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Why Worry About Hourglassing in Explicit Dynamics? Part I

Hourglassing Explicit FEA
January 9, 2015 By: Steven Hale

Explicit dynamics software codes such as LS-Dyna, AUTODYN, and ANSYS/Explicit are great for simulating high energy dynamic events and even some very difficult statics problems. One of the challenges to getting an accurate solution with these solvers is selecting an element type that is both fast and accurate. For the majority of explicit dynamics analyses, reduced-integration element types are preferred because they are very fast, robust under high distortion conditions, and not susceptible to shear-locking which can over-stiffen the response. As a result, these are usually the default element types used in commercial explicit dynamics codes. Fully-integrated elements are more typically used with implicit solvers because fewer time integration steps are required, smaller element distortions are expected, and more element formulations are available to counter shear locking. However, a drawback to reduced integration elements is their susceptibility to hourglass modes. 

In this post, I will discuss what hourglassing is, and basic methods to detect and avoid it. 

Hourglass modes are non-physical, zero energy modes that do not generate any stress or strain but can affect solution accuracy by interfering with the structure’s true response. This often leads to inaccurate stress, strain, deflection, and contact results. The elements that are susceptible to hourglassing are reduced-integration hex and quad-shaped solid and shell elements. Triangular shells and tetrahedral solids are not susceptible. Hourglass modes in a hex element can take on any of the shapes shown in blue in the figure above.

In a complete model, these modes typically appear as a region of hourglass-shaped elements and can sometimes be quite obvious in the shape of the deformed mesh. Figure 2 shows a simple mesh with no hourglassing on the left, and the same mesh with hourglassing on the right. While close inspection of the deformed mesh should be done to check for hourglass modes, hourglassing is not always obvious. In such cases, checking the hourglass energy is necessary. A high hourglass energy relative to the system internal energy is a good indicator that hourglassing is significant and needs further suppression.  Hourglass energy will be discussed in more detail in Part II of this post, so stay tuned!


Figure 2: Mesh showing no visible hourglassing (left) and visible hourglassing (right)

Since hourglassing can lead to an inaccurate solution, how can we reduce or eliminate it? One way is to use fully-integrated elements but, as mentioned previously, this has its drawbacks. Another method is to refine your mesh in regions that exhibit hourglassing, although this generates smaller (and more) elements which increases run time.  Also, point or edge loads and/or point or edge contact can excite hourglass modes. So, spreading a load or contact area over more elements is another way to reduce hourglassing.  A pressure load, for example, is preferred to a point force load. 

In Part II of this post, I will show examples of why hourglassing can be such a problem and discuss more advanced methods for reducing hourglassing and how to use them effectively. I am very interested to hear from any of you that have comments or experience with hourglassing in explicit dynamics analysis!