Hydrostatic stress

In <a href="/facts/Continuum_mechanics/vI7LpFDk">continuum mechanics</a>, hydrostatic stress, also known as isotropic stress or volumetric stress, is a component of <a href="/facts/Stress_(mechanics)/ErAXDbbd">stress</a> which contains <a href="/facts/Cylinder_stress/wwe71u8U">uniaxial stresses</a>, but not <a href="/facts/Shear_stress/aWWnzIhE">shear stresses</a>. A specialized case of hydrostatic stress contains <a href="/facts/Isotropic/mc3QEY2x">isotropic</a> compressive stress, which changes only in volume, but not in shape. Pure hydrostatic stress can be experienced by a point in a <a href="/facts/Fluid/wLnMhBC0">fluid</a> such as water. It is often used interchangeably with "mechanical <a href="/facts/Pressure/eyc37GRG">pressure</a>" and is also known as confining stress, particularly in the field of <a href="/facts/Geomechanics/jNybz7oH">geomechanics</a>.
Hydrostatic stress is equivalent to the average of the uniaxial stresses along three <a href="/facts/Orthogonal/JVIjYPog">orthogonal</a> axes, so it is one third of the first invariant of the <a href="/facts/Cauchy_stress_tensor/5MsXPQVH">stress tensor</a> (i.e. the <a href="/facts/Trace_(linear_algebra)/dchFFvHt">trace</a> of the stress tensor):

σ
 
 h
 
 
 =
 
 
 
 I
 
 i
 
 
 3
 
 
 =
 
 
 1
 3
 
 
 tr
 ⁡
 (
 
 σ
 
 )
 
 
 {\displaystyle \sigma _{h}={\frac {I_{i}}{3}}={\frac {1}{3}}\operatorname {tr} ({\boldsymbol {\sigma }})}

For example in <a href="/facts/Cartesian_coordinates/lkTqvMmB">cartesian coordinates</a> (x,y,z) the hydrostatic stress is simply:

σ
          
            h
          
        
        =
        
          
            
              
                σ
                
                  x
                  x
                
              
              +
              
                σ
                
                  y
                  y
                
              
              +
              
                σ
                
                  z
                  z
                
              
            
            3
          
        
      
    
    {\displaystyle \sigma _{h}={\frac {\sigma _{xx}+\sigma _{yy}+\sigma _{zz}}{3}}}

Hydrostatic stress open-in-new

Hydrostatic stress