Energy methods terminology: The total strain energy stored in a body due to external loading (within the elastic range) is termed as what?

Introduction / Context:
Several energy-based terms are used in strength of materials: strain energy, resilience, proof resilience, and modulus of resilience. Correct identification supports design against shock and fatigue, and informs material selection for energy absorption.

Given Data / Assumptions:

• Loading remains within the elastic limit of the material.
• We are concerned with the total energy stored under the applied loading.

Concept / Approach:
Strain energy is the energy stored in a body due to deformation. When this is considered up to the elastic limit, it is called resilience. Proof resilience is specifically the maximum strain energy stored per unit volume up to the elastic limit. Modulus of resilience is that proof resilience expressed per unit volume. Toughness (for comparison) relates to total energy absorption up to fracture (area under the entire stress–strain curve).

Step-by-Step Solution:

Verification / Alternative check:
Consulting standard definitions: resilience (overall stored energy within elastic limits), proof resilience (maximum at elastic limit), modulus of resilience (per unit volume measure at elastic limit).

Why Other Options Are Wrong:

• Proof resilience: specifically the maximum energy at yield, not just any total stored energy.
• Modulus of resilience: energy per unit volume measure, not the total for the body.
• Impact energy / toughness: concern energy to fracture, typically beyond elastic range.

Common Pitfalls:
Using the terms interchangeably; forgetting the 'per unit volume' qualifier for modulus of resilience; confusing toughness with resilience.

Final Answer:
resilience