Elasticity of material

Solids have a definite shape and size means they are rigid bodies but in reality these bodies can be stretched, compressed, bent and deform. Even the hard material can be deformed by applying sufficient external force on it. The property of a body by virtue of which its tendency to regain its original size and shape when the applied force is removed from the body is known as the elasticity of the body and that the formation is known as elastic deformation. But there are some exceptional cases if you apply force to a lump of mud they will not retain their previous shape and they get permanently deformed. Such kinds of substances are called plastic and this property is known as plasticity.

Elastic Behaviour of solids

In solids each atom and molecule are bonded together by an intermolecular force of attraction which makes them stay in a stable equilibrium position. When we apply a force on a solid material it tends to deform, the atoms of molecules are displaced from their equilibrium position causing a change in intermolecular distance. When we stop applying the force they regain their original size and position. This restoring mechanism of solids is known as the elastic behaviour of solid. For example if you try to pull a spring, its shape increases due to the force you apply on it but when the force is removed it will drive back to its original position.

Stress and strain

When we apply a force on a body it is deformed to a small or large extend depending upon the nature of the material and the force applied. In some cases defamation may not be noticeable but it is there. When a body is subjected to a deforming force there is a force developed in the body which is equal in magnitude but opposite in direction to the applied force. This restoring force is known as stress. If force is applied on the body and a is the area of cross section then,

stress= force/ area.

SI unit of stress is Nm-2 or Pascal(P).  Its dimensional formula is [ML-1T-2].

Types of stress

1. Tensile and compressive stress- If we stretch a cylindrical object by applying force normal to its cross sectional area. The restoring force per unit area in this case is called tensile stress. Whereas if a cylindrical object is compressed by applying force, then the restoring force is known as compressive stress.

2. Tangential stress or shearing stress- If two equal and opposite forces are applied parallel to the cross-sectional area of the cylinder there is a displacement between the opposite faces of the cylinder. This restoring force developed due to the applied tangential force and is known as tangential stress.

3. Hydraulic stress- When a solid sphere is placed in  in a fluid due to high pressure it is compressed uniformly from all the sides. The force applied by the fluid is in a perpendicular direction at each point of the surface which its volume decreases without any change in its true metrical shape. That body develops internal restoring force that is equal and opposite to the force applied by the fluid and this is known as hydraulic stress.

Strain: The amount of deformation and object undergoes when stress is applied on it. It refers to the physical effect on the object due to the force applied.

1. When a tensile stress a compressive stress is applied on an object there is a change in length of the object. This change in the length of an object is known as longitudinal strain.

Longitudinal strain = ∆L/L, Where ∆L- change in length , L- original length.

2. Tangential strain- When we apply a force tangentially on a body a stress occurs known as tangential stress which causes a relative displacement between two opposite faces of the cylinder this strain is known as shearing strain. It is the ratio of displacement of faces∆x to the length of the cylinderL. Shearing strain= ∆x/L = tanθ . (Where θ is the angular displacement)

3. Volume strain: The strain produced by a hydraulic pressure is called volume strain. It is the ratio of change in volume ∆V to original volume V. Volume strain = ∆VV.

Elastomers: Substances having high elasticity to cause large strains are known as elastomers like rubber tissue of aorta.

Classification of Elastic Moduli:

1. Young’s Modulus (Y) of Elasticity

2. Bulk Modulus of Elasticity

3. Shear Modulus of Elasticity

Hooke’s law

Stress and strain take different forms in different situations. The stress and strain are proportional to each other in case of small defamation. This is known as Hooke’s law.

Stress∝  strain

stress=k* strain

where K is the proportionality constant and known as modulus of elasticity.

Hooke’s law is found valid for most of the material however there are some exceptional cases where this linear relationship does not exhibit.

Conclusion

Stress is the restoring force per unit area and strain is the ratio of original to change in dimension. There are three types of stress

1. Tensile stress-(longitudinal or compressive)

2.  Shearing stress

3.  Hydraulic stress.  The strain produced by hydraulic stress is known as volume strain. When an object is under tension or compression the Hooke’s law takes place stress=k* strain. The materials which do not give their original shape after the external force is removed are known as plastic material. 

Longitudinal strain = ∆L/L, Where ∆L- change in length , L- original length.

Shearing strain= ∆x/L = tanθ . (Where θ is the angular displacement)

Volume strain = ∆V/V.