A wood material model was developed, implemented into the LSDYNA finite element code, and evaluated for use in roadside safety applications. Eight evaluation calculations (four quasistatic and four dynamic) were performed by the developer with the results documented in chapters 1 through 7 of this report. The main evaluation calculations were dynamic bogie impact at 9.6 m/s into southern yellow pine (grade 1 unfrozen, grade 1 frozen, and DS65 unfrozen) and Douglas fir (grade 1) posts. The wood model calculates post breakage just below ground level (in agreement with the measured breakage locations). The wood model also calculates bogie kinetic energy and velocity reductions that are in reasonable agreement with final measured quantities. However, the evaluation calculations indicate some limitations in both the test data and model formulation. Recommendations for future efforts, based on these limitations, are itemized here. These enhancements are not required for achieving good correlation between the wood model and post data.

Parallel Fracture Energy: Perform quasistatic tensile tests of clear wood specimens to directly measure the paralleltothegrain fracture energy as a function of moisture content.
Fracture energy is the area under the stressdisplacement curve from peak stress to zero stress, measured during unconfined tension tests conducted parallel to the grain. Parallel fracture energy is an important input parameter whose value has a strong effect on post response in bogie impact and static bending simulations. Although the suite of FPL clear wood pine data implemented into the wood model as default properties is quite extensive, it does not include fracture energy measurements. Therefore, correlations with bogie impact and static bending test data were used to set the default fracture energies. However, the parallel fracture energy selected from the static bending correlations is five times greater than that selected from the bogie impact correlations. This should be clarified.
A minimum of 15 quasistatic tensile tests of clear wood pine are recommended in order to develop quadratic equations for parallel fracture energy as a function of moisture content. These tests should be conducted at five moisture content levels, with each test repeated three times. Additional tests conducted on grade 2 and DS65 pine would provide information on the variation of fracture energy as a function of grade. Dynamic tensile tests (e.g., at 0.1 or 1.0 s^{1} (a typical strain rate in the post)) would also provide useful information on the variation of fracture energy with strain rate.

Perfect Plasticity: Perform quasistatic compression tests of clear and graded wood pine specimens to moderate compression levels to evaluate the assumption of perfect plasticity in compression.
The wood material model simulates perfectly plastic behavior in compression both parallel and perpendicular to the grain (as the default behavior). An option is also included to model postpeak hardening in compression; however, no option is included to model softening in compression.
FPL conducted a suite of laboratory compression tests on clear wood samples for strain levels up to about 4 percent that were used to set the model behavior. The measured stressstrain data indicate that perfect plasticity is a reasonable assumption (at least for strains up to 4 percent). However, parallel strain levels up to 30 percent are noted in the bogie impact simulations. Therefore, the user conducted a few quicklook compression tests of graded pine specimens for strains up to 90 percent. Their measured stressstrain data indicate softening parallel to the grain and hardening perpendicular to the grain.^{1}
Future efforts could generate hardening and/or softening data for wood in compression to moderate strain levels (about 30 percent). A suite of tests are recommended for clear wood and two grades of saturated pine (grade 1 and DS 65) to obtain plots of load versus axial and lateral deflection for strains up to 30 percent. Tests should be conducted both parallel and perpendicular to the grain as a function of moisture content. If a review of the test data indicates that softening is evident, then a compressive softening formulation is recommended for implementation, which may or may not affect post fracture. It is not clear to the developer that a compressive softening formulation is needed or that it would enhance post fracture behavior.

