Volume stress
When several forces uniform in magnitude but perpendicular to the surface everywhere act on an object, all dimensions of the object will change in an equal ratio and the volume of the object will change thereby.
Volume strain
Volume strain is defined as the change in volume \(\Delta V\) divided by the original volume \(V_0\):
\[\epsilon = \frac{\Delta V}{V_0}.\]
Volume strain, as a ratio of quantities having the same unit, is unitless.
Pressure
Volume stress is called pressure. Pressure is defined as the ratio of the force to the area upon which it acts:
\[p := \frac{F}{A}.\]
The SI unit of pressure is the newton per square metre, called the pascal:
\[\left[p\right] = 1\,\frac{\mathrm{N}}{\mathrm{m}^2} = 1\,\mathrm{Pa}.\]
Bulk modulus
For relatively small volume stresses, the volume stress is directly proportional to the volume strain. The constant of proportionality is called the bulk modulus \(B\):
\[p = B \frac{\Delta V}{V_0}.\]
The SI unit of bulk modulus is the newton per square metre, also called the pascal:
\[\left[B\right] = 1\,\frac{\mathrm{N}}{\mathrm{m}^2} = 1\,\mathrm{Pa}.\]
Compressibility
The reciprocal of the bulk modulus is called compressibility.
\[\kappa := \frac{1}{B} = \frac{\Delta V / V_0}{p}.\]