The shear modulus, also known as the modulus of rigidity, measures how much a material can deform or change its shape when subjected to shear stress. In simpler terms, it quantifies a substance’s resistance to being twisted or sheared.
For instance, Imagine holding a book with one hand on the top and the other on the bottom, then trying to tilt or deform it by sliding your hands in opposite directions. The shear modulus characterises how much the book resists this kind of deformation caused by shear stress.
Daily Life Examples
- Twisting a Plastic Cap: Twisting the cap of a plastic water bottle involves shear deformation, and the shear modulus of plastics can range from 1×107to 4×108 N/m2.
- Turning a Bolt: Tightening a bolt with a wrench involves applying shear stress, and the shear modulus of metals, like steel, is typically around 8×1010 N/m2.
- Walking on Gel Insoles: The gel insoles in shoes experience shear stress as they deform under the weight of a person, with shear moduli ranging from 1×103 to 1×106 N/m2.
- Rubber Band Stretch: Stretching a rubber band causes shear deformation, and rubber has a shear modulus ranging from 1×106 to 6×106 N/m2.
- Squeezing Toothpaste: Applying pressure to squeeze toothpaste out of a tube involves shear stress, and the shear modulus of toothpaste can vary but is generally low.
Mathematical Form
The shear modulus (G) is mathematically related to the shear stress (τ) and the shear strain (γ) in a material. The formula for shear modulus is given by:
G=τ/γ
Where:
- G is the shear modulus,
- τ is the shear stress (force per unit area),
- γ is the shear strain (angular deformation).
This equation expresses how the shear modulus quantifies the ratio of shear stress to shear strain, representing a material’s resistance to deformation under shear loading.
The unit of shear modulus (G) is the pascal (Pa).
