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Why Worry About Hourglassing in Explicit Dynamics? Part II

Hourglassing Explicit FEA Model
January 16, 2015 By: Steven Hale

In Part I of this post, I explained what hourglassing is in an explicit dynamics analysis, and some basic techniques to detect and reduce it. In this post, I will show some examples that illustrate why hourglassing can be such a problem and discuss additional methods for reducing hourglassing and how to use them effectively. 

The methods for suppressing hourglassing I discussed in Part I are not always practical. Fully-integrated elements have their own problems, a finer mesh leads to longer run times, and spreading out loads and contacts is not always easy or practical. Another way to reduce hourglassing is to use one of the hourglass control algorithms that are common to commercial explicit dynamics codes. These algorithms add either stiffness or damping forces in the direction of the hourglass mode and do not affect general rigid body motion or distortional motion. 

The following two examples show the importance of using these hourglass control algorithms. The first example, (Figure 1 above) shows a spinning disk with (left) and without (right) hourglass controls. The contours show the maximum principal stress in the disk. A stiffness-based hourglass control algorithm was used in this example. The hourglass modes are visually obvious in the case without hourglass control and it’s very apparent that hourglass controls are needed to obtain an accurate stress solution.

The second example (Figure 2) shows the results of a rigid block impacting a flexible cantilevered bar, both with and without hourglass control. In both cases, the block impacts the flexible bar on the corner, which tends to excite hourglassing. These images show contours of total deformation at the same point in time. The hourglassing is very apparent in the case without hourglass control. This affects the results including peak deflection in the bar after impact - which is 23% lower in the case without hourglass control.

Figure 2: Block-bar impact without hourglass control (left) and with hourglass control (right)

 

 

The animation below shows severe hourglassing in the block-bar impact model when no hourglass control is used.
 

 

Improper use of hourglass controls can also lead to problems, however.  Even though these controls are intended only to affect the hourglass motion, they can artificially remove system energy if not applied correctly. Users need to select an appropriate hourglass control algorithm and coefficient. Too much hourglass control can lead to an overly-stiff response. As a general rule, stiffness-based algorithms are more effective for lower energy simulations like drop tests, and viscosity-based algorithms are more effective for high energy simulations like ballistic impacts.  Another general rule of thumb is to track the hourglass energy, which is the energy added by the hourglass control forces, and make sure that it is less than 10% of the total system internal energy. Many tests have shown that values higher than this suggest that the hourglass control forces are artificially dissipating enough system energy to affect critical results. 

FEA consultants and analysts need to be aware that hourglass modes are a potential problem in explicit dynamics models because they can lead to inaccurate predictions of critical stress, strain, displacement, and contact results. These can be controlled by refining the mesh, spreading out the load or contact interface, or by using an hourglass control algorithm. Wise use of these techniques is a critical part of the modeling process for explicit dynamics and should not be underestimated. 

I am very interested to hear from any of you that have comments or experience with hourglassing in explicit dynamics analysis. Have you had any models that have been particularly prone to hourglassing? If so, how has it affected your analysis results? What have you done to control hourglassing?