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Stress, Strain and Hooke's Law

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Stress, Strain and Hooke's Law - Lesson Summary

If a body is deformed, the intermolecular distance of separation changes from its equilibrium value. This causes intermolecular forces to be generated, which try to restore the body to its original state once the deforming external forces are removed.
The sum total of intermolecular restoring forces per unit area is called stress.
Stress is measured as the deforming force applied per unit area. If ‘F’ is the force applied on the surface of a body with an area ‘A’, then stress is equal to force ‘F’ by area ‘A’. The S.I unit of Stress is newton per metre square, which is also called  pascal. Its dimensional formula is M L -1 T -2.
 
The fractional deformation produced in the body by the external deforming forces is called strain. It is calculated as the ratio of the change in the body’s dimension to the original value of the same dimension.
 
For example, if the original length of a rubber band is L and the increase in its length is D L, then the strain is equal to the ratio D L to L.
 
As strain is the ratio of two similar quantities, it has no units. Thus, strain is a dimensionless quantity.
 
A body can be deformed in one or more of three possible ways, namely, longitudinal deformation, volume or bulk deformation and deformation in shape. Based on the manner in which deforming external forces are applied and deform a body, we define three different types of stress and strain.
 
When deforming forces are a pair of equal and opposite outward forces, applied normal to a pair of opposite-end faces of a rod, the length of the rod increases, and the stress generated is called tensile stress.
 
When the deforming forces are a pair of equal and opposite inward forces, applied normal to a pair of opposite-end faces of a rod, the length of the rod decreases, and the stress generated is called compressive stress.
Inward or outward deforming forces applied along the length of a body cause a change in its length. The change in length causes tensile stress or compressive stress, and these are collectively called longitudinal stress. Longitudinal stress is measured as the ratio of the applied force F to the area of the face (A).
 
If the length of the rod (L) changes by D L, the fractional deformation, called the longitudinal strain, is equal to the ratio of DL to L.
 
When deforming forces are applied perpendicularly to a body’s surface at every point, the volume of a body changes, and the stress generated is called bulk stress or volume stress.
 
Forces acting perpendicularly inward at each point on the surface of a body are equivalent to a uniform increase in external pressure. Therefore, bulk stress is defined as a change in pressure, D p.
If the volume of a body, V changes by DV, then the fractional deformation, also called the bulk strain or volume strain is equal to the ratio of D V to V.
 
If two equal and opposite forces act parallel to two opposite faces of a body, the shape of the body is distorted.
When the deforming forces are a pair of equal and opposite forces applied tangentially to a pair of opposite-end faces of a body, the shape of the body is distorted, and the stress generated is called t
Shear stress is measured as the applied tangential force (F) / the area of the face (A)
 
Robert Hooke found that for most materials, for small values of strain, the stress is directly proportional to the strain. Thus, we have stress is equal to k into strain, where ‘k’ is the constant of proportionality called elastic modulus of the material. If on increasing the stress, the strain is increased beyond a certain value, the proportionality between stress and strain is lost.
There are some materials that do not obey Hooke’s Law. For example, for materials such as polymers like rubber, human muscles and blood vessels, stress is not proportional to the strain.
Hooke’s Law states that for small values of strain, stress is directly proportional to strain.
Note: All materials do not follow Hooke’s Law.

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