elasticity    It is a property of solids by which a body returns to its original form when external deforming force is removed.

The  external deforming force is measured in terms of stress, which   is   defined as external  force  per  unit  area.  The deformation  is  measured  in terms of strain which is defined as fractional deformation.

Below  a  certain  limiting  value  of stress, strain is proportional  to  stress (Hook's  Law).  The ratio of stress to strain is a constant called the elastic constant.

Stress  can  be  of the following kinds : 1) a tension or compression  causing a change  in  length.  The  corresponding elastic modulus is called Young's modulus.

Y = tensile stress/tensile strain = force per unit area/(change in length/original elength)

2)  A  compression  acting  on  the  whole  surface of the body causing change in the volume. The corresponding elastic constant is called bulk modulus, which is

 bulk modulus = volume stress / volume strain = Force acting per unit area / 9Change in the volume/original volume)

3) A  tangential  stress  acting  on  opposite faces of a body causing  change  in shape.  This  is  called shear stress. The elastic modulus is called shear modulus, which is

 shear modulus = shear stress/ shear strain

 The  shear  stress  is the force acting per unit area. The shear strain is the angle f (in radians), called the angle of the shear as shown in fig.e1. Because f is small f = s/d.

Elastic limit: Beyond a certain limiting stress the deformation produced   is permanent.  The  minimum  stress  that  produces permanent deformation is called the elastic limit.

Poisson's  ratio:  When a wire is subjected to a tensile stress causing  an increase in its length, the cross section of the wire decreases. The lateral strain is defined as the ratio of change in  the  radius  to  the original radius. Poisson's ratio is the ratio of the lateral strain the longitudinal strain.