# Shear modulus

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An important elastic modulus, also known as *rigidity* or the modulus of rigidity, or the second Lamé parameter. Symbolized as `μ` or sometimes `G`.

## Definition

The ratio of shear stress to shear strain:

## Other expressions

Shear modulus can be expressed in terms of elastic properties:

And it can be expressed in terms of acoustic properties:

from which it follows that

where `I`_{S} is shear impedance and `ρ` is density.

## Typical values

Usually about 3 × 10^{10} Pa.

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The elastic properties of homogeneous isotropic linear elastic materials are uniquely determined by any two moduli. Given any two, the others can thus be calculated. Key reference: Mavko, G, T Mukerji and J Dvorkin (2003), The Rock Physics Handbook, Cambridge University Press.
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P-wave velocity |
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S-wave velocity |
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Velocity ratio |
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1st Lamé parameter |
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Shear modulus |
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Young's modulus |
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Bulk modulus |
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Poisson's ratio |
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P-wave modulus |