Computers and Concrete

  • 제23권3호
  • /
  • Pages.171-188
  • /
  • 2019
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Isogeometric analysis of gradient-enhanced damaged plasticity model for concrete

  • Xu, Jun (Department of Bridge Engineering, Tongji University) ;
  • Yuan, Shuai (Department of Bridge Engineering, Tongji University) ;
  • Chen, Weizhen (Department of Bridge Engineering, Tongji University)
  • 투고 : 2018.10.14
  • 심사 : 2019.03.05
  • 발행 : 2019.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study proposed a new and efficient 2D damage-plasticity model within the framework of Isogeometric analysis (IGA) for the geometrically nonlinear damage analysis of concrete. Since concrete exhibits complicated material properties, two internal variables are introduced to measure the hardening/softening behavior of concrete in tension and compression, and an implicit gradient-enhanced formulation is adopted to restore the well-posedness of the boundary value problem. The numerical results calculated by the model is compared with the experimental data of three benchmark problems of plain concrete (three-point and four-point bending single-notched beams and four-point bending double-notched beam) to illustrate the geometrical flexibility, accuracy, and robustness of the proposed approach. In addition, the influence of the characteristic length on the numerical results of each problem is investigated.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Chinese Scholarship Council

참고문헌

  1. Aifantis, E.C. (1984), "On the microstructural origin of certain inelastic models", J. Eng. Mater. Technol., 106(4), 326-330. https://doi.org/10.1115/1.3225725
  2. Al-Rub, R.K.A. and Voyiadjis, G.Z. (2009), "Gradient-enhanced coupled plasticity-anisotropic damage model for concrete fracture: computational aspects and applications", Int. J. Damage Mech., 18(2), 115-154. https://doi.org/10.1177/1056789508097541
  3. Anitescu, C., Jia, Y., Zhang, Y.J. and Rabczuk, T. (2015), "An isogeometric collocation method using superconvergent points", Comput. Meth. Appl. Mech. Eng., 284, 1073-1097. https://doi.org/10.1016/j.cma.2014.11.038
  4. Areias, P., Msekh, M.A. and Rabczuk, T. (2016a), "Damage and fracture algorithm using the screened Poisson equation and local remeshing", Eng. Fract. Mech., 158, 116-143. https://doi.org/10.1016/j.engfracmech.2015.10.042
  5. Areias, P., Rabczuk, T. and Camanho, P.P. (2013a), "Initially rigid cohesive laws and fracture based on edge rotations", Comput. Mech., 52(4), 931-947. https://doi.org/10.1007/s00466-013-0855-6
  6. Areias, P., Rabczuk, T. and Camanho, P.P. (2014), "Finite strain fracture of 2D problems with injected anisotropic softening elements", Theor. Appl. Fract. Mech., 72, 50-63. https://doi.org/10.1016/j.tafmec.2014.06.006
  7. Areias, P., Rabczuk, T. and Dias-Da-Costa, D. (2013b), "Elementwise fracture algorithm based on rotation of edges", Eng. Fract. Mech., 110(3), 113-137. https://doi.org/10.1016/j.engfracmech.2013.06.006
  8. Areias, P., Rabczuk, T. and Sa, J.C.D. (2016b), "A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement", Comput. Mech., 1-16.
  9. Areias, P., Reinoso, J., Camanho, P. and Rabczuk, T. (2015), "A constitutive-based element-by-element crack propagation algorithm with local mesh refinement", Comput. Mech., 56(2), 1-25. https://doi.org/10.1007/s00466-015-1150-5
  10. Arrea, M. and Ingraffea, A.R. (1982), "Mixed-mode crack propagation in mortar and concrete", Department of Structural Engineering, Cornell University, Ithaca, NY.
