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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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7 - Additional Evaluation Calculations
A number of LS-DYNA parameter calculations were performed in order to understand wood model issues related to: (1) plasticity algorithm iterations, (2) use of fully integrated elements, (3) the erosion criteria, and (4) the assumption of perfect plasticity. These issues are discussed here for both the static post and dynamic bogie impact simulations.
Static post bending simulations indicate that the calculated load-deflection curves are insensitive to the number of plasticity algorithm iterations. Figure 45 demonstrates that there is little difference in the load-deflection curves calculated with one or five iterations. However, bogie impact calculations performed with five iterations produced erroneous behavior in which damage, followed by erosion, was overcalculated.
All default parameters were selected from static and dynamic calculations performed with one iteration. Therefore, one iteration is selected as the default number of iterations. The user may override this number. Caution is suggested when using more than one iteration because the iterations parameter has not been thoroughly evaluated. Additional evaluations of the iterations parameter are recommended for future efforts.
Figure 45. The default number of plasticity algorithm iterations is set to one because
The static post peak-load deflection comparisons previously shown in figure 27 indicate that the fully integrated S/R (type 2 eight-point integration) elements produce a more brittle behavior than the standard under-integrated elements. This is probably because the fully integrated elements erode when just one of the eight integration points fails. By failure, we mean that the wood material model calculates a 99.9-percent reduction in stiffness and strength (in all six stress components both parallel and perpendicular to the grain) at that integration point. Therefore, seven of the eight integration points could still be loaded in tension when the element erodes.
As a check, static bending calculations were performed with and without erosion using both the standard and fully integrated elements (as shown in figure 46). There is essentially no difference between the responses calculated with and without erosion when standard elements are used (not shown). However, some difference is calculated when fully integrated elements are used. This indicates that the fully integrated elements are eroding prematurely (while still carrying load). One possible consequence of premature erosion is a fracture energy that is mesh-size sensitive and problem-dependent.
Figure 46. Erosion affects the fully integrated element curves, but not the under-integrated element
Roadside safety applications are primarily dynamic, so bogie impact simulations were also performed with fully integrated elements in the breakaway region for comparison with under-integrated elements. Deformed configurations with damage fringes are shown in figure 47. Energy-deflection and velocity-reduction histories are shown in figure 48. The damage fringes and histories calculated with eight-point integration are similar to those calculated with single-point integration. These bogie impact simulations suggest that eight-point integration can currently be used in the breakaway region of bogie impact simulations; however, analysts are urged to use it with caution. Preliminary calculations performed with eight-point integration in the impact region simulate excessive erosion. Therefore, use of eight-point integration in the impact region is not currently recommended.
Checks were also performed on the erosion criteria. As the default setup, elements erode when failure occurs parallel to the grain because all six components of stress are degraded to near zero. Elements do not erode when failure occurs perpendicular to the grain because only three components of stress (perpendicular to the grain) are degraded to near zero. The parallel-to-the-grain stress components are not degraded with perpendicular damage. Thus, the element is still able to carry load parallel to the grain after perpendicular failure occurs. All default parameters were selected from static and dynamic calculations performed with the default erosion criteria.
As an option, a flag is included to request erosion once perpendicular-to-the-grain failure occurs. For simplicity, this flag is called the perpendicular erosion flag and this erosion option is referred to as perpendicular erosion. Both static and dynamic simulations were performed with and without perpendicular erosion. The static calculations are discussed first, followed by the dynamic calculations.
Static deformed configurations and load-deflection curves are shown in figures 49 and 50, respectively, for calculations performed with and without perpendicular erosion. The deformed configuration calculated with perpendicular erosion is more realistic than the deformed configuration calculated without perpendicular erosion. To see the perpendicular damage in the calculation without perpendicular erosion, one can look at damage fringes (as shown in figure 49(c)). Red denotes elements with damage levels of d > 0.80, blue denotes elements with a damage range of 0.60 < d < 0.80, and cyan denotes elements with a damage range of 0.40 < d < 0.60.
Perpendicular erosion also has a minor effect on the static load-deflection curves. The post-peak softening behavior calculated with perpendicular erosion is slightly more brittle than that calculated without perpendicular erosion (figure 50).
