What does shear modulus (G) represent in material science?

Shear modulus, often denoted as G, represents the ratio of shearing stress to the corresponding shearing strain in a material. This property quantifies how a material deforms under shear stress, which is the type of stress that acts parallel to the surface of a material. When a shearing force is applied, the material experiences a change in shape without a change in volume, and the shear modulus provides a measure of the material's rigidity or stiffness in response to that shear deformation.

In practical terms, the shear modulus is important in evaluating how different materials will perform under various loading conditions, particularly in structural applications where shear forces are present. The higher the shear modulus, the less a material will deform under a given shear load, indicating it is stiffer.

The other choices relate to different types of stress and strain relationships that do not describe shear behavior. The ratio of compressive stress to compressive strain pertains to the bulk modulus or modulus of elasticity under compression, while the ratio of tensile stress to tensile strain refers to Young's modulus, which deals with axial (tensile) loading. The elastic limit describes the maximum stress a material can withstand without permanent deformation, which is a different concept altogether.