Bulkmodulus

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.