Computers and Concrete

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Multi-cracking modelling in concrete solved by a modified DR method

  • Yu, Rena C. (ETSI de Caminos, C. y P., Universidad de Castilla-La Mancha) ;
  • Ruiz, Gonzalo (ETSI de Caminos, C. y P., Universidad de Castilla-La Mancha)
  • Received : 2004.05.19
  • Accepted : 2004.09.13
  • Published : 2004.11.25
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Abstract

Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.

Keywords

References

  1. Bazant, Z. P. and Planas, J. (1998), Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton, Florida.
  2. Brew, J. and Brotton, D. M. (1971), "Non-linear structural analysis by dynamic relaxation", Int. J. Num. Meth. Eng., 3, 436-483.
  3. Camacho, G. T. and Ortiz, M. (1996), "Computational modelling of impact damage in brittle materials", Int. J. Solids Structs., 33(20-22), 2899-2938. https://doi.org/10.1016/0020-7683(95)00255-3
  4. Chen, B. K., Choi, S. K. and Thomson, P. F. (1989), "Analysis of plane strain rolling by the dynamic relaxation method", Int. J. Mech. Sci., 31(11/12), 839-851. https://doi.org/10.1016/0020-7403(89)90028-3
  5. Comite Euro-International du Beton (CEB) and the Federation Internationale de la Precont (FIP) (1993), CEBFIP
  6. Model Code 1990, Thomas Telford Ltd, London, UK.
  7. Cook, R. D., Malkus, D. S. and Plesha, M. E. (1989), Concepts and Applications of Finite Element Analysis, third edition, John Wiley & Sons, Inc., New York.
  8. Day, A. (1965), "An introduction to dynamic relaxation", The Engineer, 219, 218-221.
  9. De Andres, A., P'erez, J. L. and Ortiz, M. (1999), "Elastoplastic finite-element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading", Int. J. Solids Structs., 36(15), 2231-2258. https://doi.org/10.1016/S0020-7683(98)00059-6
  10. Metzger, D. (2003), "Adaptive damping for dynamic relaxation problems with non-monotonic spectral response", Int. J. Num. Meth. Eng., 56, 57-80. https://doi.org/10.1002/nme.555
  11. Metzger, D. R. and Sauve, R. G. (1997), "The effect of discretization and boundary conditions on the convergence rate of the dynamic relaxation method", Current Topics in the Design and Analysis of Pressure Vessels and Piping, ASME PVP 354, 105-110.
  12. Oakley, D. R. and Knight, N. F. J. (1995a), "Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures. Part I. formulation", Comput. Meth. Appl. Mech. Eng., 126, 67-89. https://doi.org/10.1016/0045-7825(95)00805-B
  13. Oakley, D. R. and Knight, N. F. J. (1995b), "Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures. part ii. single processor implementation", Comput. Meth. Appl. Mech. Eng., 126, 91-109. https://doi.org/10.1016/0045-7825(95)00806-C
  14. Oakley, D. R. and Knight, N. F. J. (1995c), "Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures. part iii. parallel implementation", Comput. Meth. Appl. Mech. Eng., 126, 111-129. https://doi.org/10.1016/0045-7825(95)00807-D
  15. Oakley, D. R. and Knight, N. F. J. (1996), "Non-linear structural response using adaptive dynamic relaxation on a massively parallel processor system", Int. J. Num. Meth. Eng., 39, 235-259. https://doi.org/10.1002/(SICI)1097-0207(19960130)39:2<235::AID-NME855>3.0.CO;2-W
  16. Ortiz, M. and Pandolfi, A. (1999), "Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis", Int. J. Num. Meth. Eng., 44, 1267-1282. https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
  17. Otter, J. (1965), "Computations for prestressed concrete reactor pressure vessels using dynamic relaxation", Nucl. Struct. Eng., 1, 61-75. https://doi.org/10.1016/0369-5816(65)90097-9
