What is the shear modulus defined as?

What is the shear modulus defined as?

• A. The ratio of shear stress to shear strain.
• B. The ratio of normal stress to normal strain.
• C. The ratio of shear strain to shear stress.
• D. The product of shear stress and shear strain.

Answer: (A)

Shear modulus measures a material’s resistance to shape change when a shear force is applied. It is defined as the ratio of shear stress to shear strain in the elastic, small-strain regime: G = τ / γ. Here, τ is the shear stress (force per area applied parallel to a surface) and γ is the shear strain (the angular distortion in radians, a dimensionless measure). The higher G is, the less the material will shear under a given tangential load, so this ratio directly captures stiffness against shear. This matches the concept of the correct choice: it is the ratio of shear stress to shear strain. The ratio of normal stress to normal strain defines Young’s modulus, not the shear modulus. The ratio of shear strain to shear stress would be the reciprocal of G, and the product of shear stress and shear strain does not yield a modulus with the correct units.

Shear modulus measures a material’s resistance to shape change when a shear force is applied. It is defined as the ratio of shear stress to shear strain in the elastic, small-strain regime: G = τ / γ. Here, τ is the shear stress (force per area applied parallel to a surface) and γ is the shear strain (the angular distortion in radians, a dimensionless measure). The higher G is, the less the material will shear under a given tangential load, so this ratio directly captures stiffness against shear.

This matches the concept of the correct choice: it is the ratio of shear stress to shear strain. The ratio of normal stress to normal strain defines Young’s modulus, not the shear modulus. The ratio of shear strain to shear stress would be the reciprocal of G, and the product of shear stress and shear strain does not yield a modulus with the correct units.