Bulk modulus is a term used to describe what happens to a material when uniform isostatic pressure is applied. The polyurethane used here at the Gallagher Corporation has a very high bulk modulus, which means it is virtually incompressible.

*Check out our video to see how Bulk Modulus is measured in the Gallagher Corp materials testing lab and why it’s important.*

The bulk modulus ** K > 0** can be defined by the equation

where

*is pressure,*

**P***is volume, and*

**V***denotes the derivative of pressure with respect to volume.*

**dP/****dV**Equivalently

where* ρ* is density and

*denotes the derivative of pressure with respect to density (i.e. pressure rate of change with volume).*

**dP/dρ**The inverse of the bulk modulus gives a substance’s compressibility.

Other moduli describe the material’s response (strain) to other kinds of stress.

The shear modulus describes the response to shear.

Young’s modulus describes the response to linear stress.

## Thermodynamic relation

Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify, it is necessary to specify how the temperature varies during compression: constant-temperature (isothermal ** K_{T}**), constant-entropy (isentropic

**), and other variations are possible.**

*K*_{S}For an ideal gas, the isentropic modulus ** K_{S}** is given by

and the isothermal modulus

**is given by**

*K*_{T}where

*is the heat capacity ratio*

**γ****is the pressure.**

*p*When the gas is not ideal, these equations give only an approximation. In a fluid, ** K** and the density

**determine the speed of sound**

*ρ**(pressure waves), according to the Newton-Laplace formula*

**c**In solids, ** K_{S}** and

**have very similar values. Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example, the shear modulus, is needed to determine wave speeds.**

*K*_{T}