Manual for LS-DYNA Wood Material Model 143

FHWA-HRT-04-097, August 2007

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Preface
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List of Figures
List of Tables

Foreword

This report documents a wood material model that has been implemented into the dynamic finite element code, LS-DYNA, beginning with version 970. This material model was developed specifically to predict the dynamic performance of wood components used in roadside safety structures when undergoing a collision by a motor vehicle. This model is applicable for all varieties of wood when appropriate material coefficients are inserted. Default material coefficients for two wood varieties―southern yellow pine and Douglas fir―are stored in the model and can be accessed for use.

This report is one of two that completely documents this material model. This report, Manual for LS-DYNA Wood Material Model 143 (FHWA-HRT-04-097), completely documents this material model for the user. The companion report, Evaluation of LS-DYNA Wood Material Model 143 (FHWA-HRT-04-096), completely documents the model’s performance and the accuracy of the results. This performance evaluation was a collaboration between the model developer and the model evaluator. Regarding the model performance evaluation, the developer and the evaluator were unable to come to a final agreement regarding the model’s performance and accuracy. These disagreements are itemized and thoroughly discussed in section 17 of the second report.

This manual will be of interest to research engineers associated with the evaluation and crashworthy performance of roadside safety structures, particularly those engineers responsible for the prediction of the crash response of such structures when using the finite element code LS-DYNA.

Michael F. Trentacoste      
Director, Office of Safety   
Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

Table of Contents

Introduction
   Theoretical Manual
      Behavior of Wood
      Overview of Formulation
      Elastic Constitutive Equations
         Measured Clear Wood Moduli
         Review of Equations
         Default Elastic Stiffness Properties
         Orientation Vectors
      Failure Criteria
         Measured Clear Wood Strengths
         Wood Model Failure Criteria
         Default Strength Properties
      Plastic Flow
         Consistency Parameter Updates
         Elastoplastic Stress Updates
      Hardening
         Model Overview
         Default Hardening Parameters
         Hardening Model Theory
         Implementation Aspects
      Postpeak Softening
         Degradation Model
         Regulating Mesh-Size Dependency
         Default Damage Parameters
         Modeling Breakaway
      Rate Effects
         High Strain-Rate Data
         Shifted Surface Model Theory
         Viscoplastic Model Theory
         Default Rate-Effect Parameters
      Model Input
      Moisture Effects
         Southern Yellow Pine
         Douglas Fir
      Temperature Effects
      Variability By Grade

   User’s Manual
      Ls-Dyna Input
      Description of Properties
      Fitting the Model to the Data
      Model Formulation
      Wood Model Output

   Examples Manual
      Single-Element Simulations
      Bogie Impact Simulation

Appendix A. Measured Variability of Southern Yellow Pine

Appendix B. Quadratic Equations Fit to Moisture Content Data

Appendix C. Analytical Form of Candidate Failure Criteria

Appendix D. Graphical Comparison of Candidate Failure Criteria

Appendix E. Derivation of Consistency Parameter for Plasticity Algorithm

Appendix F. Derivation of Limiting Function for Hardening Model

Appendix G. Single-Element Input File

References

List of Figures

Figure 1. Wood material properties vary with orientation. The wood material coordinate system does not necessarily coincide with the board coordinate system. Source: American Society of Civil Engineers

Figure 2. Ultimate tensile strength of Douglas fir measured in off-axis tests drops rapidly as the load is oriented at increasing angles to the grain. Source: Society of Wood Science and Technology

Figure 3. Measured stress-strain relationships of southern yellow pine depend on load direction (parallel or perpendicular), load type (tensile or compressive), and moisture content

Figure 4. Temperature affects the dynamic behavior of wood posts impacted by bogies at 9.4 m/s.

Figure 5. Wood exhibits progressive softening. Source: Forest Products Laboratory

Figure 6. Wood exhibits modulus reduction and permanent deformation (splitting test data for spruce wood from Stanzi-Tschegg, et al.). Source: Kluwer Academic Publishers, with the permission of Springer Science and Business Media

Figure 7. Variability of southern yellow pine clear wood data at 12-percent moisture content depends on load direction and type

Figure 8. Wood material properties vary with position. Board strength depends on position and size of knot. Source: Society of Wood Science and Technology

Figure 9. Dynamic strength of wood increases with impact velocity in Hopkinson bar tests and is most pronounced in the perpendicular direction. Source: Pergamon, Elsevier Science Ltd

Figure 10. Organization of wood material model

Figure 11. Failure criteria for wood depend on four of the five invariants of a transversely isotropic material

Figure 12. Failure criteria for wood produce smooth surfaces in stress space

Figure 13. Prepeak nonlinearity is modeled in compression with translating yield surfaces that allow user to specify the hardening response

Figure 14. Postpeak hardening is modeled in compression with positive values of the parameter G_hard

Figure 15. Damage d accumulates with energy t once an initial threshold t₀ is exceeded

