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Publication Number: FHWA-HRT-04-096
Date: August 2005

Evaluation of LS-DYNA Wood Material Model 143

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15 - Element Formulation: Hourglassing

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

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

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

Current simulation practices often use all three element formulations in a typical application where the post is considered to be critical for detailed modeling. A post is divided into three parts: (1) the area of loading, (2) the area around the ground line (breakage area), and (3) the remaining sections. Reasonable results have been obtained using element formulation 2 for the area of loading, formulation 3 for the ground line area, and formulation 1 for the rest of the post. An important goal of the new wood material model is too eliminate this cumbersome task of dividing a wood post into multiple parts.

When using element formulation 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 is qm = 0.1.

The new wood material model has exhibited hourglassing when element formulation 1 was used for the entire wood post. To quantify this phenomenon, the static wood post model was divided into three parts as described above. Hourglass energy and internal energy were compared for part 8002, which is the section of the post that breaks at ground level.

Using default wood parameters for grade 1 southern yellow pine, hourglass control was investigated. The default hourglass control (type 1, qm = 0.1) results are shown in figure 97, while the results for hourglass control type 3 with qm = 0.1 are shown in figure 98. Clearly, both of these simulations resulted in excessive hourglassing (this is shown both graphically and numerically in the figures). When using hourglass control type 4 with qm = 0.005, the hourglass is brought under control for this model (as shown in figure 99). Note that hourglassing is considered to be under control when there are no obvious element distortions caused by hourglassing, and the hourglass energy measurement is less than 10 percent of the internal energy of the elements within a reasonable neighborhood of where the hourglassing is occurring.

Unfortunately, when using the same hourglass control that worked well for grade 1 southern yellow pine wood material properties for the grade DS 65 southern yellow pine wood material properties, significant hourglassing reappeared in the model (as shown in figure 100).

Note that for chapters 13 and 14 of this report, hourglass control type 4 with qm = 0.005 was used throughout.

Figure 97a.
(a) Deformed configuration
Figure 97b.
(b) Hourglass energy

Figure 97. Southern yellow pine, grade 1: Hourglass control type 1, qm = 0.1.

Figure 98a.
(a) Deformed configuration
Figure 98b.
(b) Hourglass energy

Figure 98. Southern yellow pine, grade 1: Hourglass control type 3, qm = 0.1.

Figure 99a.
(a) Deformed configuration
Figure 99b.
(b) Hourglass energy

Figure 99. Southern yellow pine, grade 1: Hourglass control type 4, qm = 0.005.

Figure 100a.
(a) Deformed configuration
Figure 100b.
(b) Hourglass energy

Figure 100. Southern yellow pine grade, DS-65: Hourglass control type 4, qm = 0.005.

To eliminate hourglassing completely and to increase the accuracy of the simulation, element formulations 2 and 3 were tried. Unfortunately, the results were undesirable because of the way failure (i.e., eroding) was handled for elements with multiple integration points. Thus, the developer has recommended that fully integrated element formulations not be used for the wood material. However, the user believes that fully integrated element formulations for the wood material model are critical for the success of the current implementation of the new wood material model. This would reduce the trial-and-error approach for finding the appropriate hourglass control parameters.

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