Impact energy concepts: proof resilience per unit volume Statement: The proof resilience per unit volume of a material is called the modulus of resilience.

Introduction / Context:
Designers often need a measure of how much elastic energy a material can absorb before permanent deformation. The terms proof resilience and modulus of resilience are closely related yet used at different scales, and clarity helps in impact and energy storage problems like springs.

Given Data / Assumptions:

• Elastic loading up to yield or proof stress.
• Material follows Hooke's law within the elastic limit.

Concept / Approach:
Proof resilience is the maximum strain energy stored in a body up to the elastic limit. When expressed per unit volume, it is called modulus of resilience. For linear elasticity, area under the stress–strain curve up to yield is triangular.

Step-by-Step Solution:
Strain energy density up to yield = area under curve.For linear elastic region: Uv = (1/2) * sigma_y * epsilon_y.Since epsilon_y = sigma_y / E, Uv = (1/2) * sigma_y * (sigma_y / E).Therefore Uv = (sigma_y^2) / (2 * E), which is the modulus of resilience.

Verification / Alternative check:
For a spring, energy stored at proof load equals area under load–deflection curve up to the elastic limit; dividing by volume gives the same modulus value.

Why Other Options Are Wrong:
False: contradicts standard definitions. Constraints about brittleness, temperature, or compression do not redefine the term; it is a general elastic property.

Common Pitfalls:
Confusing resilience (elastic energy) with toughness (total energy to fracture); mixing up proof load with ultimate load.

Final Answer:
True