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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:
σ h = I i 3 = σ x x + σ y y + σ z z 3 {\displaystyle \sigma _{h}={\frac {I_{i}}{3}}={\frac {\sigma _{xx}+\sigma _{yy}+\sigma _{zz}}{3}}}
Its magnitude in a fluid, σ h {\displaystyle \sigma _{h}} , can be given by: