In strength of materials, the total strain energy stored in a body is commonly termed strain energy. The term 'proof resilience' specifically refers to the maximum strain energy stored up to the elastic limit (not merely any strain energy). State whether the given statement is correct.

Introduction:
This question distinguishes between strain energy, proof resilience, and modulus of resilience — closely related but different terms in materials engineering.

Given Data / Assumptions:

• Body subjected to gradually applied loading.
• Elastic limit is well defined for the material.

Concept / Approach:
Strain energy is the work done by internal forces stored as recoverable energy during deformation. Proof resilience is the maximum strain energy a body can store up to the elastic limit. Modulus of resilience is this maximum per unit volume.

Step-by-Step Solution:
1) Let U be strain energy at any load within the elastic range.2) Increase load up to the elastic limit; the maximum stored energy is U_max.3) Definition: proof resilience = U_max (value at elastic limit).4) Therefore, calling “the total strain energy stored in a body” proof resilience is inaccurate unless it is specifically the maximum at the elastic limit.

Verification / Alternative check:
If stress–strain is linear: U_max = 0.5 * sigma_y * epsilon_y * Volume; modulus of resilience = 0.5 * sigma_y * epsilon_y.

Why Other Options Are Wrong:
Agree: ignores the crucial qualifier “up to elastic limit”.
Agree only for elastic bodies: still misses the “maximum at elastic limit” definition.
Agree if volume is unit: that corresponds to modulus of resilience, not proof resilience.

Common Pitfalls:
Confusing proof resilience (total at elastic limit) with modulus of resilience (per unit volume), and with generic strain energy at arbitrary load levels.

Final Answer:
Disagree