SOLIDS

Stress is defined as the tensile force per unit cross-sectional area.

Strain is defined as the extension per unit length

Young Modulus is defined as the stress per unit strain.

Hooke's Law :  F = kx

Elastic energy stored in stretching

Total work done for the whole extension

= area under F - x curve

=

Elastic energy stored per unit volume

=

= area under the stress-strain curve

Microscopic interpretation of Young Modulus

Suppose a solid rod consists of many layers is stretched a little by a tensile force

F so that the interatomic spacing changes from x to x + △x.

Force between 2 atoms in adjacent layers is  k △x.

If there are N atoms in each layer, total force,  F = N k △x

Area of each layer, A = N x²