Fresh concrete consists of cement, water, aggregates, admixtures and maybe more additives. In the fresh state, concrete behaves like a fluid when it is vibrated, or like a cohesive soil when it is at rest. However, this state is only relevant during construction and not the topic of this chapter.


Compressive Strength Stress Intensity Factor Material Modelling Fracture Energy Failure Surface 
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  1. [1.1]
    Frenaij, J.W.: Time-dependent shear transfer in cracked reinforced concrete. Doctoral Thesis, Delft University of Technology, Delft 1989.Google Scholar
  2. [1.2]
    Gambarova, P.G. and M. DiPrisco: Interface Behaviour, in: CEB Bulletin No. 210, Lausanne 1991.Google Scholar
  3. [1.3]
    Kupfer, H., H. K. Hilsdorf, and H. Rüsch: Behavior of concrete under biaxial stresses, ACI Journal, August 1969, 656 – 666.Google Scholar
  4. [1.4]
    Schickert, G. and J. Danssmann: Behavior of concrete stressed by high hydrostatic compression, Int. Conf. on Concrete under Multiaxial Conditions, Toulouse, May 22 – 24, 1984.Google Scholar
  5. [1.5]
    Balaguru, P. N. and S. P. Shah: Fiber-Reinforced Cement Composites, McGraw-Hill Book Co., New York 1992.Google Scholar
  6. [1.6]
    Neville, A. M.: Properties of Concrete, 3rd Ed., Longman Scientific and Technical, 1987.Google Scholar
  7. [1.7]
    Sinha, B. P., K. H. Gerstle, and L. G. Tulin: Stress-strain relations for concrete under cyclic loadings, ACI Journal, February 1964.Google Scholar
  8. [1.8]
    Bennet, E. W. and N. K. Raju: Cumulative fatigue damage of plain concrete in compression, Structures Solid Mech. and Engin. Design (1971), 1089 – 1102.Google Scholar
  9. [1.9]
    Paskova, T.: Low-Cycle Fatigue Behavior of Concrete With and Without Fiber Reinforcement, Ph. D. Dissertation, Columbia University, New York 1994.Google Scholar
  10. [1.10]
    Meyer, C.: An Energy-Based Damage Model for Inelastic Dynamic Analysis of Reinforced Concrete Frames, in: Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings, (Eds. P. Fajfar and H. Krawinkler ), Elsevier Applied Science, London 1992.Google Scholar
  11. [1.11]
    Su, E. C. M. and T. C. Hsu: Biaxial compression fatigue and discontinuity of concrete, ACI Materials Journal, May-June 1988.Google Scholar
  12. [1.12]
    Stankowski, T. and K. H. Gerstle: Simple formulation of concrete behavior under multiaxial load histories, ACI Journal, Mar-Apr 1985.Google Scholar
  13. [1.13]
    Nilson, A. H. (Ed.): Finite Element Analysis of Reinforced Concrete, Special Publication, ASCE, New York 1982.Google Scholar
  14. [1.14]
    Meyer, C. and H. Okamura (Eds.): Finite Element Analysis of Reinforced Concrete Structures, Special Publication, ASCE, New York 1986.Google Scholar
  15. [1.15]
    Isenberg, J. (Ed.): Finite Element Analysis of Reinforced Concrete II, Special Publication, ASCE, New York 1993.Google Scholar
  16. [1.16]
    Darwin, D. and D. A. Pecknold: Analysis of RC shear panels under cyclic loading, ASCE J. Struct. Div., February 1976.Google Scholar
  17. [1.17]
    Bazant Z. P. and T. Tsubaki: Total strain theory and path-dependence of concrete, ASCE J. Eng. Mech. Div., Dec. 1980.Google Scholar
  18. [1.18]
    Elwi, A. A. and D. W. Murray: A 3D hypoelastic concrete constitutive relationship, ASCE J. Eng. Mech. Div., Aug. 1979.Google Scholar