  18. Pandolfi, A., Krysl, P. and Ortiz, M. (1999), "Finite element simulation of ring expansion and fragmentation", Int. J. Fract., 95, 279-297. https://doi.org/10.1023/A:1018672922734
  19. Pandolfi, A. and Ortiz, M. (1998), "Solid modeling aspects of three-dimensional fragmentation", Eng. Comput, 14(4), 287-308. https://doi.org/10.1007/BF01201761
  20. Pandolfi, A. and Ortiz, M. (2002), "An efficient adaptive procedure for three-dimensional fragmentation simulations", Eng. Comput, 18(2), 148-159. https://doi.org/10.1007/s003660200013
  21. Papadrakakis, M. (1981), "A method for automated evaluation of the dynamic relaxation parameters", Comput. Meth. Appl. Mech. Eng., 25, 35-48. https://doi.org/10.1016/0045-7825(81)90066-9
  22. Pica, A. and Hinton, E. (1980), "Transient and pseudo-transient analysis of mindlin plates", Int. J. Num. Meth. Eng., 15, 189-208. https://doi.org/10.1002/nme.1620150204
  23. Rericha, P. (1986), "Optimum load time history for non-linear analysis using dynamic relaxation", Int. J. Num. Meth. Eng., 23, 2313-2324. https://doi.org/10.1002/nme.1620231212
  24. Ruiz, G., Elices, M. and Planas, J. (1999), "Size effect and bond-slip dependence of lightly reinforced concrete beams", Minimum Reinforcement in Concrete Beams, ESIS Publications 24, 67-98. https://doi.org/10.1016/S1566-1369(99)80062-4
  25. Ruiz, G., Ortiz, M. and Pandolfi, A. (2000), "Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders", Int. J. Num. Meth. Eng., 48, 963-994. https://doi.org/10.1002/(SICI)1097-0207(20000710)48:7<963::AID-NME908>3.0.CO;2-X
  26. Ruiz, G., Pandolfi, A. and Ortiz, M. (2001), "Three-dimensional cohesive modeling of dynamic mixed-mode fracture", Int. J. Num. Meth. Eng., 52, 97-120. https://doi.org/10.1002/nme.273
  27. Sauve, R. G. and Badie, N. (1993), "Nonlinear shell formulation for reactor fuel channel creep", Design Analysis, Robust Methods and Stress Classification, ASME PVP 265, 269-275.
  28. Sauve, R. G. and Metzger, D. (1995), "Advances in dynamic relaxation techniques for nonlinear finite element analysis", Trans. ASME 117, 170-176.
  29. Sauve, R. G. and Metzger, D. (1996), "A hybrid explicit solution technique for quasi-static transients", Computer Technology: Applications and Methodology, ASME PVP 326, 151-157.
  30. Siddiquee, M., Tanaka, T. and Tatsouka, F. (1995), "Tracing the equilibrium path by dynamic relaxation in materially nonlinear finite element problems", Int. J. Num. Anal. Meth. Geomech., 19, 749-767. https://doi.org/10.1002/nag.1610191102
  31. Thoutireddy, P., Molinari, J. F., Repetto, E. A. and Ortiz, M. (2002), "Tetrahedral composites finite elements", Int. J. Num. Meth. Eng., 53, 1337-1351. https://doi.org/10.1002/nme.337
  32. Underwood, P. (1983), "Dynamic relaxation", Comput. Meth. Trans. Anal., 1, 145-265.
  33. Yu, R. C., Pandolfi, A., Coker, D., Ortiz, M. and Rosakis, A. J. (2002), "Three-dimensional modeling of intersonic shear-crack growth in asymmetrically-loaded unidirectional composite plates", Int. J. Solids Structs., 39(25), 6135-6157. https://doi.org/10.1016/S0020-7683(02)00466-3
  34. Yu, R. C., Ruiz, G. and Pandolfi, A. (2004), "Numerical investigation on the dynamic behavior of advanced ceramics", Eng. Fract. Mech., 71, 897-911. https://doi.org/10.1016/S0013-7944(03)00016-X
  35. Zhang, L. G. and Yu, T. X. (1989), "Modified adaptive dynamic relaxation method and its application to elasticplastic bending and wrinkling of circular plates", Comput. Struct., 33(2), 839-851. https://doi.org/10.1016/0045-7949(89)90258-7

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