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FHWA-HRT-05-062, May 2007
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This report documents a concrete material model that has been implemented into the dynamic finite element code, LS-DYNA, beginning with version 971. This model is in keyword format as MAT_CSCM for Continuous Surface Cap Model. This material model was developed to predict the dynamic performance-both elastic deformation and failure-of concrete used in roadside safety structures when involved in a collision with a motor vehicle. An example of a roadside safety structure is a concrete safety barrier that divides opposing lanes of traffic on a roadway. Default input parameters for concrete are stored in the model and can be accessed for use. This material model only replicates the concrete aggregate. Appropriate reinforcement bars or rods must be included in the structure model separately.
The Users Manual for LS-DYNA Concrete Material Model 159 is the first of two reports that completely document this material model. This report documents the theoretical basis, the required input format, and includes limited hypothetical problems for the user. The second report, Evaluation of LS-DYNA Concrete Material Model 159 (FHWA-HRT-05-063), documents the testing performed to document the model's performance and accuracy of results.
This report will be of interest to research engineers who are associated with the evaluation and crashworthy performance of roadside safety structures, particularly engineers responsible for predicting the crash response of such structures when using the finite element code, LS-DYNA.
Michael Trentacoste
Director, Office of Safety R&D
This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its content or use thereof. This report does not constitute a standard, specification, or regulation.
The United States 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.
The Federal Highway Administration 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.
1. Report No. FHWA-HRT-05-062 |
2. Government Accession No. |
3. Recipient's Catalog No. |
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4. Title and Subtitle USERS MANUAL FOR LS-DYNA CONCRETE MATERIAL MODEL 159 |
5. Report Date May 2007 |
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6. Performing Organization Code |
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7. Author(s) Yvonne D. Murray |
8. Performing Organization Report No. |
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9. Performing Organization Name and Address APTEK, Inc. |
10. Work Unit No. (TRAIS) |
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11. Contract or Grant No. DTFH61-01-C-00075 |
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12. Sponsoring Agency Name and Address Volpe National Transportation Systems Center Federal Highway Administration |
13. Type of Report and Period Covered Final Report September 27, 2001 through |
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14. Sponsoring Agency Code |
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15. Supplementary Notes The Contracting Officer's Technical Representative (COTR) for this project is Martin Hargrave, Office of Safety Research and Development, HRDS-04, Turner-Fairbank Highway Research Center. |
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16. Abstract An elasto-plastic damage model with rate effects was developed for concrete and implemented into LS-DYNA, a commercially available finite element code. This manual documents the theory of the concrete material model, describes the required input format, and includes example problems for use as a learning tool. A default material property input option is provided for normal strength concrete. The model was developed for roadside safety applications, such as concrete bridge rails and portable barriers impacted by vehicles, but it should also be applicable to other dynamic applications. The companion report to this manual is entitled Evaluation of LS-DYNA Concrete Material Model 159, FHWA-HRT-05-063. |
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17. Key Word concrete, LS-DYNA, material model, plasticity, damage, rate effects, reinforced beam |
18. Distribution Statement No restrictions. This document is available through the National Technical Information Service, Springfield, VA 22161. |
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19. Security Classif. (of this report) Unclassified |
20. Security Classif. (of this page) Unclassified |
21. No. of Pages 89 |
22. Price |
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
Chapter 2. Theoretical Manual
Critical Concrete Behaviors
Overview of Model Theory
Elastic Update
Plastic Update
Yield Surface
Damage Formulation
Rate Effects Formulation
Kinematic Hardening
Model Input
Bulk and Shear Moduli
Triaxial Compression Surface
Triaxial Extension and Torsion Surfaces
Cap Location, Shape, and Hardening Parameters
Damage Parameters
Strain Rate Parameters
Units
Chapter 3. Users Manual
LS-DYNA Input
Model Formulation and Input Parameters
Appendix A. Modeling Softening
Appendix C. Single Element Input File
Appendix D. CEB Specification for Rate Effects
Figure 1. Graph. Example concrete data from Mills and Zimmermann plotted in the meridian plane.(8)
Figure 3. Graph. Example plots of the failure surfaces of LS-DYNA Model 159 in the meridian plane
Figure 6. Graph. Variation of concrete softening response with confinement. Source: Joy and Moxley.(12)
Figure 15. Illustration. General shape of the concrete model yield surface in three dimensions
Figure 17. Equation. Stress invariant J 1, J′2, and J′3
Figure 18. Equation. Yield function f.
Figure 19. Equation. Shear failure surface function Ff.
Figure 20. Graph. Schematic of shear surface
Figure 21. Graph. Schematic of two-part cap function
Figure 22. Graph. Schematic of multiplicative formulation of the shear and cap surfaces
Figure 23. Equation. Cap failure surface function Fc
Figure 24. Equation. L of kappa
Figure 25. Equation. Simple cap failure surface function Fc
Figure 26. Equation. X as a function of kappa.