  19. [1.19]
    de Borst, R.: Non-Linear Analysis of Frictional Materials, Ph. D. Dissertation, Delft University of Technology, Delft, The Netherlands, 1986.Google Scholar
  20. [1.20]
    Bazant, Z. P. and S. S. Kim: Plastic-fracturing theory for concrete, ASCE J. Eng. Mech. Div., June 1979.Google Scholar
  21. [1.21]
    Valanis, K. C.: A Theory of viscoplasticity without a yield surface, Archiwum Mechaniki Stossovaneij (Archives of Mechanics, Warsaw) 23 (1971), 517 – 551.MathSciNetMATHGoogle Scholar
  22. [1.22]
    Bazant, Z. P. and P. Bhat: Endochronic theory of inelasticity and failure of concrete, ASCE J. Eng. Mech. Div., 1976, 701 – 722.Google Scholar
  23. [1.23]
    Bazant, Z. P., ed.: Fracture Mechanics of Concrete Structures, Elsevier Applied Science, London and New York 1992.Google Scholar
  24. [1.24]
    Wittmann, F. H.: Fracture Mechanics of Concrete, Elsevier Applied Science, 1983.Google Scholar
  25. [1.25]
    Carpinteri, A. and A. R. Ingraffea: Fracture Mechanics of Concrete, Martinus Nijhoff Publishers, 1984.Google Scholar
  26. [1.26]
    Perzyna, P.: Fundamental problems in viscoplasticity, Advances in Applied Mechanics 9, 1966, 243 – 377.CrossRefGoogle Scholar
  27. [1.27]
    Nilsson, L.: Finite element analysis of impact on concrete structures, in: Finite Elements in Nonlinear Mechanics, (Eds. P. Bergan et al ), Tapir, Trondheim 1978.Google Scholar
  28. [1.28]
    Nilsson, L. and R. Glemberg: A constitutive model for concrete in high rate of loading conditions, Proc., IABSE Colloquium, Delft (1981), 159 – 174.Google Scholar
  29. [1.29]
    Bicanic, N.: Nonlinear Finite Element Transient Analysis of Concrete Structures, Ph. D. Thesis, C/Ph/50/78, University College of Swansea, Wales, 1978.Google Scholar
  30. [1.30]
    Bicanic, N. and O. C. Zienkiewicz: Constitutive model for concrete under dynamic loading, Earthquake Engineering and Structural Dynamics 11 (1983), 689 – 711.CrossRefGoogle Scholar
  31. [1.31]
    Meyer, C. and H. E. Delgado-Saavedra: Modeling large inelastic cyclic response of concrete, in: Finite Element Analysis of Reinforced Concrete Structures, (Eds. C. Meyer and H. Okamura ), Special Publication, ASCE, 1986.Google Scholar
  32. [1.32]
    Willam, K. J. and E. P. Warnke: Constitutive model for triaxial behavior of concrete, Proc., IABSE Seminar on Concrete Structures Subjected to Triaxial Stresses, Paper III-1, Bergamo, Italy, 1974.Google Scholar
  33. [1.33]
    Hatano, T. and H. Tsutsumi: Dynamical compressive deformation and failure of concrete under dynamic load, Proc., Second World Conference on Earthquake Engineering, Tokyo, Vol. 3, 1960, 1963 – 1978.Google Scholar
  34. [1.34]
    Kachanov, L. M.: Time of rupture process under creep conditions, Izvestia Akademii Nauk USSR 8 (1958), 26 – 31 (in Russia).Google Scholar
  35. [1.35]
    Rabotnov, Y. N.: Creep rupture, Proc., XII Int. Congress of Applied Mechanics, Stanford University, Springer Verlag, 1968.Google Scholar
  36. [1.36]
    Lemaitre, J.: A Course on Damage Mechanics, Springer Verlag, Berlin 1992.CrossRefMATHGoogle Scholar
  37. [1.37]
    Mazars, J.: Application de la mecanique de l’endommangement au comportement non lineaire et a la rupture du beton de structure, These de Doctorate d’Etat, L. M. T., Universite Paris, France, 1984.Google Scholar
