Name: volume change under hydrostatic pressure
Uploaded: 2025-05-22T09:06:18.000Z
Duration: 1 min 21 s
Channel: JoVE

The bulk modulus measures a material&#39;s resistance to uniform compression. It is defined as the proportionality constant between a change in pressure and the resulting relative volume change.
Consider an isotropic cube of unit volume. When subjected to normal stresses, it deforms into a rectangular parallelepiped with a new volume.
The difference between this new volume and the original one is termed the dilatation of the material. Dilatation can be expressed as the sum of the strains in all three directions.
In the case of a body subjected to uniform hydrostatic pressure, each component of stress equals the negative of hydrostatic pressure.
Substituting these values into the dilatation equation yields an expression that introduces the constant known as the bulk modulus, expressed in the same units as the modulus of elasticity.
Stable materials under hydrostatic pressure decrease in volume, making the dilatation negative and the bulk modulus positive.
An ideal material with a zero Poisson&#39;s ratio can stretch without lateral contraction. Conversely, Poisson&#39;s ratio of 0.5 signifies perfect incompressibility.

bulk modulus

The bulk modulus is a scientific term used to describe a material's resistance to uniform compression. It is the proportionality constant that links a change in pressure to the resulting relative volume change.
<img alt="Bulk modulus equation, \(k = -\Delta p/(\Delta v/v)\), illustrating pressure-volume relation." src="/files/ftp_upload/15601/15601_Equation_1.svg" style="text-align: center; height: 44px;" data-altupdatedat="1754904545000" data-alt="Elasticity coefficient formula, k=-Δp/Δv/v, equation for elasticity in economics or physics.">
This concept becomes clearer when an isotropic material element is visualized as a cube of unit volume. When this cube is subjected to normal stresses, it undergoes deformation, changing its shape into a rectangular parallelepiped with a different volume. The discrepancy between this new volume and the original one is termed the dilatation of the material. Dilatation can be computed as the cumulative sum of the strains in the three spatial directions. When the body is under uniform hydrostatic pressure, each stress component equals the negative of this pressure. Inserting these values into the dilatation formula gives an expression that introduces the bulk modulus.
<img alt="Elasticity formula k=E/3(1-2v), equation related to bulk modulus concepts in materials science." src="/files/ftp_upload/15601/15601_Equation_2.svg" style="text-align: center; height: 48px;" data-altupdatedat="1754904545000" data-alt="Bulk modulus equation \(k = \frac{E}{3(1-2\nu)}\) formula, material properties analysis.">
This modulus has the same units as the modulus of elasticity. Under hydrostatic pressure, stable materials reduce in volume, rendering the dilatation negative and the bulk modulus positive. An ideal material with a zero Poisson's ratio could stretch in one direction without lateral contraction. On the other hand, a material with a Poisson's ratio of 0.5 would be perfectly incompressible.

Bulk Modulus

The bulk modulus is a scientific term used to describe a material&#39;s resistance to uniform compression. It is the proportionality constant that links a ...

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Mechanical Engineering

Unit 1

Stress and Strain - Axial Loading

KEY TERMS AND CONCEPTS

volume change under hydrostatic pressure

Bulk modulus describes how much a material resists a uniform squeeze. It links a change in pressure to the relative change in volume. For high school students, it is easiest to think of it as a measure of how hard it is to compress a material evenly from all sides.

The idea becomes clearer when an isotropic material element is treated as a cube with unit volume. When normal stresses act on the cube, it deforms into a rectangular parallelepiped and its volume changes. The difference between the new volume and the original volume is called dilatation. Dilatation is found by adding the strains in the three spatial directions.

Under uniform hydrostatic pressure, each stress component is equal to the negative of that pressure. Substituting those stress values into the dilatation formula leads to the expression for bulk modulus. The bulk modulus has the same units as the modulus of elasticity. Stable materials usually lose volume under hydrostatic pressure, so dilatation is negative and the bulk modulus is positive.

The transcript also connects bulk behavior to Poisson's ratio. An ideal material with a Poisson's ratio of zero could stretch in one direction without a lateral contraction. A material with a Poisson's ratio of 0.5 would be perfectly incompressible.

Volume Change Under Hydrostatic Pressure

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Bulk modulus describes how much a material resists a uniform squeeze. It links a change in pressure to the relative change in volume. For high school students, it is easiest to think of it as a measure of how hard it is to compress a material evenly from all sides. The idea becomes clearer when an isotropic material element is treated as a cube with unit volume. When normal stresses act on the cube, it deforms into a rectangular parallelepiped and its volume changes. The difference between the...

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key terms and concepts

Learn how hydrostatic pressure changes a material’s volume, how dilatation is calculated, and why bulk modulus stays positive for stable materials.

Volume Change Under Hydrostatic Pressure | JoVE K12

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mechanical engineering

Volume Change Under Hydrostatic Pressure

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