Figure 27. Equation. Plastic volume strain ε pv
Figure 29. Equation. Angle beta hat in the deviatoric plane
Figure 30. Equation. Relationship between beta hat and J hat
Figure 31. Equation. Rubin scaling function ℜ
Figure 32. Equation. Most general form for Q1 and Q2
Figure 33. Equation. Mohr-Coulomb form for Q1, Q2
Figure 34. Equation. Willam-Warnke form for Q1
Figure 35. Equation. Damaged stress σ dij
Figure 36. Graph. This cap model simulation demonstrates strain softening and modulus reduction
Figure 37. Equation. Brittle damage threshold τb
Figure 38. Equation. Ductile damage threshold τd
Figure 39. Equation. Viscoplastic damage threshold r0
Figure 40. Equation. Incremental damage threshold, small rn+1
Figure 41. Equation. Brittle damage small d of tau
Figure 42. Equation. Ductile damage small d of tau
Figure 43. Equation. Variation of dmax with stress invariant ratio
Figure 44. Equation. Variation of dmax with rate effects
Figure 45. Schematic representation of four stress paths and their stress invariant ratios
Figure 46. Equation. Reduction of A with confinement
Figure 47. Equation. Fracture energy integral for Gf
Figure 48. Equation. Brittle damage fracture energy Gf
Figure 49. Equation. Brittle damage threshold difference τ minus small r0b
Figure 50. Equation. Brittle softening parameter C
Figure 51. Equation. Ductile damage fracture energy Gf
Figure 52. Equation. Ductile damage threshold difference τ − r0d
Figure 53. Equation. Ductile softening parameter A
Figure 54. Equation. Brittle damage threshold Gf Brittle
Figure 55. Equation. Ductile damage threshold Gf Ductile
Figure 56. Equation. The fracture energy with rate effects, Gvpf
Figure 57. Equation. Default damage recovery of d of τt
Figure 58. Equation. Optional damage recovery of d of τt
Figure 59. Equation. Viscoplastic stress update for σvpij
Figure 60. Equation. Two-parameter η
Figure 61. Equation. Dynamic strengths, f ′T dynamic, and f ′C dynamic
Figure 62. Equation. Effective strain rate
Figure 63. Equation. Variation of fluidity parameter η in tension
Figure 64. Equation. Variation of fluidity parameter η in compression
Figure 65. Equation. Effective fluidity parameters, ηt, ηc, and η s
Figure 66. Equation. Overstress limit of η
Figure 67. Equation. Back stress α ij n + 1
Figure 68. Equation. Updated stress with hardening, σPij n+1
Figure 69. Equation. Incremental back stress, Δαij
Figure 70. Equation. Brittle rate of translation CH Brittle
Figure 71. Equation. Ductile rate of translation CH Ductile
Figure 72. Equation. The limiting function Gα.
Figure 73. Equation. Modified shear failure surface, Ff
Figure 74. Equation. Default Young's modulus E
Figure 75. Equation. Shear and bulk moduli, G and K
Figure 76. Equation. ACI Young's modulus, Ec
Figure 77. Equation. Reduced ACI Young's modulus, Ec
Figure 78. Equation. TXC Strength
Figure 79. Equation. Interpolation parameter P
Figure 80. Equation. Most general form for Q1, Q2
Figure 82. Equation. The default fracture energy GF
Figure 84. Illustration. General shape of the concrete model yield surface in two dimensions
Figure 85. Equation. Three stress invariants, J1, J′2, J′3
Figure 86. Equation. Plasticity yield function f
Figure 87. Equation. Shear surface function Ff
Figure 88. Equation. Most general form for scaling functions Q1, Q2
Figure 89. Equation. Cap surface function, Fc
Figure 90. Equation. Definition of L of kappa
Figure 91. Equation. Pressure invariant X as a function of kappa
Figure 92. Equation. Plastic volume strain hardening rule, ε pv
Figure 93. Equation. Transformation of viscoplastic stress to damaged stress, σdij.
Figure 94. Equation. Ductile damage accumulation, τ d
Figure 95. Equation. Brittle damage accumulation, τb
Figure 96. Equation. Brittle damage, d of tb
Figure 97. Equation. Ductile damage, d of τd
Figure 98. Equation. Reduction of A with confinement
Figure 99. Equation. Brittle and ductile damage thresholds, Gf
Figure 100. Equation. Viscoplastic stress, σvpij
Figure 101. Equation. Variation of the fluidity parameter η in tension and compression
Figure 102. Definition of effective strain rate
Figure 103. Equation. Overstress limit of η
Figure 104. Equation. Fracture energy with rate effects
Figure 108. Equation. Old generic damage, small d of τ
Figure 109. Equation. New generic damage, small d of τ
Figure 110. Graph. Behavior of the original softening function
Figure 111. Graph. Behavior of the updated softening function
Figure 114. Equation. CEB tensile strength dynamic increase factor, DIFten
Figure 115. Equation. CEB compressive strength dynamic increase factor, DIFcomp
Figure 116. Graph. Dynamic increase factors specified in CEB
Table 3. Approximate strength measurements used to set default TXC yield surface parameters.
