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In Science, What Is Shear Modulus?

By Ray Hawk
Updated: May 21, 2024

Shear modulus, which is also often referred to as the modulus of rigidity or torsion modulus, is a measure of the rigid or stiff nature of different types of solid materials. It is derived from the material's ratio of its shear stress value to that of shear strain. Shear stress is a value of how much force is applied to a square area of a material, usually measured in pressure values of pascals. Strain is the amount that the material has deformed under stress divided by its original length. The shear modulus value is always a positive number and is expressed as an amount of force per unit area, which is generally recorded as metric gigapascals (GPa) because the values are more practical than English equivalents.

Since gigapascals equal billions of pascals of force per unit area, shear modulus numbers can sometimes look deceptively small. An example of how large shear modulus values can be is demonstrated when they are converted to English values of pounds per square inch (lb/in2). Diamond is estimated to have a modulus of rigidity of 478 GPa (69,328,039 lb/in2), pure aluminum one of 26 GPa (3,770,981 lb/in2), and rubber ranges from 0.0002 to 0.001 GPa (29 to 145 lb/in2). To make these units more practical with English numbers, the practice is to express them in kips per square inch, where a kip is equal to a weight of 1,000 pounds.

The harder a substance is, the higher its shear modulus value, depending on the ambient temperature when the value is measured. As the shear modulus value rises, this indicates that a much greater amount of force or stress is required to strain or deform it along the plane of the direction of the force. Strain values themselves tend to be rather small, however, in the calculations, because strain is only a measure of deformation of a solid material before it breaks or fractures. Most solids like metals will stretch only a small amount before breaking down.

The exception to this limitation on small strain values are elastic materials like rubber, which can stretch a great deal before degrading. These materials are often measured instead using the shear modulus of elasticity, which is also a ratio of stress versus strain. Values for the modulus of elasticity on materials are based on how much a material can be stretched before it undergoes permanent deformation.

The modulus of elasticity is often the same measurement as Young's modulus, which specifically is a measure of linear stress on a solid defined as longitudinal strain to longitudinal stress. Another closely related value in this series of measurements is bulk modulus, which takes Young's modulus and applies it to all three dimensions in space. Bulk modulus measures the elasticity of a solid when pressure to deform it is universally applied from all sides, and is the opposite of what happens when a material is compressed. It is a value of volumetric stress divided by volumetric strain, and can be visualized in one example as what would happen to a uniform solid under internal pressure when placed in a vacuum, which would cause it to expand in all directions.

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