Computers and Concrete

  • 제15권4호
  • /
  • Pages.515-545
  • /
  • 2015
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Computational simulations of concrete behaviour under dynamic conditions using elasto-visco-plastic model with non-local softening

  • Marzec, Ireneusz (Faculty of Civil and Environmental Engineering, Gdansk University of Technology) ;
  • Tejchman, Jacek (Faculty of Civil and Environmental Engineering, Gdansk University of Technology) ;
  • Winnicki, Andrzej (Institute of Building Materials and Structures, Cracow University of Technology)
  • 투고 : 2014.07.21
  • 심사 : 2014.11.15
  • 발행 : 2015.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The paper presents results of FE simulations of the strain-rate sensitive concrete behaviour under dynamic loading at the macroscopic level. To take the loading velocity effect into account, viscosity, stress modifications and inertial effects were included into a rate-independent elasto-plastic formulation. In addition, a decrease of the material stiffness was considered for a very high loading velocity to simulate fragmentation. In order to ensure the mesh-independence and to properly reproduce strain localization in the entire range of loading velocities, a constitutive formulation was enhanced by a characteristic length of micro-structure using a non-local theory. Numerical results were compared with corresponding laboratory tests and available analytical formulae.

키워드

과제정보

연구 과제번호 : Innovative ways and effective methods of safety improvement and durability of buildings and transport infrastructure in the sustainable development

