### Elasticity

Elasticity – The elasticity is the ability of a solid to return to its original shape or form after being subject to strain. Most solid materials display elasticity, up to a load point called the elastic limit; loads higher than this limit cause permanent deformation of the material.

Elastic Limit- The elastic limit is the maximum value of deforming force upto which a material displays elastic properties and above which a material losses its elastic properties.

Stress- The restoring force per unit area set up inside the body subjected to deform force is called Stress. Mathematically, Stress = Force / Area or F/A

Units of Stress - The SI unit of stress is the Newton per square meter, also called the Pascal

1 Pascal = 1 Pa = 1 N/m2

Strain- The relative change in dimensions or shape of a body which is subjected to stress is called Strain.

Strain is measured by ratio of change in length to the original length or longitudinal length, change in volume to original volume or volume strain.

### Hooke’s Law

Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.

Alternatively, Hooke's law may also be written as ‘stress is directly proportional to strain’.

Mathematically, F = -kX

Where; x is the displacement of the spring's end from its equilibrium position (a distance, in SI units: metres); F is the restoring force exerted by the spring on that end (in SI units: N or kg•m/s2); and k is a constant called the rate or spring constant (in SI units: N/m or kg/s2).

• Young Modulus of Elasticity Y = Longitudinal Stress / Longitudinal Strain
• Bulk Modulus of Elasticity K = Volume Stress / Volume Strain
• Rigidity Modulus = Tangential or Shear Stress / Shear Strain