Answer: b) Area under the elastic portion of the stress-strain curve
Explanation:
By definition, resilience is the strain-energy density stored by the material when it is stressed to the proportional limit defined by Hooke's Law. Resilience is given by the following expression:
μ(r) = / 2E
μ(r) is the modulus of resilience
σ(pl) is the stress to the proportional limit
E is the elastic modulus
When you look at the stress-strain curve, the area under the elastic portion (up to the proportional limit) can be obtained by the area of a triangle with base equal to the strain (σ) and height equal to the stress (ε):
Ω = (b . h) / 2 = (σ(pl) . ε) / 2
Using Hooke's Law: σ = E . ε → ε = σ/E
Replacing the expression in the area equation:
Ω = (σ(pl) . ε) / 2 = / 2E = μ(r)