measured by a quantity known as strain, and the reaction produced in the body in response to the external force is measured by a quantity known as stress. Stress and strain are proportional to each other.
If an unbalanced force acts on a body, the body may become deformed. After the removal of the deforming force, the body often returns to its normal shape. This property of the material bodies is regarded as elasticity. On the other hand, some bodies retain their deformation after the removal of deforming force, and the corresponding property is known as plasticity. A body that always recovers its original configuration whenever the deforming force is withdrawn, regardless of the magnitude of deforming force, is regarded as a perfectly elastic body. And a body that retains its changed configuration even after the removal of the deforming force, regardless of its magnitude, is known as a perfectly plastic body. In real life, however, such ideal bodies do not exist, and most of the substances behave like perfectly elastic bodies up to a certain level of an applied deforming force. When the magnitude of the deforming force crosses a certain threshold, the body can no longer regain its original configuration and attains a permanent deformation, at which point, the body starts to behave like a perfectly plastic body. This particular limit is known as the elastic limit, which is a characteristic property of material bodies and varies from one type of substance to another. The cause of elasticity is attributed to the interplay between the molecular forces of the substance.
In studying the elastic properties of materials, two quantities are extremely important, namely stress and strain.
Strain: The strain measures the amount of deformation produced in the body due to the application of a deforming force. The strain is defined as the fractional change in dimension of a body relative to its original configuration. Mathematically,
{\rm{Strain = }}\frac{{{\rm{Change \ in \ dimension}}}}{{{\rm{original \ dimension}}}}Strain=
original dimension
Change in dimension
​
Since strain is a ratio of two similar quantities, it is dimensionless and has no unit.
Stress: Whenever a deforming force acts on a body and changes its configuration, internal reaction forces come into play, which try to restore the original configuration of the body. The reaction forces are equal and opposite to the external deforming force following Newton’s third law of motion. Stress is defined as the reaction force generated per unit area of the body. Mathematically,
{\rm{Stress = }}\frac{{{\rm{Internal \ restoring \ force}}}}{{{\rm{area}}}}Stress=
area
Internal restoring force
​
Since the internal force is equal to the applied deforming force, we can also write,
{\rm{Stress = }}\frac{{{\rm{Applied \ force}}}}{{{\rm{area}}}}Stress=
area
Applied force
​
The unit of stress is as follows:
SI – {\rm{N}} \cdot {{\rm{m}}^{ – {\rm{2}}}}{\rm{ \ or \ Pa}}Nâ‹…m
−2
or Pa
C.G.S – {\rm{dyne}} \cdot {\rm{c}}{{\rm{m}}^{ – 2}}dyneâ‹…cm
−2
Dimensional formula of stress: \left[ {{\rm{M}}{{\rm{L}}^{ – 1}}{{\rm{T}}^{ – 2}}} \right][ML
−1
T
−2
]
Types of stress and strain
The stress is proportional to the strain. However, the strain also depends on the axis of the stress.
Longitudinal strain and stress: If the material subject to a deforming force is in the form of a bar or wire such that its length is much greater than the cross-section, then the deformation produced in the material is primary along the length. Any deformation along the cross-section is negligible. The body is said to be under longitudinal strain. The corresponding stress is known as longitudinal stress.
Volume strain and stress: If the deforming forces acting on the body are such that only the volume of the body is deformed, whereas the shape remains intact, then the body is said to be under volume strain. The corresponding stress is known as volume stress.
Shear strain and stress: If the deforming forces acting on the body are such that only the shape of the body is changed, whereas the volume remains the same before and after deformation, then the body is said to be under shearing strain. The corresponding stress is known as shearing stress.
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