FEA for beginners (Part III)
One of the dangers of FEA is that it provides results, even if they are wrong. Hence it is the engineer’s responsibility to critically analyse and validate them. In these terms, one of the most common rookie mistakes is “hourglass”. If you want to learn what it is and how to correct it, this is your place.
To begin with, let me introduce two different concepts: underintegrated elements and fully integrated ones. Underintegrated elements are only evaluated at one single integration point, whereas fully integrated ones have more than one. In order to illustrate this idea, Figure 1 is introduced.
By default, most of the FEA packages uses underintegrated elements due to the fact that they require less computational effort.
Once I have introduced these two concepts, there is a phenomenon known as “hourglass” or “zero-energy” mode which can be suffered by underintegrated elements. These are modes of deformation that cannot be resisted by internal stresses, producing zero strain and no stress. Therefore, when this phenomenon occurs, non-physical behaviour is obtained. In order to solve this problem, the FEA packages always include some options in order to control these hourglass modes by the addition of artificial forces that resist these modes of deformation. Therefore, we have to be careful not to make our model too stiff as it can also lead to non-realistic solutions. Another approach can be the use of fully integrated elements.
All of this sounds great, but in reality you may find difficulties when trying to identify this issue by looking at the way the elements deform. As a matter of fact, the first tie I dealt with hourglass was when I was simulating a drop test of a pedestrian headform, a device which is used for testing vehicles. After performing the corresponding experimental tests, a Finite Element model was developed and the exact same conditions were simulated. Despite the fact that the acceleration curves extracted from the model were quite accurate when compared to the real tests, in the FE model there was a plastic deformation which was not present in the real world. The way it was deforming did not indicate a clear hourglass effect but after applying some controls within the software, the behaviour was successfully corrected.
Because of that experience, I felt curious about how I could identify hourglass when no evident signs were observed. Surprisingly, the solution is very simple: we just have to check that the so called “hourglass energy” is not greater than 10% of the peak value of the internal energy.
Now that you know this, don’t forget to include those energies as your output variables so you can easily check if there is hourglass or not in your model. After reading this post, I hope you will be able to solve this problematic if you ever find a model which is suffering this zero-energy mode!