# Terms used in analysis - Set 2 - #12-18

Blog Post created by Joe Galliera on Jul 26, 2010
I thought it might be a good idea to provide some basic definitions of terms that  are used in analysis that are good to know to be able to communicate  intelligently about Simulation.  These are not meant to be  definitive technical definitions but more fundamental knowledge of these  terms (i.e. they are mostly coming off the top of my head as I'm typing).  If  you believe that I am off on any of these, please let me  know.

Last time two of  the terms that I gave were von Mises and shear stresses; there's many more  components of stress than that.  Here's 12 to 18:

12. normal  stress - if you were to take a look at an infinitesimally small cube  oriented in the global coordinate system, the normal stress is the stress  that develops normal to the face.  Normal stress is denoted by the Greek letter sigma, σ, and subscript is the face that it is normal to, eg. σx.  From last time, shear stress is defined as  the stress that is tangential to the face, usually denoted by a Greek tau, τ, and subscript is the face and then the direction of  shear, for example τxz is on the x-face in the  z-direction.  Thus for a given cube face, there is a single normal stress and  two shear stresses.  Both normal and shear stresses are vectors, having  direction and magnitude, and since the proposed cube we are looking at is  infinitesimally small, the stresses on opposing faces are equal in magnitude but  in the opposite direction.  Thus for a given cube, there are a grand total of 3  normal stresses and 6 shear stresses.  The below image can be helpful in  describing the stress vectors:

13. shear  modulus - primarily denoted as G, is the ratio of shear stress to shear  strain.  For a linear isotropic material, it is useful to know that any 2 moduli  can determine any other elastic moduli (a full matrix can be found at the bottom  of http://en.wikipedia.org/wiki/Elastic_modulus).   G = (E/2)/(1+ν), where E is Young's modulus and ν is Poisson's ratio.  In SW SIM, if you define E and ν for a linear isotropic material, I recommend keeping shear  modulus blank and the software will compute it by itself (if you put in a value  it will use that one instead so again best to keep it  blank).

14.  principal stresses - at any point in a stressed body (in this case  let's take the same point as given above), there exists three planes where there  are no shear stresses and the normal stress vectors to these planes are in  "principal" directions, and are denoted σ1, σ2, and σ3, (or  in SW SIM we name them P1, P2 and P3).  The normal and shear stresses from the  stress cube above go through a matrix transformation (resulting in a matrix  where all off-axis terms are zero) to obtain the principal directions, which are  orthogonal to one another meaning that they are completely independent  directions.  It is always true that P1 ≥ P2 ≥ P3.  In an pure tensile load, all  three principal stresses are positive; in a pure compressive load, all 3 are  negative; and when the signs of the principal stresses are mixed (P1 is positive  and P3 is negative), then this usually means the body is in bending.  I  typically recommend to set your Simulation options to always show P1 and P3  stress components in addition to von Mises stress.

15. bending  stress - Thinking of shell elements, they tend to bend easily because  they are thin.  During bending, compressive and tensile stresses develop; the  maximum value of these stresses are on opposite sides of the outermost thickness  of the shell, and the stress varies linearly through its thickness.  The bending  stress is the slope of the line between compressive and tensile stresses through  the thickness of the shell.

16.  membrane stress - is the stress in the plane of the shell that develops  if the compressive and tensile stresses have different magnitudes.  If the  tensile stress is greater, then the membrane is pulled along the direction  of the shell plane; if the compressive stress is greater, then the material in  the membrane is compressed.
So in conclusion  for a shell, show P1 & P3 for both top and bottom of the shells and both the  membrane and bending stresses.

17. torsional stress - is a stress due  to a twisting of an object due to an applied torque.  It is a type of shear  stress with an specific equation Tr/J to calculate it by hand based on the  applied torque T, the radius r from the axis of torque, and the object  (typically a cylindrical shaft) with a polar moment of inertia J.  The max  torsional stress is on the outer max radius, or surface, of the  shaft.

18.  Hertzian contact stress - the compressive stress due to contact of two  curved parts under load.  The important thing to note for Hertzian stresses is  that the max stress occurs close to the area of contact in the subsurface, or  just below its surface, thus the mesh needs to be finest below the surface so  creating a mesh control just inside the sphere near the contact is important.   Another important thing to know is that it is very difficult to get an accurate  Hertzian contact stress result.