Dynamic deformed configurations and load-deflection curves are shown in figures 51 and 52, respectively, for calculations performed with and without perpendicular erosion. As similarly noted for the static simulations, the breakaway region calculated dynamically with perpendicular erosion looks more realistic than that calculated without perpendicular erosion. However, slight erosion is also calculated in the impact region even though no visible damage was reported in the tests. Perpendicular erosion has little demonstrated effect on the load-deflection curves.
Figure 50. Load-deflection curves calculated with perpendicular erosion are
In fact, in some cases, perpendicular erosion can have an unrealistic effect on the calculated response. Some preliminary calculations performed with the simplest elastic bogie (without neoprene on the cylinder) simulated excessive erosion in the impact region. One such calculation is demonstrated in figure 53. One possible approach is to request perpendicular erosion in the breakaway region, but not request it in the impact region. Therefore, perpendicular erosion is not the default option (it must be specifically requested), nor is it recommended for general use.
Figure 53. Use of perpendicular erosion causes excessive erosion to be
The default behavior of the wood model is perfectly plastic in both parallel- and perpendicular-to-the-grain compression. This means that there is no increase or decrease in strength with increasing strain. Perfectly plastic behavior was previously demonstrated in figure 1(c).
The FPL clear wood and timber compression data previously analyzed in figures 3 and 5 exhibit perfect plasticity, at least for perpendicular strains as great as 4 percent. However, parallel strains of 20 to 30 percent are typically calculated at ground level in the compressive region of the post in the bogie impact calculations. Recent uninstrumented, unconfined compression tests of pine samples conducted by the user indicate softening at large strain parallel to the grain and hardening perpendicular to the grain.
Post-peak softening in compression (parallel or perpendicular) is not currently available in the wood material model. Although the damage model (which is responsible for softening) is applied to the stresses in compression, the stresses do not soften, because a compressive fracture energy of infinity is assumed. Fracture energy in compression is not currently an input value (as it is for tension and shear). Infinite fracture energy is hardwired into the model. To elicit softening, finite fracture energy needs to be included as input.
Post-peak hardening in compression is currently available as an option in the wood model. Single-element simulations with and without post-peak hardening are demonstrated in figure 54 parallel to the grain. Post-peak hardening requires the input of a single hardening parameter. A value of zero models perfect plasticity. Values greater than zero model hardening. At this time, the same parameter is used for both parallel and perpendicular modes (because of the limited input parameter slots available during development as a user-supplied material model). Separate parameters are recommended as a future modification to the model.
Figure 54. These single-element simulations demonstrate post-peak hardening in compression with positive values of Ghard.
All default parameters were selected from calculations run with perfect plasticity in compression. Small amounts of post-peak hardening have little effect on the static or bogie impact simulations. However, calculations involving high levels of compaction may benefit from post-peak hardening. This is demonstrated in figure 55 for a calculation performed with post-peak hardening (parallel and perpendicular). The post exhibits substantial compression in the elements in the vicinity of the rigid support. However, this same calculation aborted, prior to achieving the deformed configuration shown, when perfect plasticity was modeled.
Figure 55. Inclusion of post-peak hardening, both parallel and perpendicular to the grain, prevented this calculation from aborting at a large deflection.
Recommendations for future efforts include laboratory compression measurements and wood model enhancements. The laboratory compression measurements should include stress displacement and fracture energy for clear wood and graded wood samples, both parallel and perpendicular to the grain. These measurements should be made as a function of moisture content. If these measurements show softening, as recently measured parallel to the grain, then model enhancements should proceed. The wood model enhancements should include an input slot for compressive fracture energy; smooth variation of the fracture energy between compression, shear, and tension; and identification of default compressive fracture energy values as a function of moisture content. If these measurements show hardening, as recently measured perpendicular to the grain, then the existing post-peak hardening model should be evaluated for accuracy and for selection of default post-peak hardening parameters. Some porous materials exhibit substantial stiffening at high strain levels (70 to 80 percent) after all pores are compacted, which is called lockup. The current post-peak hardening formulation does not model lockup. The need for a lockup model should be assessed with regards to roadside safety applications.