Quality Factors: Perform static tensile and compression tests of dry, partially saturated, and saturated pine to determine how quality factors vary as a function of moisture content.
The suite of pine data implemented into the wood model as default properties is for clear wood, whereas real posts are graded wood such as grades 2, 1, or DS 65. Clear wood is stronger than graded wood. The approach for setting default properties for graded wood is to apply quality factors (strengthreduction factors) to the clear wood to account for reductions in strength as a function of grade. Two quality factors are set. One quality factor is applied to the tensile and shear strengths, the other is applied to the compressive strengths.
Default quality factors are estimated from correlations of calculations with static bending test data. However, the quality factors estimated from simulations of the user’s saturatedpost bending tests are about twice as high as those estimated from the simulation of FPL’s partially saturated timberbending tests. This suggests that quality factors vary as a function of moisture content. Quality factors currently implemented in the model as default properties are those from the saturatedpost correlations.
Static tests (compression and tension) of graded wood are recommended at a minimum of three moisture content levels in order to develop quadratic equations for quality factors as a function of moisture content. Conducting compression and tension tests, rather than bending tests, would isolate the tensile quality factors from the compressive factors. A related issue is whether the same quality factors should be applied perpendicular to the grain as those applied parallel to the grain, as is the current default implementation (although an option is available to neglect quality factors perpendicular to the grain). If possible, tests should be conducted both parallel and perpendicular to the grain.

Coupling Between Parallel and Perpendicular Modes: Evaluate and enhance the parallel and perpendicular yield surface and plasticity formulations to include coupling between the parallel and perpendicular modes. Evaluation of such coupling would require measurement of the volume expansion/contraction (effective Poisson’s ratio in the plastic region) behavior of wood.
One theoretical limitation of the wood model is that there is no coupling between the parallel and perpendicular modes in the plastic region. Such coupling affects volumetric behavior. The suite of clear wood data provided by FPL included measurement of the major Poisson’s ratio in the elastic region. Typical values are around ν_{LT} = 0.16 for pine at the fiber saturation point. No measurements were reported for the effective Poisson’s ratio in the plastic/damage regions (once the material yields or softens). The effective Poisson’s ratio is the ratio of the lateral strain to the axial strain in uniaxial stress tests (without lateral confinement). Porous materials tend to flow during yielding and softening, which can result in an effective Poisson’s ratio that is larger or smaller than the elastically measured value. For example, for porous geological materials such as concrete, the effective Poisson’s ratio is typically modeled as being greater than the elastic ratio in unconfined compression (with values greater than 1) and less than the elastic ratio in unconfined tension.
The user has examined the behavior of the wood model for single elements of pine in unconfined tension. An increase in the volume of the element was noted. The user believes that there should be no change in the volume of wood in tension (i.e., wood is incompressible). To achieve no change in volume, the elastic and effective Poisson’s ratios would have to be 0.5. The FPL data indicate that the elastic Poisson’s ratio parallel to the grain is not 0.5. However, no lateral strain or change in volume measurements is available to confirm or refute an effective Poisson’s ratio of 0.5 in the plastic region. Therefore, we recommend that all additional test data generated should include lateral strain measurements. The unconfined compression and tension tests recommended in items 2 and 3 above should include measurement of both axial and lateral strain.
Setting the compressibility or effective Poisson’s ratio behavior of the wood model is not simply a matter of specifying an input value, rather, it requires that changes be made to the formulation of the model to include coupling between the parallel (axial) plasticity and perpendicular (lateral) plasticity. The current wood model includes separate yield surfaces and plasticity computations for yielding parallel and perpendicular to the grain. As a result, yielding parallel to the grain does not induce plastic flow perpendicular to the grain. Similarly, yielding perpendicular to the grain does not include plastic flow parallel to the grain. We recommend exploring and implementing methods of coupling the plastic flow once sufficient test data are generated to set the coupling via measurement of the effective Poisson’s ratio or volume change. This could be done regardless of whether or not the tests indicate incompressibility.