  38. [1.38]
    Pijaudier-Cabot, G.: Caracterisation et modelisation du comportement du beton par un essai multiaxial au tomatique, These de 3eme cycle, L. M. T., Universite Paris, France, 1985.Google Scholar
  39. [1.39]
    Simo, J. C. and J. W. Ju: Strain-and stress-based continuum damage models — I. Formulation, I.t. J. Solids and Structures 23, no. 7 (1987), 821 – 840.CrossRefMATHGoogle Scholar
  40. [1.40]
    Suaris, W. and S.P. Shah: Inertial effects in instrumented impact testing of cementitious composites, ASTM J. Cement, Concrete and Aggregates 3, no. 2, (1981), 77 – 83.CrossRefGoogle Scholar
  41. [1.41]
    Gopalaratnam, V.S., S.P. Shah, R. John: A modified instrumented Charpy test for cement-based composites. Experimental Mechanics 24, no. 3, (1984), 102–111.Google Scholar
  42. [1.42]
    Suaris, W. and S.P. Shah: Properties of concrete subjected to impact, ASCE J. Struct. Eng. 109, no. 7 (1983), 1727 – 1741.CrossRefGoogle Scholar
  43. [1.43]
    Kobayashi, A.S., N.M. Hawkins, J.J. Du: An impact damage model of concrete. University of Washington, Seattle (1989).Google Scholar
  44. [1.44]
    Bentur, A., S. Mindess, N. Banthia: The behaviour of concrete under impact loading: Experimental procedures and method of analysis, Materials and Structures 19, no, 113 (1986), 371 – 378.CrossRefGoogle Scholar
  45. [1.45]
    Yon, J.H., N.M. Hawkins, A.S. Kobayashi: On the strain rate sensitivity of concrete mechanical properties. University of Washington, Seattle, paper (5–1589) (1989).Google Scholar
  46. [1.46]
    Hughes, G. and A.W. Beeby: Investigation of the effect of impact loading on concrete beams, The Structural Engineer 60 B, no. 3 (1982), 45 – 52.Google Scholar
  47. [1.47]
    van Mier, J.M., A.F. Pruijssers, H.W. Reinhardt, T. Monnier: Load-time response of colliding concrete bodies, ASCE J. Struct. Eng. 117, no. 2 (1991), 354 – 374.CrossRefGoogle Scholar
  48. [1.48]
    Rossi, P. and F. Le Maour: Ouvrages d’art: le contrôle des fissurations. La Revue des Laboratoires d’essais, no. 6, (1986), 25 – 27.Google Scholar
  49. [1.49]
    Rossi, P.: Fissuration du béton: Du materiau à la structure. Application de la méchanique linéaire de la rupture. Doctoral thesis ENPC, Paris, Dec. 1986.Google Scholar
  50. [1.50]
    Mindess, S., N.P. Banthia, A. Ritter, J.P. Skalny: Crack developments in cementitious materials under impact loading, in: MRS Symp. Proc. Voc., (Eds. S. Mindess and S.P. Shah), 64, Pittsburgh, PA 1986, 217 – 233.Google Scholar
  51. [1.51]
    Reinhardt, H.W., H.A. Körmeling, A.J. Zielinski: The split Hopkinson bar, a versatile tool for the impact testing of concrete, Materials and Structures 19, no. 109 (1986), 55 – 63.CrossRefGoogle Scholar
  52. [1.52]
    John, R. and S.P. Shah: Fracture of concrete subjected to impact loading, ASTM Cement, Concrete and Aggregates 8 (1986), 24 – 32.CrossRefGoogle Scholar
  53. [1.53]
    Bur, A.J. and S.C. Roth: A polymer pressure gage for dynamic pressure measurements. Proc. 2nd Symp. Interaction of non-nuclear munitions with structures. Panama City Beach, Florida, April 1985, 291 – 295.Google Scholar
  54. [1.54]
    Frank, T.: Beeinflussung der Prüfergebnisse durch die Messeinrichtung bei der Stossbeanspruchung von Beton. Materialprüfung 26, no. 4 (1984), 96 – 100.Google Scholar
