Elastic constants (materials science): The ratio of shear stress to shear strain is called what material property?

Introduction / Context:
Elastic constants describe linear relationships between stress and strain for small deformations. Correctly identifying which modulus applies to which loading condition is foundational in mechanical design and strength of materials.

Given Data / Assumptions:

• Small, elastic (Hookean) strains.
• Isotropic, homogeneous material behavior assumed for definitions.
• Standard engineering notation for moduli (E, G, K, ν).

Concept / Approach:
Shear stress–strain relation is τ = G * γ, where τ is shear stress and γ is shear strain. The proportionality constant G is called the shear modulus, also known as the modulus of rigidity. By contrast, Young’s modulus E relates normal stress to normal strain in uniaxial loading; bulk modulus K relates volumetric stress to volumetric strain; Poisson’s ratio ν relates lateral to axial strain.

Step-by-Step Solution:
Identify loading mode: shear.Hooke’s law for shear: τ = G γ → ratio τ/γ = G.Therefore, the property name is shear modulus (modulus of rigidity).

Verification / Alternative check:
Relationships among elastic constants for isotropic materials include E = 2G(1 + ν) and E = 3K(1 − 2ν), corroborating definitions.

Why Other Options Are Wrong:
Bulk modulus concerns volumetric compression; Young’s modulus concerns axial loading; Poisson’s ratio is a dimensionless strain ratio, not a stress/strain modulus.

Common Pitfalls:

• Using “modulus of elasticity” generically for E when G is the correct modulus for shear.
• Applying small-strain linear theory outside its valid range.

Final Answer:
Shear modulus (modulus of rigidity, G)