Strength of materials terminology: the maximum strain energy stored by a material at the elastic limit is called what?

Introduction / Context:
Energy concepts in elasticity help compare materials and design components subject to impact or cyclic loading. Three terms are commonly examined: resilience, proof resilience, and modulus of resilience.

Given Data / Assumptions:

• Elastic limit is the highest stress for which the stress–strain relation remains elastic.
• Strain energy is the energy stored due to deformation.
• Definitions distinguish total energy vs energy per unit volume.

Concept / Approach:
Proof resilience is the maximum total strain energy stored at the elastic limit for the whole body. Modulus of resilience is the strain energy per unit volume at the elastic limit (area under the elastic portion of the stress–strain curve divided by volume). The general term resilience is sometimes used qualitatively for the capacity to absorb elastic energy, but the precise exam distinction is as above.

Step-by-Step Solution:
Identify what is asked: 'maximum energy stored at elastic limit' → total energy in the component.Recall definitions: proof resilience = maximum total strain energy at elastic limit.Distinguish from modulus of resilience = energy density at elastic limit.Hence, the correct technical term is 'proof resilience'.

Verification / Alternative check:
Strength of materials texts show for linear elastic materials: modulus of resilience = σ_y^2 / (2E). Multiplying by volume gives proof resilience.

Why Other Options Are Wrong:

• Resilience (generic) lacks the 'maximum at elastic limit' and total energy specificity.
• Modulus of resilience is per unit volume, not total energy.
• Bulk resilience is not a standard term in this context.

Common Pitfalls:

• Mixing up total energy with energy density.

Final Answer:
proof resilience