Erosion Method: All erosion criteria could be enhanced to be userspecified, including the damagebased criteria. Future efforts could also include modifications, additions, and/or elimination of the distorted element checks and possible inclusion of an input flag to turn these checks on and off.
The primary erosion mechanism is based on damage. Element erosion, by default, is based on parallel damage in excess of 99 percent. Erosion, by option, may also be based on perpendicular damage in excess of 98.9 percent. As element damage approaches 99 percent, strength and stiffness approach 1 percent of their original values. Elements with nearly zero strength and stiffness could possibly experience shooting nodes and drastically deform, invert, expand, or contract in response to very small loads. Such behavior can cause a calculation to abort. Element erosion is a technique that prevents the calculation from aborting by removing these elements from the calculation before large distortions occur. Erosion also provides a good visual image of breakage in the damage region.
Because elements do not automatically erode with perpendicular damage, the model includes a check on the maximum strains perpendicular to the grain to determine whether they are greater than 90 percent. If so, the element erodes if perpendicular damage has already exceeded 98 percent.
In addition to the damagebased erosion criteria, a number of checks are implemented in the model to prevent highly distorted elements from causing computational problems. These distorted element checks were implemented for the explicit purpose of debugging the model during use of the userdefined material model interface and do not necessarily need to be retained in the final model. They include:
A check on the element volume to determine whether it is less than zero.
A check on the current relative volume to determine whether it is less than 10 percent.
A check on the maximum strain increment to determine whether it is greater than 1 percent.
Element erosion will occur if any of these conditions are met.

MeshSize Dependency: Future efforts could include directpull and unconfined compression simulations of wood specimens at different mesh refinements to demonstrate meshsize response. The issue here is to isolate the material response without the complicating effects of other materials and contact issues.
A related issue that is recommended for evaluation is whether to use the initial element length or the updated element length in the calculation of the damage parameter. The updated element length is currently implemented. Damage is based on element length in an effort to regulate meshsize sensitivity.

Iterations Parameter: Evaluate and enhance the plasticity algorithm iterations method.
The plasticity algorithm returns the stress state to the yield surface if the elastic stress state is predicted to lie outside the yield surface. The purpose of the iterations parameter is to increase the accuracy of the return through iteration and subsequent tolerance checks to ensure that the stress state lies on the yield surface. Static calculations indicate that one iteration is just as accurate as five iterations. In contrast, bogie impact simulations calculate excessive damage and erosion with five iterations. Therefore, the default number of iterations has been set to one. Future model enhancements should include debugging of the iterations parameter for dynamic applications.

Accelerometer Measurements: Perform future bogie impact tests with measurements made on the post rather than on the bogie.
The forcedeflection and energydeflection performance envelopes from the user’s bogie impact tests are measurements processed from an accelerometer located at the center of the bogie frame. The highfrequency measurements are filtered to produce a smooth signal. Because all measurements are made on the bogie rather than on the post, good correlations between the calculations and the processed data require an accurate bogie model (geometric and material) as well as an accurate wood post model.
Calculations completed to date indicate that the computed bogie accelerations strongly depend on the bogie model type (rigid or elastic) and output sampling rate. For example, the calculated bogie acceleration (force) histories contain a higher frequency content than that measured. The calculated histories are also more oscillatory than those measured. On the other hand, computed force histories derived from crosssectional forces in the post are much less sensitive to the sampling rate and bogie model type than those derived from the bogie accelerometer location. This suggests that measurements recorded directly on the post would isolate wood performance and facilitate evaluation of the wood model. Instrumenting the wood posts could prove to be a challenging endeavor.

Boundary Conditions: Perform future static and bogie impact tests on posts with welldefined boundary conditions.
Posts are typically situated in highly deformable media, such as soil. Therefore, static and bogie impact tests were intended to be conducted under fixedbase conditions. The posts in the static tests were placed in a rigid base with steel and neoprene shims to wedge the post into the support. The posts in the dynamic tests were loosely placed in a steel tube in the ground and wedged in with neoprene and plywood shims.
LS DYNA results calculated with simple (post nodal constraints) to sophisticated (support and neoprene modeled explicitly) meshes produce different computational results. Performing future tests with simple, easytomodel boundary conditions would help with future evaluation of the wood model.
 The measured hardening behavior perpendicular to the grain was unexpected. It looked similar to the behavior of the isotrophic porous materials in uniaxial strain, not uniaxial stress. This unexpected behavior may be because wood is orthotropic.