Figure 16. Softening depends on the values of the damage parameters C and D (calculated with dmax = 1)

Figure 17. Softening response modeled for parallel modes of southern yellow pine

Figure 18. Softening response modeled for perpendicular modes of southern yellow pine

Figure 19. Hopkinson bar tests indicate that the measured strength of pine increases with impact velocity. Source: Pergamon, Elsevier Science Ltd.⁽¹¹⁾

Figure 20. Hopkinson bar data indicate that strength and stiffness increase with strain rate. Source: EDP Sciences

Figure 21. These single-element simulations demonstrate the rate-effect behavior of the shifted surface formulation at 500/s

Figure 22. Two-parameter viscoplastic model is flexible in fitting data

Figure 23. These single-element simulations demonstrate the rate-effect behavior of the viscoplastic formulation at 500/s

Figure 24. Effect of temperature and moisture interaction on longitudinal modulus

Figure 25. Temperature effects are more pronounced for the strength parallel to the grain than for the modulus parallel to the grain. Source: Forest Products Laboratory

Figure 26. Yield criteria for wood produce smooth surfaces in stress space

Figure 27. Prepeak nonlinearity in compression is modeled with translating yield surfaces that allow user to specify hardening response

Figure 28. Softening response modeled for parallel modes of southern yellow pine

Figure 29. Example wood model input for selection of default input parameter (option MAT_WOOD_PINE)

Figure 30. Example wood model input for user specification of input parameters (option MAT_WOOD)

Figure 31. Example single-element stress-strain results for clear wood pine

Figure 32. Deformed configuration of post at 40 ms, including fringes of damage

Figure 33. Post deflection and cross-sectional force histories

Figure 34. Measured load displacement curves of southern yellow pine exhibit variability in tension parallel to the grain. Source: Forest Products Laboratory⁽¹⁴⁾

Figure 35. Measured load displacement curves of southern yellow pine exhibit variability in compression perpendicular to the grain. Source: Forest Products Laboratory

Figure 36. Effect of moisture content on tensile modulus parallel to the grain. Source: Forest Products Laboratory

Figure 37. Effect of moisture content on tensile modulus perpendicular to the grain. Source: Forest Products Laboratory

Figure 38. Effect of moisture content on tensile strength parallel to the grain. Source: Forest Products Laboratory.⁽¹⁴⁾

Figure 39. Effect of moisture content on tensile strength perpendicular to the grain. Source: Forest Products Laboratory.⁽¹⁴⁾

Figure 40. Effect of moisture content on compressive strength parallel to the grain. Source: Forest Products Laboratory.⁽¹⁴⁾

Figure 41. Effect of moisture content on compressive strength perpendicular to the grain. Source: Forest Products Laboratory.⁽¹⁴⁾

Figure 42. Effect of moisture content on shear strength parallel to the grain. Source: Forest Products Laboratory.⁽¹⁴⁾

Figure 43. Effect of moisture content on mode I fracture intensity. Source: Forest Products Laboratory

Figure 44. Effect of moisture content on mode II fracture intensity. Source: Forest Products Laboratory

Figure 45. Compressive strength variation of clear wood is readily modeled by a sinusoidal correction in the R-T plane. Source: Krieger Publishing Company.⁽¹⁶⁾

Figure 46. Geometry of an off-axis test specimen. Source: Krieger Publishing Company.⁽¹⁶⁾

Figure 47. Most of the interactive failure criteria are in agreement with Hankinson’s formula for the off-axis strength of southern yellow pine in the L-T plane

Figure 48. Effect of ring angle variation at 90-degree grain angle on the relative compression strength of four wood species. Source: Society of Wood Science and Technology

Figure 49. Failure criteria comparison for perpendicular modes as a function of the ring angle

Figure 50. Predicted effect of perpendicular confinement and extension on the longitudinal strength of southern yellow pine in tension and compression

Figure 51. Predicted effect of parallel shear and tangential stresses on the longitudinal strength of southern yellow pine in tension and compression

Figure 52. Predicted effect of parallel shear invariant on the longitudinal strength of southern yellow pine in tension and compression

Figure 53. Predicted strength of southern yellow pine perpendicular to the grain (no perpendicular shear stress applied)

Figure 54. Shape of the failure surface is sensitive to perpendicular shear strength if the criteria are transversely isotropic

Figure 55. Combinations of perpendicular and shear stresses that satisfy the failure criteria in the isotropic plane

Figure 56. Single-element input file

Figure 57. First continuation of single-element input file

Figure 58. Second continuation of single-element input file

List of Tables

Table 1. Average elastic moduli of southern yellow pine

Table 2. Average elastic moduli of Douglas fir

Table 3. LS-DYNA default values for the room-temperature moduli (graded or clear wood) of southern yellow pine and Douglas fir at saturation

Table 4. Average strength data for southern yellow pine

Table 5. Average strength data for Douglas fir

Table 6. LS-DYNA default values for room-temperature clear wood strengths of southern yellow pine and Douglas fir at fiber saturation.^*

