Question

The modulus of resilience is the .......

• A. Area under the entire stress-strain curve
• B. Area under the stress-strain curve up to yield point
• C. Maximum stress multiplied by maximum strain
• D. Ratio of stress to strain

Hint:

Think “Resilience = Elastic Energy.” Only the area up to the yield point counts — that's the elastic limit.

Answer 1

The Correct Option is B

The modulus of resilience is the amount of energy per unit volume that a material can absorb without permanent deformation — i.e., within the elastic range. It quantifies how much energy a material can store when loaded elastically and is a key indicator of toughness for elastic loading.
This value is represented by the area under the stress-strain curve from zero to the yield point. 
After the yield point, plastic deformation begins, and energy is no longer stored elastically.
Mathematically, for linearly elastic materials: \[ \text{Modulus of Resilience} = \frac{\sigma_y^2}{2E} \] where:  $\sigma_y$ = yield stress $E$ = Young’s modulus of elasticity Therefore, the correct answer is the area under the stress-strain curve up to the yield point.