Table 4. TXC yield surface input parameters as a function of unconfined compression strength.
Table 6. TOR yield surface input parameters as a function of unconfined compression strength.
Table 7. TXE yield surface input parameters as a function of unconfined compression strength.
Table 9. Coefficients for the fracture energy equation.
Table 10. Tensile fracture energies tabulated in CEB as a function of concrete strength.
Table 11. Example load curve for modeling rebar strain rate effects with LS-DYNA Material Model #24.
a a0 a1 a2 |
Rubin function internal parameters |
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A B C D |
softening parameters (compression and tension) |
AP BP CP |
quadratic equation coefficients |
b b0 b1 b2 |
Rubin function internal parameters |
Bs |
term used in one rate effects formula |
CH |
hardening rate parameter |
d d b d d |
scalar damage parameter (general, brittle, ductile) |
dm |
maximum of brittle and ductile scalar damage parameters |
dmax |
maximum damage allowed to accumulate |
D1 D2 |
cap linear and quadratic shape parameters |
E EcEs |
Young's modulus (general, concrete, steel) |
f |
yield surface function |
f* |
trial elastic yield surface function |
Ff |
shear failure surface |
Fc |
hardening cap surface |
G |
shear modulus |
Gα |
hardening model translational limit function for shear surface |
Gft Gfc Gfs |
fracture energies (tension, compression, shear) |
J1 |
first invariant of the stress tensor |
J ¢2 J ¢3 |
second and third invariants of the deviatoric stress tensor |
J1T J ¢2T J ¢3T |
trial elastic stress invariants |
J1P J ¢2P J ¢3P |
inviscid elastic stress invariants |
normalized invariant of the deviatoric stress tensor | |
K |
bulk modulus |
L |
element length |
NH |
hardening initiation |
nt nc |
rate effects fluidity parameters (tension, compression) |
Nt NC |
rate effects power parameters (tension and compression) |
P |
pressure |
Q1 Q2 |
Rubin scaling functions for torsion and triaxial extension |
ℜ |
Rubin strength reduction factor |
R |
cap aspect ratio |
rS |
initial damage before activation of rate effects |
r0 r0b r0d |
initial damage threshold (general, brittle, ductile) |
Sij |
deviatoric stress tensor |
W |
maximum plastic volume compaction |
x x0 |
instantaneous displacement and displacement at peak strength |
X X0 |
current cap location and initial cap location |
y |
integrand of dilogarithm function |
αij Δαij |
hardening model back stress and incremental back stress tensors |
β β1 α2 |
shear surface constant term (compression, torsion, extension) |
βs |
term used in one rate effects formula |
β β1 β2 |
shear surface exponent (compression, torsion, extension) |
angle in deviatoric plane (invariant) | |
plasticity consistency parameter | |
Δt |
time step increment |
εij Δ εij |
strain tensor and strain increments |
effective strain rate and effective strain rate increment | |
term used in one rate effects equation | |
εmax |
maximum principal strain |
εx εy εz εxy εyz εxz |
strain components |
εv |
volumetric strain |
ε pv |
plastic volumetric strain |
γ |
viscoplastic interpolation parameter |
γ s |
term used in one rate effects formula |
ηηt ηcηs |
rate effects fluidity parameters (general, tension, compression, shear) |
η0t nt |
rate effects input parameters in uniaxial tension stress |
η0c nc |
rate effects input parameters in uniaxial compressive stress |
κ κT κP κ0 |
cap hardening parameters (general, trial elastic, inviscid, initial) |
λ1 λ2 |
shear surface nonlinear term (compression, torsion, extension) |
η |
Poisson's ratio |
θ θ1 θ2 |
shear surface linear term (compression, torsion, extension) |
ρ ρc ρs |
density (general, concrete, steel) |
ρt ρc ρσ |
meridians (tensile, compressive, shear) |
σ σT |
a stress component (general, trail elastic) |
σ x σ r |
axial and radial stresses measured in triaxial compression tests |
σvp σd |
stress components calculated without and with damage |
stress tensors (viscoplastic, trial elastic, plastic) | |
σ 1 σ 2 σ 3 |
principal stress components |
τbτd |
instantaneous strain energy-type terms for damage accumulation |
ACI |
American Concrete Institute |
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CEB |
Comité Euro-Internacional du Béton |
CSCM |
continuous surface cap model |
DIF |
dynamic increase factor |
FIP |
Federation for Prestressing |
NCHRP |
National Cooperative Highway Research Program |
TOR |
torsion |
TXC |
triaxial compression |
TXE |
triaxial extension |
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FHWA-HRT-05-062