  11. Bazant, Z.P. (1991), "Why continuum damage is nonlocal: micromechanics arguments", J. Eng. Mech., 117(5), 1070-1087. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:5(1070)
  12. Bazant, Z.P. and Jirasek, M. (2002), "Nonlocal integral formulations of plasticity and damage: survey of progress", J. Eng. Mech., 128(11), 1119-1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)
  13. Bazant, Z.P. and Pijaudier-Cabot, G. (1988), "Nonlocal continuum damage, localization instability and convergence", J. Appl. Mech., 55(2), 287-293. https://doi.org/10.1115/1.3173674
  14. Bazant, Z.P. and Pijaudier-Cabot, G. (1989), "Measurement of characteristic length of nonlocal continuum", J. Eng. Mech., 115(4), 755-767. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:4(755)
  15. Bazant, Z.P., Belytschko, T.B. and Chang, T.P. (1984), "Continuum theory for strain-softening", J. Eng. Mech., 110(12), 1666-1692. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1666)
  16. Bazilevs, Y., Calo, V.M., Hughes, T.J.R. and Zhang, Y. (2008), "Isogeometric fluid-structure interaction: theory, algorithms, and computations", Comput. Mech., 43(1), 3-37. https://doi.org/10.1007/s00466-008-0315-x
  17. Bocca, P., Carpinteri, A. and Valente, S. (1990), "Size effects in the mixed mode crack propagation: softening and snap-back analysis", Eng. Fract. Mech., 35(1-3), 159-170. https://doi.org/10.1016/0013-7944(90)90193-K
  18. Borden, M.J., Hughes, T.J.R., Landis, C.M. and Verhoosel, C.V. (2014), "A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework", Comput. Meth. Appl. Mech. Eng., 273(5), 100-118. https://doi.org/10.1016/j.cma.2014.01.016
  19. Bui, T.Q., Hirose, S., Zhang, C., Rabczuk, T., Wu, C.T., Saitoh, T. and Lei, J. (2016), "Extended isogeometric analysis for dynamic fracture in multiphase piezoelectric/piezomagnetic composites", Mech. Mater., 97, 135-163. https://doi.org/10.1016/j.mechmat.2016.03.001
  20. Chen, A.C.T. and Chen, W.F. (1975), "Constitutive relations for concrete", J. Eng. Mech., 101, Proc. Paper 11529.
  21. Cottrell, J.A., Reali, A., Bazilevs, Y. and Hughes, T.J.R. (2006), "Isogeometric analysis of structural vibrations", Comput. Meth. Appl. Mech. Eng., 195(41-43), 5257-5296. https://doi.org/10.1016/j.cma.2005.09.027
  22. Darwin, D. and Pecknold, D.A. (1977), "Nonlinear biaxial stressstrain law for concrete", J. Eng. Mech., 103(EM2), 12839.
  23. de Borst, R. and Pamin, J. (1996), "Some novel developments in finite element procedures for gradient-dependent plasticity", Int. J. Numer. Meth. Eng., 39(14), 2477-2505. https://doi.org/10.1002/(SICI)1097-0207(19960730)39:14<2477::AID-NME962>3.0.CO;2-E
  24. de Borst, R., Benallal, A. and Heeres, O.M. (1996), "A gradientenhanced damage approach to fracture", Le Journal de Physique IV, 06(C6), 491-502.
  25. de Borst, R., Hughes, T.J.R., Scott, M.A. and Verhoosel, C.V. (2011), "Isogeometric failure analysis", Multiscale and Multiphysics Processes in Geomechanics, Springer, 113-116.
  26. Dorgan, R.J. and Voyiadjis, G.Z. (2006), "A mixed finite element implementation of a gradient-enhanced coupled damageplasticity model", Int. J. Damage Mech., 15(3), 201-235. https://doi.org/10.1177/1056789506060740
  27. Elwi, A.A. and Murray, D.W. (1979), "A 3D hypoelastic concrete constitutive relationship", J. Eng. Mech. Div., 105(4), 623-641. https://doi.org/10.1061/JMCEA3.0002510
  28. Engelen, R.A.B., Geers, M.G.D. and Baaijens, F.P.T. (2003), "Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour", Int. J. Plast., 19(4), 403-433. https://doi.org/10.1016/S0749-6419(01)00042-0
  29. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  30. Feist., C. and Hofstetter, G. (2007), "Validation of 3d crack propagation in plain concrete. Part I: Experimental investigation - the pct3d test", Comput. Concrete, 4(1), 49-66. https://doi.org/10.12989/cac.2007.4.1.049
  31. Gopalaratnam, V.S. and Shah, S.P. (1985), "Softening response of plain concrete in direct tension", ACI J. Proc., 82(3), 310-323.
