* To read part 1 of this series please click here.
This is the second half of the article which explains what
exactly von Mises stress is, and why it is such a crucial
measurement in a SolidWorks Simulation study. When we left off, we
were beginning to uncover some of the complications that occur when
working with stress induced by complex (multi-directional)
Since the forces have directions, the induced stresses also have
directions associated with them. For the purpose of this example,
let's think of it like the sides of a right triangle. Each leg has
a magnitude (length of the side) and direction (the angle between
it and another leg). Pythagorean Theorem says for a right triangle,
the square of the length of the longest side is equal to the sum of
the squares of the other two sides. Therefore, we know if two legs
are length 3 and 4, we solve for the hypotenuse side and find it's
the longest, at 5. Similarly, since stress has direction, we need
to resolve the stresses into a resultant direction, and that would
determine the magnitude. Similarly to the results of the
Pythagorean Theorem, just because your individual normal stresses
are smaller than the yield, doesn't mean that the resultant stress
in the part is... It could easily be greater!
We need to find a way to combine these six individual principal
and shear stresses into a single resolved
stress value, to which we can compare. The resolved stress will
have a direction as well as magnitude. Maybe we don't particularly
care about the direction, but we need to know what the magnitude of
this is to make sure this part isn't breaking. This is where
Richard Elder von Mises comes into play.
Von Mises is credited with coming up with what is arguably the
most accepted yield criterion (way of resolving these stresses). He
designed an equation that takes in each shear and principal stress
value, and in turn spits out a single "von Mises stress value"
which can be simply compared to a yield strength of the material.
If it's greater than the yield strength, the part is failing
according to his criteria. If it is less, then the part is said to
be within the yield criteria, and is not failing. The equation for
von Mises stress is shown below.
Once again, the sigmas (σ) correspond to normal stress values,
and the taus (τ) are the shear stress values.
...OK, you lost me...
I know that formula is scary, but hopefully you're still with
me. All that this formula does is convert each of the six numbers
that you input (the right side of the equals sign) into a single
value (left side) that we can compare to. This is exactly what
SolidWorks does in creating simulation results. The von Mises
stress is the default stress plot because it's a way to show the
one value we're concerned about - resolved stress. Once again,
SolidWorks has done all the work for you here. It's gone through
and calculated the principal and shear at each location, and then
plugged them into this formula to give one resolved value which is
If you've ever dug around in what options you have for stress
plots, you will find that you can verify this. You may have noticed
that you can actually plot the principal or shear stresses
individually. There might be scenarios where you'd want to look at
these. In most cases you're simply asking "is my part failing?" In
that scenario, von Mises stress plot is the way to go.
Fantastic! I'll remember that when I'm looking at my
Now that you know all the steps that SolidWorks goes through in
solving your simulation study, don't you feel more confident in the
results that it gives you? Of course, it is always important to
verify that your simulation is set up correctly and meshed properly
to produce accurate results. Still, SolidWorks Simulation is an
incredible tool that utilizes valid strength of materials equations
to solve for its results. There's no guessing involved; it knows
what's going on, and has done the math to back it up.
Hopefully you didn't find this too complicated, or boring. As I
said before, strength of materials is something I'm interested in.
If you share that interest, keep your eyes open for articles about
SolidWorks Simulation, and other strength of materials
applications. I'll try to write about some interesting scenarios,
or give you some tips and tricks.