Shear Modulus from Elastic Constants
Shear Modulus from Elastic Constants
For an isotropic material the elastic constants are linked, so the shear modulus follows from the more commonly quoted Young’s modulus.
The relation is G = E/(2·(1 + ν)). where E is Young’s modulus and ν Poisson’s ratio.
Inputs
E := 200 GPa=200000 MPa
nu := 0.3=0.3
Apply the isotropic elastic-constant relation.
G := E/(2·(1 + nu))=76923.08 MPa
Results
For steel this gives about 77 GPa. The relation means only two elastic constants are independent for an isotropic material.
Assumptions & limitations
- Isotropic, homogeneous material.
- Linear elasticity.
- Poisson’s ratio between 0 and 0.5.