연구 과제 주관 기관 : European Union

참고문헌

  1. ABAQUS Theory Manual, (2004), Hibbit, Karlsson & Sorensen Inc.
  2. Azevedo, M.N., Lemos, J.V. and de Almeida, J.R. (2008), "Influence of aggregate deformation and contact behavior on discrete particle modeling of fracture of concrete", Eng. Fract. Mech., 75(6), 1569-1586. https://doi.org/10.1016/j.engfracmech.2007.06.008
  3. Bazant, Z.P. (1978), "Spurious reflection of elastic waves in non-uniform finite element grids", Comput. Method. Appl. M., 16, 91-100. https://doi.org/10.1016/0045-7825(78)90035-X
  4. Bazant, Z.P. and Planas, J. (1998), Fracture and Size Effect in Concrete and Other Quasi-brittle Materials, CRC Press LLC.
  5. Bazant, Z.P., Caner, F.C., Adley, M.D. and Akers, S.A. (2000), "Fracturing rate effect and creep in microplane model for dynamics", J. Eng. Mech. ASCE, 126, 9, 962-970.
  6. 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)
  7. Bazant, Z.P. and Caner, F.C. (2013), "Dynamic comminution of quasibrittle solids at high-rate shear under impact and analogy with turbulence", Proceeding of the Third International Conference on Computational Modeling of Fracture and Failure of Materials and Structures, CFRAC 2013, Prague, Czech Republic, 5-7.06.2013.
  8. Bischoff, P.H. and Perry, S.H. (1991), "Compressive behaviour of concrete at high strain rates", Mat. Struct., 24, 425-450. https://doi.org/10.1007/BF02472016
  9. Bischoff, P.H. and Perry, S. H. (1995), "Impact behaviour of plain concrete loaded in uniaxial compression", J. Eng. Mech. Div ASCE, 121, 6.
  10. Bobinski, J. and Tejchman, J. (2004), "Numerical simulations of localization of deformation in quasi brittle materials within non-local softening plasticity", Comput. Concr., 4, 433-455.
  11. Bobinski, J. and Tejchman, J. (2013), "A coupled continuous and discontinuous approach to concrete elements", Proc. VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-8 (eds.: J.G.M. van Mier, G. Ruiz, C. Andrade, R.C. Yu nd X.X. Zhang), Toledo, Spain, 11-15.03.2013.
  12. Brara, A. and Klepaczko, J.R. (2006), "Experimental characterization of concrete in dynamic tension", Mech. Mater., 38, 253-267. https://doi.org/10.1016/j.mechmat.2005.06.004
  13. Brinkgreve, R.B. (1994), "Geomaterial models and numerical analysis of softening", Ph.D. Dissertation, Delft University of Technology, Delft.
  14. CEB-FIP Model Code 1990. (1993), Thomas Telford, London.
  15. Cervera, M., Olivier, J. and Manzoli, O. (1996), "A rate-dependent isotropic damage model for the seismic analysis of concrete dams", Earthq. Eng. Struct. Dyn., 25, 987-101. https://doi.org/10.1002/(SICI)1096-9845(199609)25:9<987::AID-EQE599>3.0.CO;2-X
  16. de Borst, R. and Sluys, L.J. (1991), "Localization in a cosserat continuum under static and dynamic loading conditions", Comput.Method. Appl. M., 90, 1-3, 805-827. https://doi.org/10.1016/0045-7825(91)90185-9
  17. Denoual C. (1998), "Approche probabiliste du comportement l'impact du carbure de silicium: application aux blindages moyens", Ph.D. Dissertation, ENS de Cachan.
  18. Denoual, C. and Hild, F. (2000), "A damage model for the dynamic fragmentation of brittle solids", Comp. Meth. Apll. Mech. Eng., 183, 247-258. https://doi.org/10.1016/S0045-7825(99)00221-2
  19. Duvaut, G. and Lions, J.L. (1972), Les Inequations en Mecanique et en Physique, Dunod, Paris.
  20. Drucker, D.C. and Prager, W. (1952), "Soil mechanics and plasticity analysis of limit design", Quart. J. Appl. Math., 10, 157-162. https://doi.org/10.1090/qam/48291
  21. Eibl, J. and Schmidt-Hurtienne, B. (1999), "Strain-rate-sensitive constitutive law for concrete", J. Eng. Mech., 125, 1411-1420. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:12(1411)
  22. Ferrara, I. and di Prisco, M. (2001), "Mode I fracture behaviour in concrete: nonlocal damage modelling", ASCE J. Eng. Mech., 127(7), 678-692. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:7(678)
  23. fib. Model Code 2010 (2012), Final draft, fib Bulletin 65.
  24. Gary, G. (1990), Essais a Grande Vitesse sur Beton. Problemes Specifiques, Scientifique Rapport GRECO (edite par J. M. Reynouard).
  25. Gatuingt, F. and Pijaudier-Cabot, G. (2002), "Coupled damage and plasticity modelling in transient dynamic analysis of concrete", Int. J. Numer. Anal. Meth. Geomech., 26, 1-24. https://doi.org/10.1002/nag.188
  26. Georgin, J.F. and Reynouard, J.M. (2003), "Modelling of structures subjected to impact: concrete behaviour under high strain rate", Cement Concrete Compos., 25, 131-143. https://doi.org/10.1016/S0958-9465(01)00060-9
  27. Grady, D. (2008), "Fragment size distributions from the dynamic fragmentation of brittle solids", Int. J. Imp. Eng., 35, 1557-1562. https://doi.org/10.1016/j.ijimpeng.2008.07.042
  28. Haussler-Combe, U. and Kuhn, T. (2012a), "Failure modelling of concrete with a novel strain rate sensitive viscoelastic retarded damage material formulation", European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 2012.
