Shear Modulus Calculator Formula

Understand the math behind the shear modulus calculator. Each variable explained with a worked example.

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Formulas Used

Shear Modulus (G)

shear_mod = elastic_mod / (2 * (1 + poisson))

Bulk Modulus (K)

bulk_mod = elastic_mod / (3 * (1 - 2 * poisson))

Variables

VariableDescriptionDefault
elastic_modElastic Modulus (E)(GPa)200
poissonPoisson's Ratio (nu)0.3

How It Works

Shear Modulus (Modulus of Rigidity)

The shear modulus G measures a material's resistance to shear deformation. For isotropic materials, it is directly related to the elastic modulus and Poisson's ratio.

Formula

G = E / (2(1 + nu))

This relationship means only two independent elastic constants are needed to fully describe an isotropic material. The bulk modulus K = E / (3(1 - 2*nu)) is also computed for completeness.

Worked Example

Steel with E = 200 GPa and nu = 0.3.

elastic_mod = 200poisson = 0.3
  1. 01G = 200 / (2 × (1 + 0.3))
  2. 02G = 200 / 2.6 = 76.92 GPa
  3. 03K = 200 / (3 × (1 - 0.6)) = 200 / 1.2 = 166.67 GPa

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