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Concept
Shear modulus
Summary
In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
where
= shear stress
is the force which acts
is the area on which the force acts
= shear strain. In engineering , elsewhere
is the transverse displacement
is the initial length of the area.
The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing force by mass times acceleration.
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law:
Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
the Poisson's ratio ν describes the response in the directions orthogonal to this uniaxial stress (the wire getting thinner and the column thicker),
the bulk modulus K describes the material's response to (uniform) hydrostatic pressure (like the pressure at the bottom of the ocean or a deep swimming pool),
the shear modulus G describes the material's response to shear stress (like cutting it with dull scissors).
These moduli are not independent, and for isotropic materials they are connected via the equations
The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood, paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions.
Official source
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