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What is Bulk Modulus?

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The bulk modulus of a material is the ratio of volumetric stress to volumetric strain. It is not to be confused with Young’s modulus, the ratio of tensile stress to tensile strain, or with shear modulus, the ratio of shear stress to shear strain. Bulk modulus can be thought of as an expansion of Young’s modulus but in all three dimensions, hence the term “bulk.”

Bulk modulus values can be calculated for any material, but it is mostly used to describe the behaviour of fluids (liquids and gases). For anisotropic solids (solids with different properties along different axes), all three moduli are insufficient to predict the behaviour of that material accurately, and so a generalised Hooke’s law is required. There are material-specific formulas that can derive the bulk modulus of the material from its Young’s modulus, shear modulus and Poisson’s ratio.

Bulk modulus is a measure of how compressible a material is, and so the higher the bulk modulus, the lower the compressibility of that material and vice versa. Bulk modulus has the same units as pressure since strain is unitless, and it is often expressed in Pascals, N.m-2 or PSI.

In this article, you will learn:

  • What bulk modulus is
  • The measurement of bulk modulus
  • Applications of bulk modulus

What is bulk modulus?

Bulk modulus, also known as modulus of compression (denoted as either K or B) is a measurement of a substance’s resistance to isostatic compression [1]. It is the ratio of the infinitesimal change in pressure to the infinitesimal change in volume.

The bulk modulus of a material can be expressed as

`K=-Vfrac{d P}{d V}`

Where K is the bulk modulus, V is volume and P is pressure.

For ideal isotropic and elastic materials, the bulk modulus, modulus of elasticity, and Poisson’s ratio are related by the following equation [1]:

`K=frac{E}{3(1-2v)}`

Where K is the bulk modulus, E is the modulus of elasticity, and

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