  55. [1.55]
    Curbach, M., P. Maliszkiewicz, J. Eibl: Acoustic emission measurement of concrete under high loading rates. Transactions of the 10th International Conference on Structural Mechanics in Reactor Technology SMiRT, 1989.Google Scholar
  56. [1.56]
    Diederichs, U., U. Schneider, M. Terrien: Formation and propagation of cracks and acoustic emission, in: Fracture Mechanics of Concrete, (Ed. F.H. Wittmann ), Elsevier, Amsterdam 1983.Google Scholar
  57. [1.57]
    Hillerborg, A.: Stability problems in fracture mechanics testing, in: Fracture of Concrete and Rock: Recent Developments, (Eds. S.P. Shah, S.E. Swartz, B. Barr ). Elsevier Appl. Sci. London, New York 1989, 369 – 378.Google Scholar
  58. [1.58]
    Zukas, J.A. et al.: Impact Dynamics, John Wiley & Sons, New York 1982.Google Scholar
  59. [1.59]
    Paulmann, K. and J. Steinert: Beton bei sehr kurzer Belastungsgeschichte, Beton 32, no. 6 (1982), 225 – 228.Google Scholar
  60. [1.60]
    Takeda, J.: A loading apparatus for high speed testing of building materials and structures, Proc. 2nd Japan Congress on Testing Materials, Jap. Soc. Testing Mat., Kyoto, Japan (1959), 236 – 238.Google Scholar
  61. [1.61]
    Zhurkov, S.N.: Kinetic concept of the strength of solids, Int. J. Fracture Mechanics 1 (1965), 311 – 323.Google Scholar
  62. [1.62]
    Gran, J.K.: A new technique for studying the dynamic tensile response of concrete, Proc. 2nd Symp. Interaction of non-neclear munitions with structures, Panama City Beach, Florida (1986), 206 – 210.Google Scholar
  63. [1.63]
    Brühwiler, E. and F.H. Wittmann: Effect of rate of loading on fracture energy and strain softening, Contribution to RILEM Committee 89–FMT, Stevin report no. 25–87–16 ( 1987 ), Delft University of Technology, April 1987.Google Scholar
  64. [1.64]
    Lieberum, K.H. and H.W. Reinhardt: Strength of concrete on an extremely small bearing area, ACI Structural Journal 86, no. 1 (1989), 67 – 76.Google Scholar
  65. [1.65]
    Kennedy, R.P.: A review of procedures for the analysis and design of concrete structures to resist missile impact effects, Nuclear Eng. Design 37 (1976), 183–203.CrossRefGoogle Scholar
  66. [1.66]
    Barr, P.: Guidelines for the design and assessment of concrete structures subjected to impact, Safety and Reliability Directorate, SRD R439, Issue 2, UKAEA, Calcheth, March 1988.Google Scholar
  67. [1.67]
    Mahin, S. and P.B. Shing: Pseudodynamic method of seismic testing, ASCE J. Struct. Eng. 111, no. 7 (1985), 1482 – 1503.CrossRefGoogle Scholar
  68. [1.68]
    Block, K.: Der harte Querstoss — Impact — auf Balken aus Stahl, Holz und Stahlbeton. Dissertation, Universtität Dortmund, 1983.Google Scholar
  69. [1.69]
    Reinhardt, H.W.: Simple relations for the strain rate influence on concrete, Darmstadt Concrete 2 (1987), 203 – 211.Google Scholar
  70. [1.70]
    Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. Edward Arnold Publishers Ltd., London, U.K. 1960.MATHGoogle Scholar
  71. [1.71]
    Hughes, G. and D.M. Speirs: An investigation of the beam impact problem, Technical Report 546 (1982), Cement and Concrete Assoc.Google Scholar
  72. [1.72]
    Jensen, J.J. and K. Hoiseth: Impact of dropped objects on lightweight concrete, Nordic Concr. Res., 2 (1983), 102 – 113.Google Scholar
  73. [1.73]
