BIZOMAT MAKEOS · Materials
Elastic Constants: E, G, ν and Bulk Modulus
What are the other elastic constants of an isotropic material from the two I know?
Modulus of elasticity E, shear modulus G, Poisson’s ratio ν, bulk modulus K and Lamé constant λ of an isotropic material from any two of E, G and ν.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known values | choice | Which two constants you know. |
| Elastic modulus E | GPa | Young’s modulus from material data. |
| Shear modulus G | GPa | Shear modulus from material data. |
| Poisson’s ratio ν | Poisson’s ratio from material data. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Known values
- What it is
- Which two of the three elastic constants you already know. The tool calculates the third, plus the bulk modulus and Lamé constant; the unused input is ignored.
- Units and format
- Choose one of 3 options from the list: E and ν; E and G; G and ν.
- Example
- The form opens with “E and ν” selected as a worked example. Choose the option that matches your case.
What this means: Elastic modulus E
- What it is
- Young’s modulus: the material’s stiffness in tension or compression, from the material data sheet or a tensile test. Used when the known pair includes E.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 2000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter gigapascals: 1 GPa = 1000 MPa.
What this means: Shear modulus G
- What it is
- The shear modulus (modulus of rigidity): the material’s stiffness in shear or torsion, from material data or a torsion test. Used when the known pair includes G.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 77 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter gigapascals. With E and G both known, small errors in either give a large error in Poisson’s ratio.
What this means: Poisson’s ratio ν
- What it is
- Poisson’s ratio: how much the material narrows sideways for each unit of stretch along the load. It comes from material data and is used when the known pair includes ν.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 0.4999. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is a pure ratio below 0.5, not a percentage.
Method and formulas
- G = E ÷ 2(1 + ν); ν = E ÷ 2G − 1; E = 2G(1 + ν).
- K = E ÷ 3(1 − 2ν); λ = Eν ÷ ((1 + ν)(1 − 2ν)).
- Example: E 200 GPa and ν 0.3 give G = 76.923 GPa and K = 166.67 GPa.
Limitations
- Isotropic, linear elastic materials only; composites, wood and some plastics are anisotropic.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find G for torsion and spring calculations from E and ν
- Check data sheet values for consistency
- Get the bulk modulus for pressure calculations
Who it is for
- Design engineers
- Materials engineers
- Engineering students
What you get
- E, G and ν
- Bulk modulus K
- Lamé constant λ
Interpreting the result
- Inconsistent data-sheet values (ν outside 0–0.5) indicate a typing or unit error.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 369–380, 2695. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Elastic, then plastic
In Yield and Plastic Flow by the Numbers
What it covers: How a metal stretches elastically, why it yields at a tiny fraction of its theoretical strength, and how dislocations carry plastic flow and make metals harden as they deform.
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