# Modulus of Elasticity

## Modulus of Elasticity

The modulus of elasticity (E) is a material property, that describes its stiffness and is therefore one of the most important properties of solid materials. Mechanical deformation puts energy into a material. The energy is stored elastically or dissipated plastically. The way a material stores this energy is summarized in stress-strain curves.

When a material deforms elastically, the amount of deformation likewise depends on the size of the material, but the strain for a given stress is always the same and the two are related by Hooke’s law.

Stress is directly proportional to the strain.

σ = Eε

Where,

σ = Stress,

ε = Strain,

E = Modulus of Elasticity.

From the Hooke’s Law the modulus of elasticity is defined as the ratio of the stress to the strain:

Modulus of Elasticity (E) = σ/ε

Stress is not directly measurable, we can calculate it from different formulas for different types of the loading tension, flexural stress etc.

Strain is defined as the change of the length divided by the original length.

$$Strain(\varepsilon )\,\,=\,\,\frac{\Delta l}{l}\,\,=\,\,\frac{l-{{l}_{0}}}{{{l}_{0}}}$$.

Where,

Δl = Change of length,

l = length after elongation,

l₀ = Original length.

The Modulus of Elasticity values of different materials are:

Steel – 200,

Glass – 65,

Wood – 13,

Plastic (Polystyrene) – 3.