    Pruijssers, A.F., J.G.M. van Mier, A. Mol. Impact behaviour of concrete breakwater elements, TUD/TNO Research Report (1987), Delft, The Netherlands.Google Scholar
  74. [1.74]
    Sih, G.C. ed.: Dynamic Crack Propagation, Noorhoff Intern. Publ., Leyden 1972.Google Scholar
  75. [1.75]
    Freund, L.B.: Crack propagation in an elastic solid subjected to general loading — I. Constant rate of extension. J. Mech. Phys. Solids 20 (1972), 129 – 140.MathSciNetCrossRefMATHGoogle Scholar
  76. [1.76]
    Kipp, M.E., D.E. Grady, E.P. Chen: Strain-rate dependent fracture initiation. Int. J. Fracture 16 (1980), 471 – 478.CrossRefGoogle Scholar
  77. [1.77]
    Weerheijin, J.: Concrete under impact tensile loading and latual compression. Doctoral Thesis, Delft University of Technology, Delft 1992.Google Scholar
  78. [1.78]
    Mihashi, H. and F.H. Wittmann: Stochastic approach to study the influence of rate of loading on strength of concrete. Heron 25, no. 3, Delft, The Netherlands 1980.Google Scholar
  79. [1.79]
    Lindholm, U.S., L.M. Yeakley, A. Nagy: The dynamic strength and fracture properties of Dresser basalt, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 11 (1974), 181 – 191.CrossRefGoogle Scholar
  80. [1.80]
    Krausz, A.S. and H. Eyring: Deformation Kinetics, J. Wiley & Sons, New York 1975.Google Scholar
  81. [1.81]
    Körmeling, H.A.: Impact of steel fibre concrete at −170°C, Stevin Report 5–8413, Delft University of Technology, Delft, December 1984.Google Scholar
  82. [1.82]
    Shah, S.P.: Constitutive relations of concrete subjected to a varying strain rate. Symp. Proc. The interaction of non-nuclear munitions with structures. US Air Force Academy, Colorado, May 10–13, 1983, 81 – 84.Google Scholar
  83. [1.83]
    Curbach, M.: Festigkeitssteigerung von Beton bei hohen Belastungsgeschwindigkeiten. Schriftenreihe des Instituts fur Massivbau und Baustofftechnologie, Heft 1, Karlsruhe 1987.Google Scholar
  84. [1.84]
    Zielinski, A.J. and H.W. Reinhardt: Stress-strain behaviour of concrete and mortar at high rates of tensile loading, Cement and Concrete Research 12, (1981), 309 – 319.CrossRefGoogle Scholar
  85. [1.85]
    Brühwiler, E.: Versuche über den Einfluss von Druckvorlasten auf das Verhalten von Staumauerbeton unter Zug bei hohen Dehngeschwindigkeiten. Ecole Polytechnique Fédérale de Lausanne, Lab. des Matériaux de construction, Dec. 1987.Google Scholar
  86. [1.86]
    Shah, S.P. and R. John: Rate-sensitivity of mode I and mode II fracture of concrete, Mat. Res. Soc. Symp. Proc. Vol. 64, Eds. S. Mindess and S.P. Shah, Pittsburgh, 1986, 21 – 37.Google Scholar
  87. [1.87]
    Muria Vila, D. and P. Hamelin: Comportement au choc des bétons et mortiers à matrices hydrauliques, in: Combining materials: Design, production and properties, (Ed. J.C. Maso), 1st Int. RILEM Congress Vol. 2, Chapman and Hall, London New York 1987, 725 – 732.Google Scholar
  88. [1.88]
    Carrasquillo, R.L., A.H. Nilson, and F.O. Slate: Properties of high-strength concrete subject to short-term loads, ACI Journal, May-June 1981.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • H. W. Reinhardt
    • 1
  • C. Meyer
    • 2
  1. 1.University of StuttgartStuttgartGermany
  2. 2.Columbia UniversityNew YorkUSA

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