  32. Grassl, P. and Jirasek, M. (2006a), "Damage-plastic model for concrete failure", Int. J. Solid. Struct., 43(22), 7166-7196. https://doi.org/10.1016/j.ijsolstr.2006.06.032
  33. Grassl, P. and Jirasek, M. (2006b), "Plastic model with non-local damage applied to concrete", Int. J. Numer. Anal. Meth. Geomech., 30(1), 71-90. https://doi.org/10.1002/nag.479
  34. Gutierrez, M.A. (2004), "Energy release control for numerical simulations of failure in quasi-brittle solids", Commun. Numer. Meth. Eng., 20(1), 19-29. https://doi.org/10.1002/cnm.649
  35. Han, D.J. and Chen, W.F. (1985), "A nonuniform hardening plasticity model for concrete materials", Mech. Mater., 4(3), 283-302. https://doi.org/10.1016/0167-6636(85)90025-0
  36. Hossain, K.M.A. and Olufemi, O.O. (2004), "Computational optimization of a concrete model to simulate membrane action in RC slabs", Comput. Concrete, 1(3), 325-354. https://doi.org/10.12989/cac.2004.1.3.325
  37. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194(39-41), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
  38. Jelic., I., Pavlovic, M.N. and Kotsovos, M.D. (2004). "Performance of structural-concrete members under sequential loading and exhibiting points of inflection", Comput. Concrete, 1(1), 99-113. https://doi.org/10.12989/cac.2004.1.1.099
  39. Jia, Y., Anitescu, C., Ghorashi, S.S. and Rabczuk, T. (2015), "Extended isogeometric analysis for material interface problems", IMA J. Appl. Math., 80(3), 608-633.. https://doi.org/10.1093/imamat/hxu004
  40. Jirasek, M. (1998), "Nonlocal models for damage and fracture: comparison of approaches", Int. J. Solid. Struct., 35(31), 4133-4145. https://doi.org/10.1016/S0020-7683(97)00306-5
  41. Ju, J.W. (1989), "On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects", Int. J. Solid. Struct., 25(7), 803-833. https://doi.org/10.1016/0020-7683(89)90015-2
  42. Karsan, I.D. and Jirsa, J.O. (1969), "Behavior of concrete under compressive loadings", J. Struct. Div., 95(12), 2543-2563 https://doi.org/10.1061/JSDEAG.0002424
  43. Kroner, E. (1967), "Elasticity theory of materials with long range cohesive forces", Int. J. Solid. Struct., 3(5), 731-742. https://doi.org/10.1016/0020-7683(67)90049-2
  44. Kupfer, H., Hilsdorf, H.K. and Rusch, H. (1969), "Behavior of concrete under biaxial stresses", ACI J. Proc., 66(8), 656-666.
  45. Lee, J. and Fenves, G. (1998), "Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech., 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
  46. Loland, K.E. (1980), "Continuous damage model for loadresponse estimation of concrete", Cement Concrete Res., 10(3), 395-402. https://doi.org/10.1016/0008-8846(80)90115-5
  47. Lubliner, J., Oliver, J., Oller, S. and Onate, E. (1989), "A plasticdamage model for concrete", Int. J. Solid. Struct., 25(3), 299-326. https://doi.org/10.1016/0020-7683(89)90050-4
  48. Malvar, L.J. and Warren, G.E. (1988), "Fracture energy for threepoint-bend tests on single-edge-notched beams", Exp. Mech., 28(3), 266-272. https://doi.org/10.1007/BF02329022
  49. Mazars, J. and Pijaudier-Cabot, G. (1989), "Continuum damage theory-application to concrete", J. Eng. Mech., 115(2), 345-365. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:2(345)
  50. Miehe, C., Welschinger, F. and Hofacker, M. (2010), "Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations", Int. J. Numer. Meth. Eng., 83(10), 1273-1311. https://doi.org/10.1002/nme.2861
  51. Nguyen, V.P., Anitescu, C., Bordas, S.P.A. and Rabczuk, T. (2015), "Isogeometric analysis: An overview and computer implementation aspects", Math. Comput. Simul., 117, 89-116. https://doi.org/10.1016/j.matcom.2015.05.008
  52. Ozbolt, J., Kozar, I. and Periskic, G. (2007), "Three-dimensional FE analysis of headed stud anchors exposed to fire", Comput. Concrete, 2(4), 249-266. https://doi.org/10.12989/cac.2005.2.4.249
  53. Pamin, J.K. (1994), "Gradient-dependent plasticity in numerical simulation of localization phenomena", TU Delft, Delft University of Technology.
  54. Papadakis., V.G., Efstathiou., M.P. and Apostolopoulos., C.A. (2007), "I Computer-aided approach of parameters influencing concrete service life and field validation", Comput. Concrete, 4(1), 1-18. https://doi.org/10.12989/cac.2007.4.1.001
  55. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M. and de Vree, J.H.P. (1996a), "Gradient enhanced damage for quasi-brittle materials", Int. J. Numer. Meth. Eng., 39(19), 3391-3403. https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D
  56. Peerlings, R.H.J., De Borst, R., Brekelmans, W.A.M., De Vree, J.H.P. and Spee, I. (1996b), "Some observations on localisation in non-local and gradient damage models", Eur. J. Mech. A: Solid., 15(6), 937-953.
