Material behavior: the ratio of linear (normal) stress to linear (normal) strain within the elastic limit is defined as which modulus?

Introduction / Context:
Stress–strain relationships describe how materials deform under load. Within the elastic range, deformation is reversible and a proportionality exists between stress and strain. The constant of proportionality for normal (tensile/compressive) loading defines a fundamental material property used in structural and pressure equipment design.

Given Data / Assumptions:

• Small deformations within the elastic limit (Hookean behavior).
• Uniaxial normal loading producing normal strain.
• Isotropic, homogeneous material for simplicity.

Concept / Approach:
Young’s modulus (modulus of elasticity, E) is defined as E = σ/ε for linear elastic behavior in tension or compression. Other moduli describe different loading modes: modulus of rigidity (G) relates shear stress to shear strain, while bulk modulus (K) relates volumetric stress to volumetric strain (hydrostatic loading).

Step-by-Step Solution:

Verification / Alternative check:
Interrelations E, G, and K exist for isotropic materials: E = 2G(1 + ν) and E = 3K(1 − 2ν), where ν is Poisson’s ratio, confirming distinct meanings of each modulus.

Why Other Options Are Wrong:

• Modulus of rigidity applies to shear, not normal loading.
• Bulk modulus applies to volumetric compression under hydrostatic pressure.

Common Pitfalls:
Confusing G and E; using tangent or secant moduli outside the strictly linear region; ignoring temperature dependence of elastic properties.

Final Answer:
Modulus of elasticity