SolidWorks Simulation: What is Von Mises Stress? - Part 2 of 2


* 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) loading.

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.

 Vonmises _2

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 then plotted.

Vonmises _3

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 stress plots!

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.

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7 Comments:

anonymous said...
thank you very much. :)
November 11, 2013 01:11
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Carl said...
Suppose a component's resolved Von Mises Stress, is less than the material's yield strength, and it is a ductile material. However, one of its three principal stresses exceeds the yield strength. Can it be stated that this component under this loading scenario, is safe?
March 26, 2014 19:03
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Roy M. said...
Hi Carl, The key to the question you're asking is the end: "Can it be state that this... is safe?" That's where it at the end of the day will be up to your own interpretation. Von Mises is just one of several different "yield criteria". The idea is, if the Von Mises stress is below the yield strength of the material, by THIS CRITERIA the material is not in plastic (permanent, damaging) deformation. That's saying according to this equation, it is safe. Maximum Principal Stress is an example of a different yield criteria. It states simply that if any of the maximum principal stresses are above yield stress, by this criteria the part is in failure. In a scenario where the max principal is above yield, but the Von Mises is below, the answer is the two criteria conflict as to their answer to "is it safe". Realistically speaking, even if you trust the Von Mises saying it is not yielding, the factor of safety on this part is probably right at about 1. So is it safe? Technically yes. Let's look at it this way though; if you need to lift an object that weighs 200 lbs, you're not going to use a rope rated for exactly 200 lbs, you'll use one rated for something higher to ensure it doesn't break. By this same logic, you probably would not want to build this part. At the end of the day, It is up to your evaluation as to what you think. There are several different yield criteria (from a quick search... Tresca, Drucker-Prager, Mohr-Coulomb, etc.) and they each are different evaluations. Which of these will be more or less valid can even depend on your material properties, etc. Certainly something to look into. Hopefully this answers your question! -Roy
March 27, 2014 09:03
Ravinder said...
How to get Von-mises stresses in Solid works Weldments simulation. It is showing only Axial stress and shear stress. How to calculate Von Mises Stress by using values given by solid works.
June 4, 2014 05:06
Dave Knowles said...
Hey, we have degrees in Science and Engineering. Why would we be afraid of equations? I enjoyed your article and getting refreshed on this important topic. Thankfully, SW can do these calcs for us!
June 4, 2014 14:06
Ryan said...
Thanks for the explanation! I'm still working on that engineering degree but this was extremely helpful. Now if only Solidworks would let me get a little more in-depth without the fatal "Solidworks is out of memory! Solidworks is now terminating..."
August 1, 2014 10:08
Ngula said...
Hi Carl, If one of the principal stresses exceeds the yield strength of the material, it means the von mises will also exceed, as von mises is the resultant of two orthogonal stresses (much like the hypotenuse of a triangle, von mises will be the longest vector).
September 22, 2014 22:09

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