Hydrostatic stress

In continuum mechanics, hydrostatic stress, also known as volumetric stress, is a component of stress which contains uniaxial stresses, but not shear stresses. A specialized case of hydrostatic stress, contains isotropic compressive stress, which changes only in volume, but not in shape. Pure hydrostatic stress can be experienced by a point in a fluid such as water. It is often used interchangeably with "pressure" and is also known as confining stress, particularly in the field of geomechanics.
Hydrostatic stress is equivalent to the average of the uniaxial stresses along three orthogonal axes and can be calculated from the first invariant of the stress tensor:
formula_1
Its magnitude in a fluid, formula_2, can be given by:
where formula_4 is an index denoting each distinct layer of material above the point of interest, formula_5 is the density of each layer, formula_6 is the gravitational acceleration (assumed constant here; this can be substituted with any acceleration that is important in defining weight), and formula_7 is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
where the index formula_9 indicates "water".
Because the hydrostatic stress is isotropic, it acts equally in all directions. In tensor form, the hydrostatic stress is equal to
where formula_11 is the 3-by-3 identity matrix.
Hydrostatic compressive stress is used for the determination of the bulk modulus for materials.