  57. Pijaudier-Cabot, G. and Bazant, Z.P. (1987), "Nonlocal damage theory", J. Eng. Mech., 113(10), 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  58. Poh, L.H. and Swaddiwudhipong, S. (2009), "Over-nonlocal gradient enhanced plastic-damage model for concrete", Int. J. Solid. Struct., 46(25), 4369-4378. https://doi.org/10.1016/j.ijsolstr.2009.08.025
  59. Rabczuk, T. and Belytschko, T. (2007), "A three-dimensional large deformation meshfree method for arbitrary evolving cracks", Comput. Meth. Appl. Mech. Eng., 196(29-30), 2777-2799. https://doi.org/10.1016/j.cma.2006.06.020
  60. Rabczuk, T. and Eibl, J. (2003), "Simulation of high velocity concrete fragmentation using SPH/MLSPH", Int. J. Numer. Meth. Eng., 56(10), 1421-1444. https://doi.org/10.1002/nme.617
  61. Rabczuk, T. and Eibl, J. (2006), "Modelling dynamic failure of concrete with meshfree methods", Int. J. Impact Eng., 32(11), 1878-1897. https://doi.org/10.1016/j.ijimpeng.2005.02.008
  62. Rabczuk, T., Akkermann, J. and Eibl, J. (2005), "A numerical model for reinforced concrete structures", Int. J. Solid. Struct., 42(5), 1327-1354. https://doi.org/10.1016/j.ijsolstr.2004.07.019
  63. Rots, J.G., Nauta, P.G., Kuster, G.M.A. and Blaauwendraad, J. (1985), "Smeared crack approach and fracture localization in concrete", Heron, 30(1), 1985.
  64. Saritas, A. and Filippou, F.C. (2009), "Numerical integration of a class of 3d plastic-damage concrete models and condensation of 3d stress-strain relations for use in beam finite elements", Eng. Struct., 31(10), 2327-2336. https://doi.org/10.1016/j.engstruct.2009.05.005
  65. Simo, J.C. and Ju, J.W. (1987a), "Strain- and stress-based continuum damage models - I. Formulation", Int. J. Solid. Struct., 23(7), 821-840. https://doi.org/10.1016/0020-7683(87)90083-7
  66. Simo, J.C. and Ju, J.W. (1987b), "Strain- and stress-based continuum damage models - II. Computational aspects", Int. J. Solid. Struct., 23(7), 841-869. https://doi.org/10.1016/0020-7683(87)90084-9
  67. Stroeven., P., Hu., J. and Stroeven, M. (2009), "On the usefulness of discrete element computer modeling of particle packing for material characterization in concrete technology", Comput. Concrete, 6(2), 133-153. https://doi.org/10.12989/cac.2009.6.2.133
  68. Thai, T.Q., Rabczuk, T., Bazilevs, Y. and Meschke, G. (2016), "A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 304, 584-604. https://doi.org/10.1016/j.cma.2016.02.031
  69. Verhoosel, C.V., Remmers, J.J.C. and Gutierrez, M.A. (2009), "A dissipation-based arc-length method for robust simulation of brittle and ductile failure", Int. J. Numer. Meth. Eng., 77(9), 1290-1321. https://doi.org/10.1002/nme.2447
  70. Verhoosel, C.V., Scott, M.A., Hughes, T.J.R. and De Borst, R. (2011), "An isogeometric analysis approach to gradient damage models", Int. J. Numer. Meth. Eng., 86(1), 115-134. https://doi.org/10.1002/nme.3150
  71. Vermeer, P.A. and Brinkgreve, R.B.J. (1994), "A new effective non-local strain measure for softening plasticity", Localization and Bifurcation Theory for Soils and Rocks, 89-100.
  72. Voyiadjis, G.Z., Taqieddin, Z.N. and Kattan, P.I. (2008), "Anisotropic damage-plasticity model for concrete", Int. J. Plast., 24(10), 1946-1965. https://doi.org/10.1016/j.ijplas.2008.04.002
  73. Yu, H.X. and Wu, J.H. (2009), "An elastoplastic damage constitutive model for concrete based on undamaged state", Eng. Mech., 26(10), 79-86. (in Chinese)
  74. Zhu, H., Wang, Q. and Zhuang, X. (2016), "A nonlinear semiconcurrent multiscale method for fractures", Int. J. Impact Eng., 87, 65-82. https://doi.org/10.1016/j.ijimpeng.2015.06.022
  75. Zhuang, X., Augarde, C.E. and Mathisen, K.M. (2012), "Fracture modeling using meshless methods and level sets in 3D: Framework and modeling", Int. J. Numer. Meth. Eng., 92(11), 969-998. https://doi.org/10.1002/nme.4365
  76. Zhuang, X., Cai, Y. and Augarde, C. (2014), "A meshless subregion radial point interpolation method for accurate calculation of crack tip fields", Theor. Appl. Fract. Mech., 69(2), 118-125. https://doi.org/10.1016/j.tafmec.2013.12.003

피인용 문헌

  1. A novel approach to the complete stress strain curve for plastically damaged concrete under monotonic and cyclic loads vol.28, pp.1, 2019, https://doi.org/10.12989/cac.2021.28.1.039