18.15:
Bulk Modulus
The bulk modulus measures a material'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's ratio can stretch without lateral contraction. Conversely, Poisson's ratio of 0.5 signifies perfect incompressibility.
18.15:
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.
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.
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.