# Elastic Properties of Solids

**Under Stress**

__Hooke’s Law__

“Forces can cause objects to deform (i.e. change their shape). The way in which an object deforms depends on its dimensions, the material it is made of, the size of the force and direction of the force.”

*F = ke*

Where:

*F* = tension acting on the spring.

*e* is extension = (l-lo); l is the stretched length and lo is original length.

*k* = the spring constant.

Once the spring is extended beyond the point P, it will no longer return to its original shape. This is the point of **elastic limit**.

If a material returns to its original shape after forces are applied, it demonstrates **elastic** behaviour.

If a material deforms from its original shape after forces are applied, it is a sign of **plastic** behaviour.

__Elastic Potential Energy__

“If the deformation caused is within the elastic limit, the work done in deforming the object is stored within it as potential energy. This is called (elastic) ‘strain energy’. When the applied force is removed the energy is released. The strain energy then performs work in changing the object and to its original state.”

The work done (W) by the object is the shaded triangular area under the straight line.

__Stress, strain and Young’s Modulus__

Stress is defined as the force per unit area of a material:

**Stress = force/cross sectional area **

where *s* = stress, *F* = force applied, *A*= cross sectional area

Units of s: Nm-2 or Pa.

Strain is defined as extension per unit length:

**Strain = extension/original length**

where *e* = strain, *lo* = the original length, *e* = extension = *(l-lo)* and *l* = stretched length

Strain has no units because it is a ratio of lengths.

The gradient of the straight-line graph is the Young’s modulus, E

Units of the Young modulus E: Nm-2 or Pa