Shear Modulus Calculator

This calculator determines the shear modulus, a measure of the elastic shear stiffness of a material. For isotropic materials, the shear modulus is directly proportional to Young's modulus with Poisson's ratio as a multiplier. 
CalculationTechnical assumptions
Input﻿﻿E
:200.00GPa​
﻿
﻿﻿ν
:0.10​
﻿
﻿
Output﻿﻿G
:1,000.00GPa​
﻿
﻿
G=E2(1+ν)G = \dfrac{E}{2(1 + \nu)}G=2(1+ν)E​
Where:
E is Young's modulus, a material property that is a measure of how easily a material can stretch and deform under normal stress ﻿(GPa)
﻿
﻿﻿ν
 is Poisson's ratio, a measure of how much a material expands or contracts in the direction perpendicular to its loading direction (unitless)
﻿﻿G
 is the shear modulus, a material property that is a measure of how easily a material can shear and deform under shear stress ﻿(GPa)
﻿
ExplanationThe shear modulus, ﻿G
 is defined as the ratio of the shear stress, ﻿τ
 to the shear strain, ﻿γ
.
﻿
G=τγ=F/AΔx/LG=\dfrac{\tau}{\gamma}=\dfrac{F/A}{\Delta x/L}\\ G=γτ​=Δx/LF/A​
For isotropic materials (materials with the same properties in all directions), the shear modulus is directly proportional to Young's modulus, ﻿E
 with Poisson's ratio, ﻿ν
 as a multiplier. 
﻿
G=E2(1+ν)G = \dfrac{E}{2(1 + \nu)}G=2(1+ν)E​
Take a segment of a material, as per image below, and apply an external force ﻿F
. The segment will deform by distance, ﻿Δx
 and have an angle of deformation, ﻿θ
 (i.e. the segment is shearing) caused by an external force. How easily the segment shears is measured by its shear modulus. A higher shear modulus means a stiffer material and higher shear resistance.
﻿
Segment of a material shearing by an external force
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