Which mechanical property determines the stiffness of a material?

Answer: Modulus of elasticity.

Stiffness: Stiffness is a structural property of a material which offers resistance to deformation when an external load is applied.

Stiffness of material

The unit of stiffness is N/m (Newron/meter). But Young’s modulus or modulus of elasticity determines the stiffness of a material. To understand stiffness in a simple way,

For example, consider, two different material. Material 1 and material 2. We have to increase its length by 1 mm. Material 1 needed 50 kN force and material 2 needed 100 kN force. So we can say material 2 is stiffer than material 1. Because material 1 deformed easily with less force but material 2 resist more against deformation or required more force.

On the other hand, Young’s modulus is the mechanical property of the material which shows the relationship between stress and strain. By Hook’s law, within elastic limit stress is directly proportional to strain. Which means

stress (σ) ∝ strain(ε)
or,   σ =

E is Young’s modulus or modulus of elasticity.

Because, stress (σ) = force (F)/area(A)
or, σ = F/A
and, strain(ε) = change in length(δ)/original length(L)
or, ε =δ/L

and we know, stiffness(K) = Force (F)/change in length(δ)
or, K= F/δ

σ = 
or, F/A = E x δ/L
or, F/δ = E x A/L

thus, K = E x A/L

In brief, It means stiffness depends on the modulus of elasticity or Young’s modulus of the material. And of course on geometrical shape of the object. The value of E (Young’s modulus) is higher means of stiffer material.

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