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Publication Number: FHWAHRT05062
Date: May 2007 

Users Manual for LSDYNA Concrete Material Model 159PDF Version (1.49 KB)
PDF files can be viewed with the Acrobat® Reader® ForewordThis report documents a concrete material model that has been implemented into the dynamic finite element code, LSDYNA, 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 performanceboth elastic deformation and failureof 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 LSDYNA 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 LSDYNA Concrete Material Model 159 (FHWAHRT05063), 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, LSDYNA. Michael Trentacoste Director, Office of Safety R&D 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. 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 highquality 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. Technical Report Documentation Page
Form DOT F 1700.7 (872) Reproduction of completed page authorized SI (Modern Metric) Conversion FactorsTable of ContentsChapter 2. Theoretical Manual Chapter 3. Users Manual Appendix A. Modeling Softening Appendix C. Single Element Input File Appendix D. CEB Specification for Rate Effects List of FiguresFigure 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 LSDYNA 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 F_{f}. Figure 20. Graph. Schematic of shear surface Figure 21. Graph. Schematic of twopart cap function Figure 22. Graph. Schematic of multiplicative formulation of the shear and cap surfaces Figure 23. Equation. Cap failure surface function F_{c} Figure 24. Equation. L of kappa Figure 25. Equation. Simple cap failure surface function F_{c} Figure 26. Equation. X as a function of kappa. Figure 27. Equation. Plastic volume strain ε ^{p}_{v} 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 Q_{1} and Q_{2} Figure 33. Equation. MohrCoulomb form for Q_{1}, Q_{2} Figure 34. Equation. WillamWarnke form for Q_{1} Figure 35. Equation. Damaged stress σ ^{d}_{ij} Figure 36. Graph. This cap model simulation demonstrates strain softening and modulus reduction Figure 37. Equation. Brittle damage threshold τ_{b} Figure 38. Equation. Ductile damage threshold τ_{d} Figure 39. Equation. Viscoplastic damage threshold r_{0} Figure 40. Equation. Incremental damage threshold, small r_{n+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 G_{f} Figure 48. Equation. Brittle damage fracture energy G_{f} Figure 49. Equation. Brittle damage threshold difference τ minus small r_{0b} Figure 50. Equation. Brittle softening parameter C Figure 51. Equation. Ductile damage fracture energy G_{f} Figure 52. Equation. Ductile damage threshold difference τ − r_{0d} Figure 53. Equation. Ductile softening parameter A Figure 54. Equation. Brittle damage threshold G_{f} ^{Brittle} Figure 55. Equation. Ductile damage threshold G_{f} ^{Ductile} Figure 56. Equation. The fracture energy with rate effects, G^{vp}_{f} Figure 57. Equation. Default damage recovery of d of τ_{t} Figure 58. Equation. Optional damage recovery of d of τ_{t} Figure 59. Equation. Viscoplastic stress update for σ^{vp}_{ij} Figure 60. Equation. Twoparameter 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, η_{t}, η_{c}, 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, σ^{P}_{ij} ^{n}^{+1} Figure 69. Equation. Incremental back stress, Δα_{ij} Figure 70. Equation. Brittle rate of translation C_{H} ^{Brittle} Figure 71. Equation. Ductile rate of translation C_{H} ^{Ductile} Figure 72. Equation. The limiting function G_{α.} Figure 73. Equation. Modified shear failure surface, F_{f} 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, E_{c} Figure 77. Equation. Reduced ACI Young's modulus, E_{c} Figure 78. Equation. TXC Strength Figure 79. Equation. Interpolation parameter P Figure 80. Equation. Most general form for Q_{1}, Q_{2} Figure 82. Equation. The default fracture energy G_{F} Figure 84. Illustration. General shape of the concrete model yield surface in two dimensions Figure 85. Equation. Three stress invariants, J_{1}, J′_{2}, J′_{3} Figure 86. Equation. Plasticity yield function f Figure 87. Equation. Shear surface function F_{f} Figure 88. Equation. Most general form for scaling functions Q_{1}, Q_{2} Figure 89. Equation. Cap surface function, F_{c} 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 ^{p}_{v} Figure 93. Equation. Transformation of viscoplastic stress to damaged stress, σ^{d}_{ij.} Figure 94. Equation. Ductile damage accumulation, τ _{d} Figure 95. Equation. Brittle damage accumulation, τ_{b} Figure 96. Equation. Brittle damage, d of t_{b} Figure 97. Equation. Ductile damage, d of τ_{d} Figure 98. Equation. Reduction of A with confinement Figure 99. Equation. Brittle and ductile damage thresholds, G_{f} Figure 100. Equation. Viscoplastic stress, σ^{vp}_{ij} 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, DIF_{ten} Figure 115. Equation. CEB compressive strength dynamic increase factor, DIF_{comp} Figure 116. Graph. Dynamic increase factors specified in CEB List of TablesTable 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 LSDYNA Material Model #24.
