Elastic Constants Calculator

Elastic Constants of Materials

For isotropic linear elastic materials, Young's modulus $E$ and Poisson's ratio $\nu$ determine the shear modulus $G$ and bulk modulus $K$. These constants appear in structural analysis, finite element models, and material characterization.

Conversion Formulas

$$G = \frac{E}{2(1 + \nu)}$$ $$K = \frac{E}{3(1 - 2\nu)}$$

$G$ describes resistance to shear deformation. $K$ describes resistance to uniform compression. Poisson's ratio must satisfy $-1 < \nu < 0.5$; at $\nu = 0.5$ the material is incompressible and $K$ diverges.

Example: steel with $E = 200$ GPa and $\nu = 0.3$ gives $G \approx 76.9$ GPa and $K \approx 166.7$ GPa.

Typical Values

Aluminum: $E \approx 70$ GPa, $\nu \approx 0.33$. Rubber: $\nu$ approaches 0.5. Cork and auxetic materials can have negative Poisson's ratio.

Frequently Asked Questions

What is Young's modulus?

Young's modulus $E$ is the ratio of axial stress to axial strain in uniaxial tension or compression. Higher $E$ means a stiffer material.

What is Poisson's ratio?

Poisson's ratio $\nu$ is the negative ratio of transverse strain to axial strain. Most metals have $\nu$ between 0.25 and 0.35.

When is bulk modulus undefined?

When $\nu = 0.5$, the denominator $3(1 - 2\nu)$ becomes zero. This corresponds to an incompressible material like an ideal rubber.

What is the shear modulus used for?

Shear modulus $G$ governs torsion, shear deformation, and wave propagation in solids. It appears in beam and plate bending formulas.

Can I recover E from G and ν?

Yes. Rearranging gives $E = 2G(1 + \nu)$. This calculator computes $G$ and $K$ from $E$ and $\nu$.

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Elastic Constants of Materials

Conversion Formulas

Typical Values

Frequently Asked Questions

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