Basic definitions — identify the modulus: The ratio of linear (normal) stress to linear strain is called what?

Introduction:
Material constants relate stress to strain under specific modes of deformation. This question asks for the name of the constant connecting normal stress to normal strain in uniaxial loading.

Given Data / Assumptions:

• Small strains; linear elastic behavior.
• Uniaxial (normal) stress and corresponding normal strain.

Concept / Approach:
Hooke’s law for normal loading: σ = E*ε, where E is Young’s (modulus of elasticity). Different moduli exist for shear (G) and volumetric change (K).

Step-by-Step Solution:

Verification / Alternative check:
Dimensional reasoning: [stress]/[strain] reduces to pressure units, as does E.

Why Other Options Are Wrong:

• Modulus of rigidity: relates shear stress to shear strain (G = τ/γ).
• Bulk modulus: relates hydrostatic pressure to volumetric strain (K = p/ε_v).
• Poisson’s ratio: relates lateral to longitudinal strain, dimensionless.
• Shear compliance: not the requested linear modulus.

Common Pitfalls:
Confusing E with G or K; mixing up normal vs shear vs volumetric responses.

Final Answer: