CHAPTER 6. ELEMENT FORMULATION: HOURGLASSING

There are three applicable solid element formulations available within LS-DYNA:

1. Constant stress.
2. Fully integrated selective reduced (S/R) solid.
3. Fully integrated quadratic eight-node element with nodal rotations.

These are listed in order of increasing accuracy and in order of increasing computational costs. Element formulation no. 1 can exhibit hourglassing, while formulation nos. 2 and 3 have no hourglassing. Details of hourglassing and the various hourglass control algorithms will not be provided here. The reader is referred to the LS‑DYNA user's and theoretical manuals for details.

When using element formulation no. 1, an hourglass control algorithm is mandatory. The default hourglass control is referred to as control type 1. An important parameter associated with hourglass control is called the hourglass coefficient and is given the label qm. The default value for qm is 0.1.

The new soil material model has exhibited hourglassing when element formulation no. 1 was used in the direct shear model. Default hourglass control (type 1, qm = 0.1) results are shown in figure 18, while the results from hourglass control type 4, qm = 0.005, are shown in figure 19.

Under certain conditions, hourglassing was brought under control for the majority of the simulation time, with hourglassing appearing late in the calculation. However, the results were very sensitive to both the hourglass control and the values used for the soil parameters. Quantifying this behavior was not possible in the limited amount of time available for this study.

Additionally, a limited mesh refinement study was performed in order to investigate whether a finer mesh exhibited lower hourglassing (as is often the case in LS-DYNA modeling). However, with a refined mesh, the contact between the soil and the direct shear testing device became unstable, and no firm results were obtained. A detailed investigation into the contact difficulties was not possible in the limited amount of time available for this study.

Thus, in the current implementation, it is recommended that element formulation no. 2 be used with the soil material model. Note that for all other chapters in this report, element formulation no. 2 was employed.

Figure 18. Hourglass control type 1, qm = 0.1.

Figure 19. Hourglass control type 4, qm = 0.005.

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