Dilation, $e$, is a measure of the change in [[Volume|volume]] relative to the object volume, essentially the volumetric equivalent of [[Strain|strain]].
$e=\varepsilon_x+\varepsilon_y+\varepsilon_z$
$e=\dfrac{1−2\nu}{E}(\sigma_x+\sigma_y+\sigma_z)$
Subjecting a material to a hydrostatic (uniform) [[Pressure|pressure]], $P$, results in the following dilation:
$e=−\dfrac{3(1−2\nu)}{E}P$
The bulk modulus, $k$, describes how easily a material’s volume will change when subjected to a uniform [[Force|load]]. Bulk modulus is defined by the above-mentioned hydrostatic loading condition.
$k=−\dfrac{P}{e_{hydrostatic}}$
$k=\dfrac{-P}{\dfrac{−3(1−2\nu)}{E}P}$
$k=\dfrac{E}{3(1−2\nu)}$