Material property definitions: Evaluate the statement: “Stiffness is the ability of a material to resist deformation under applied stress.”

Introduction / Context:
Accurate use of mechanical property terminology prevents design errors. Stiffness, strength, hardness, and toughness are often confused, yet they represent distinct behaviors under load. Here, stiffness refers to deformation response within the elastic range.

Given Data / Assumptions:

• Linear elastic behavior is assumed near the origin of the stress–strain curve.
• Small-strain regime is relevant for defining stiffness.
• No time-dependent effects (like creep) are considered in the definition.

Concept / Approach:
Stiffness quantifies resistance to elastic deformation. At the material level, it is captured by modulus of elasticity (Young’s modulus) in tension/compression and shear modulus in shear. A higher modulus means less elastic strain for a given stress. This differs from strength (stress at failure or yield), toughness (energy absorbed before fracture), and hardness (resistance to indentation or scratching).

Step-by-Step Solution:
Define stiffness: minimal deformation for a given applied stress.Relate to modulus: E = stress / strain in the linear elastic region.Compare to strength: high strength does not guarantee high stiffness if modulus is low.Conclude that the given statement is a correct description of stiffness.

Verification / Alternative check:
Example: Steel (high E) is stiffer than aluminum (lower E) even if a particular aluminum alloy may exhibit high strength.

Why Other Options Are Wrong:
Limiting to elastomers or to the yield point confuses stiffness with nonlinearity and plasticity.

Equating stiffness with strength is a classic misconception; stiffness is about deformation, not failure.

Common Pitfalls:
Using stiffness and strength interchangeably; ignoring anisotropy where directional moduli vary.

Final Answer:
True