Meaning of proof resilience\n\nState whether the following statement is correct: “Proof resilience is the maximum strain energy which can be stored in a body.”

Introduction / Context:
Resilience characterizes energy absorption within the elastic range. The concept is crucial for springs, impact-resistant components, and design against sudden loads where elastic recovery without permanent deformation is required.

Given Data / Assumptions:

• Elastic behavior up to an elastic limit (proportional limit or yield, as applicable).
• Strain energy refers to the work stored internally due to stress and recoverable upon unloading.

Concept / Approach:
Proof resilience is the maximum strain energy stored in a body without permanent deformation, i.e., up to the elastic limit. When expressed per unit volume, it is called modulus of resilience.

Step-by-Step Solution:
For linear elasticity: strain energy U = ∫ (0 to ε) σ dε * Volume.With σ = E ε, U/V = ∫ (0 to εe) E ε dε = (1/2) E εe^2.Thus modulus of resilience = (1/2) σe εe = σe^2 / (2E) when elastic limit stress is σe.Total proof resilience = (U/V) * Volume.

Verification / Alternative check:
Upon unloading from within elastic range, all stored energy is released; beyond elastic limit, additional work is not fully recoverable, so “maximum recoverable energy” is attained at the limit.

Why Other Options Are Wrong:
“No” contradicts standard definitions. Limiting to brittle or ductile materials is unnecessary; both possess resilience. “True only per unit volume” describes modulus of resilience, a related but distinct term.

Common Pitfalls:
Confusing total proof resilience with modulus of resilience; assuming resilience equals toughness (energy to fracture), which involves plasticity.

Final Answer:
Yes