Table 7. Default hardening parameters for clear wood southern yellow pine and Douglas fir

Table 8. LS-DYNA default values for room-temperature clear wood softening parameters for southern yellow pine and Douglas fir at saturation

Table 9. Average fracture intensity data for southern yellow pine measured perpendicular to the grain

Table 10. Room-temperature clear wood fracture energies for southern yellow pine and Douglas fir as a function of moisture content (derived from measured fracture intensities)

Table 11. Strength ratios versus strain rate derived from compressive rate-effect data

Table 12. Default LS-DYNA rate-effect parameters that provide the dynamic-to-static compressive strength ratios listed in table 11 (based on units of milliseconds for time) for pine at 12-percent moisture content

Table 13. User-supplied parameters for wood material model

Table 14. Default material property requests for wood material model

Table 15. Equations fit to moisture content data for southern yellow pine

Table 16. Equations fit to stiffness moisture content data for Douglas fir

Table 17. Input options for modeling strength reductions by grade

Symbols
B, D	Softening parameters (parallel and perpendicular)
CI, CII	Constants that relate fracture intensity to fracture energy
Cijkl	Material stiffness tensor (elastic moduli)
Cij	Material stiffness components
c||, c^	Hardening-rate parameters (parallel and perpendicular)
d, d||, d^, dm	Scalar damage parameters (general, parallel, perpendicular,    and max(d||, d^))
dmax||, dmax^	Maximum damage allowed (parallel and perpendicular)
E11, E22, E33	Normal moduli of an orthotropic material
EL, ET	Normal moduli (wood notation)
FM, FS	Factors to scale moduli and strengths with temperature
f||, f^	Yield surface functions (parallel and perpendicular)
f||*, f^*	Trial elastic yield surface functions (parallel and perpendicular)
G||, G^	Hardening model translational limit functions (parallel and perpendicular)
Gf ||, Gf ^	Fracture energies (tension and shear)
Gf I ||, Gf II ||	Parallel fracture energies (tension and shear)
Gf I ^, Gf II ^	Perpendicular fracture energies (tension and shear)
Ghard	Hardening parameter to override perfect plasticity
G12, G13, G23	Shear moduli of an orthotropic material
GLT, GLR, GTR	Shear moduli (wood notation)
I1, I2, I3, I4	Stress invariants of a transversely isotropic material
I1*, I2*,  I3*, I4*	Trial elastic stress invariants
KI, KII	Fracture intensities (tension and shear)
L	Element length
MC	Moisture content
n||, n^	Rate-effect power parameters (parallel and perpendicular)
N||, N^	Hardening initiation parameters (parallel and perpendicular)
QT, QC	Quality factors (tension/shear and compression)
Â	Stress enhancement factors (ratio of dynamic to static strength)
Sij	Compliance coefficients (reciprocals of elastic moduli)
S||, S^	Shear strengths (parallel and perpendicular)
T	Temperature
V	Impact velocity in Hopkinson pressure bar tests
X, XT, XC	Parallel wood strengths (general, tension, and compression)
Y, YT, YC	Perpendicular wood strengths (general, tension, and compression)
aij	Backstress tensor (and incremental backstress for hardening model
g, g||, g^	Viscoplastic interpolation parameters (general, parallel, and perpendicular)
eij, Deij	Strain tensor and strain increments
e11, e22, e33, e12, e13, e23	Strain components of an orthotropic material
e1, e2, e3, e4, e5, e6	Strain components (shorthand notation)
eL, eT, eR, eLT, eLR, eTR	Strain components (wood notation)
, ,	Strain-rate increments parallel to the grain (wood notation)
, ,	Strain-rate increments perpendicular to the grain (wood notation)
,	Scalar effective strain rates (parallel and perpendicular)
,	Scalar effective strain-rate increments (parallel and perpendicular)
,	Plasticity consistency parameters (parallel and perpendicular)
Dt	Time-step increment
h	General rate-effect fluidity parameter
h||, h^	Tension/shear rate-effect fluidity parameters (parallel and perpendicular)
hc||, hc^	Compression rate-effect fluidity parameters (parallel and perpendicular)
r, rs	Density of wood and of wood solid phase
,	Ultimate yield surfaces (parallel and perpendicular)
, , , ,	Stress tensors (trial elastic, inviscid, inviscid with backstress, viscid, and viscid with damage)
s11, s22, s33, s12, s13, s23	Stress components of an orthotropic material
s1, s2, s3, s4, s5, s6	Stress components (shorthand notation)
sL, sT, sR, sLT, sLR, sTR	Stress components (wood notation)
t||, t^	Instantaneous strain energy type term for damage accumulation
t0||, t0^	Initial strain energy type value for damage initiation
nij	Poisson’s ratios (indicial notation)
nLT, nLR, nTR	Major Poisson’s ratios (wood notation)

FHWA-HRT-04-097