Hydrostatic, Deviatoric Stresses http://www.continuummechanics.org/cm/hydrodeviatoricstress.html Search Continuum Mechanics Website Hydrostatic & Deviatoric Stresses home > stress > hydrostatic stress Principal Stresses Von Mises Stress Introduction This page introduces hydrostatic and deviatoric stresses. The two are subsets of any given stress tensor, which, when added together, give the original stress tensor back. The hydrostatic y s Hyd stress is related to volume change, while the deviatoric stress is related to shape change. s Hyd s Hyd Hydrostatic Stress s Hyd x Hydrostatic stress is simply the average of the three normal stress components of any stress tensor. Purchase this page for $0.99 Buy optimized PDF files of this webpage that can be read and printed offline, no internet access required. There are many alternative ways to write this. 1 of 7 5/13/2014 9:19 AM html For $0. etc).continuummechanics. Kindle. the second for tablets (iPads.5" x 11" pages.99.org/cm/hydrodeviatoricstress.Hydrostatic. Email address to receive PDFs It is a scalar quantity. although it is regularly used in tensor form as Hydrostatic Stress Example Given the following stress tensor The hydrostatic stress is which can be written as 2 of 7 5/13/2014 9:19 AM . Deviatoric Stresses http://www. you receive two optimized PDFs: the first for 8. continuummechanics. this means that no shear stresses ever arise. Hydrostatic Stress and Pressure Pressure is simply the negative of hydrostatic stress. a positive number. Also contains equal amounts of stress in all three directions. 3 of 7 5/13/2014 9:19 AM .. Hydrostatic stresses do not change under coordinate transformations.. And since the tensor does not change under any transformation.html And that's all there is to it.org/cm/hydrodeviatoricstress. It is why we talk about atmospheric pressure as 30 inches of Hg. Hydrostatic Stresses and Coordinate Transformations This could not be simpler. even though atmospheric pressure is in fact a negative stress because it is compressive. Deviatoric Stresses http://www. So using for pressure. so every direction is a principal direction with stress. The negative aspect is often confusing. This is easily accepted in light of the fact that is a function of .Hydrostatic. etc.html The stress tensor containing pressure. . Hydrostatic Stress in Incompressible Materials This is almost a nontopic because hydrostatic stresses usually have no impact on incompressible materials at all. And this is why finite element programs often fudge by making the incompressible material ever-so-slightly compressible. automobiles. The deviatoric stress will be represented by . Deviatoric Stress Deviatoric stress is what's left after subtracting out the hydrostatic stress.org/cm/hydrodeviatoricstress. which corresponds to a positive pressure.continuummechanics. which is a positive pressure. then the stress state in the air is one of hydrostatic stress alone. it is rare to talk about pressure unless the hydrostatic stress is compressive.Hydrostatic. This also means that one cannot determine the hydrostatic stress based on strain or a deformation gradient. without any shear stresses. For example 4 of 7 5/13/2014 9:19 AM . so there is very little to discuss. Also. is Of course. unless one is working with boundary layer flows over aircraft. And the hydrostatic stress is compressive. Deviatoric Stresses http://www. it is written as And in terms of pressure. it is written as Deviatoric Stress Example Given the following stress tensor The hydrostatic stress is which can be written as 5 of 7 5/13/2014 9:19 AM .Hydrostatic.continuummechanics. Deviatoric Stresses http://www.html In tensor notation.org/cm/hydrodeviatoricstress. the hydrostatic stress of a deviatoric stress tensor is zero. An interesting aspect of a traceless tensor is that it can be formed entirely from shear components. the above deviatoric stress tensor was input into the webpage. and then the coordinate system was rotated until the following stress tensor was obtained.html Subtracting the hydrostatic stress tensor from the total stress gives Note that the result is traceless. For example. Deviatoric Stresses http://www. Or put another way.Hydrostatic.continuummechanics.org/cm/hydrodeviatoricstress. In the screenshot here. a coordinate system transformation can be found to express the deviatoric stress tensor in the above example as shear stress exclusively. 6 of 7 5/13/2014 9:19 AM . Its first invariant equals zero. org/cm/hydrodeviatoricstress. Deviatoric Stresses http://www.html Table of Contents 7 of 7 5/13/2014 9:19 AM .Hydrostatic.continuummechanics.