Shear modulus

The shear modulus, also known as the modulus of rigidity, is a property that describes the material's response to shear stress. It is defined as the ratio of shear stress to the shear strain in a material. The shear modulus is denoted by the symbols G, S, or μ.

Definition

The shear modulus is mathematically expressed as:

G = \frac{\tau}{\gamma}

where:

• G is the shear modulus,
• τ (tau) is the shear stress,
• γ (gamma) is the shear strain.

Units

The SI unit of shear modulus is the pascal (Pa), which is equivalent to one newton per square meter (N/m²). In the CGS system, it is measured in dynes per square centimeter.

Relation to Other Elastic Moduli

The shear modulus is one of several elastic moduli that describe the mechanical properties of materials. It is related to the Young's modulus (E) and the Poisson's ratio (ν) by the following relationship:

G = \frac{E}{2(1 + ν)}

Applications

The shear modulus is crucial in the fields of materials science, mechanical engineering, and structural engineering. It is used to predict how materials will deform under shear forces, which is essential for designing and analyzing structures and mechanical components.

Typical Values

Different materials have different shear moduli. For example:

• Steel: ~79 GPa
• Aluminum: ~26 GPa
• Rubber: ~0.0006 GPa

Measurement

The shear modulus can be measured using various experimental techniques, such as torsion tests and dynamic mechanical analysis.

See Also

• Elasticity (physics)
• Bulk modulus
• Young's modulus
• Poisson's ratio
• Stress (mechanics)
• Strain (mechanics)