  29. Haussler-Combe, U. and Kuhn, T. (2012b), "Modeling of strain rate effects for concrete with viscoelasticity and retarded damage", Int. J. Impact. Eng., 50, 17-28. https://doi.org/10.1016/j.ijimpeng.2012.08.002
  30. Hentz, S., Daudeville, L. and Donze, F. (2004), "Identification and validation of a discrete element model for concrete", J. Eng. Mech., 130(6), 709-719. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(709)
  31. Hughes, T.J.R. and Winget, J. (1980), "Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis", Int. J. Numer. M. Eng., 15, 1862-1867. https://doi.org/10.1002/nme.1620151210
  32. Jankowiak, T. (2009), "Failure criteria under quasi-static and dynamic loads", Ph.D. Dissertation, Poznan University of Technology, Poznan.
  33. Jankowiak, T., Rusinek, A. and Lodygowski, T. (2011). "Validation of the klepaczko-malinowski model for friction correction and recommendations on split hopkinson pressure bar", Finite Elem. Anal. Des., 47(10), 1191-1208. https://doi.org/10.1016/j.finel.2011.05.006
  34. Jirasek, M., and Rolshoven, S. (2006), "Comparison of integral-type nonlocal plasticity models for strainsoftening materials", Int. J. Eng. Sci., 41, 13-14, 1553-1602. https://doi.org/10.1016/S0020-7225(03)00027-2
  35. Lee, J., and Fenves, G.L. (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)
  36. Majewski, T., Bobinski, J. and Tejchman, J. (2008), "FE-analysis of failure behaviour of reinforced concrete columns under eccentric compression", Eng. Struct., 30(2), 300-317. https://doi.org/10.1016/j.engstruct.2007.03.024
  37. Malvar, L. J. and Ross, C.A. (1998), "Review of strain rate effects for concrete in tension", ACI Mater. J., 95, 735-739.
  38. Marzec, I., Bobinski, J. and Tejchman, J. (2007), "Simulations of crack spacing in reinforced concrete beams using elastic-plasticity and damage with non-local softening", Comput. Concr., 4(5), 377-403. https://doi.org/10.12989/cac.2007.4.5.377
  39. Menetrey, P. and Willam, K.J. (1995), "Triaxial failure criterion for concrete and its generalization", ACI Struct. J., 92(3), 311-318.
  40. Moonen, P., Carmeliet, J. and Sluys, L.J. (2008), "A continuous-discontinuous approach to simulate fracture processes", Philos. Mag., 88, 3281-3298. https://doi.org/10.1080/14786430802566398
  41. Nagtegaal, J. C., Parks, D. M. and Rice J. R. (1977), "On numerically accurate finite element solutions in the fully plastic range", Comput. Method. Appl. M., 4, 153-177.
  42. Nemes, J.A. and Speciel, E. (1996), "Use of a rate-dependent continuum damage model to describe strainsoftening in laminated composites", Comput. Struct., 58, 1083-1092. https://doi.org/10.1016/0045-7949(95)00229-4
  43. Ortiz, M. and Simo, I.C. (1986), "An analysis of a new class of integration algorithms for elastoplastic constitutive relation", Int. I. Num. Method. Eng., 23, 353-366. https://doi.org/10.1002/nme.1620230303
  44. Ozbolt, J. and Reinhardt, H.W. (2005), "Rate dependent fracture of notched plain concrete beams", Proceedings of the 7th international conference CONCREEP-7, (ed. by Pijaudier Cabot, Gerard & Acker), 57-62.
  45. Ozbolt, J., Sharma, A. and Reinhardt, H-W. (2011), "Dynamic fracture of concrete compact tension specimen", Int. J. Solid. Struct., 48(10), 1534-1543. https://doi.org/10.1016/j.ijsolstr.2011.01.033
  46. Pajak, M. (2011), "The influence of the strain rate on the strength of concrete taking into account the experimental techniques", Architect. Civ. Eng.-Environ. J. (ACEE), 3, 77-86.
  47. Pedersen, R.R., Simone, A. and Sluys, L.J. (2008), "An analysis of dynamic fracture in concrete with continuum visco-elastic visco-plastic damage model", Eng. Fract. Mech., 75, 3782-3805. https://doi.org/10.1016/j.engfracmech.2008.02.004
  48. Pedersen, R.R. (2009), "Computational modelling of dynamic failure of cementitious materials", Ph.D. Dissertation, TU Delft, Delft.
  49. Perzyna, P. (1966), "Fundamental problems in viscoplasticity", Adv. Appl. Mech., Academic Press, 9, 243-377. https://doi.org/10.1016/S0065-2156(08)70009-7
  50. Pijaudier-Cabot, G. and G., Bazant, Z.P. (1987), "Nonlocal damage theory", ASCE J. Eng. Mech., 113, 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  51. Pijaudier-Cabot, G., Haidar, K. and Dube, J.F. (2004), "Non-local damage model with evolving internal length", Int. J. Numer. Anal. M., 28, 633-652. https://doi.org/10.1002/nag.367
  52. Polizzotto, C., Borino, G. and Fuschi, P. (1998), "A thermodynamic consistent formulation of nonlocal and gradient plasticity", Mech. Res. Communic., 25, 75-82. https://doi.org/10.1016/S0093-6413(98)00009-3
  53. Ragueneau, F. and Gatuingt, F. (2003), "Inelastic behaviour modelling of concrete in low and high strain rate dynamics", Comput. Struct., 81, 1287-1299. https://doi.org/10.1016/S0045-7949(03)00043-9
  54. Rankine, W.J.M. (1858), A Manual of Applied Mechanics, London and Glasgow: Richard Griffin and Company, Publishers to the University of Glasgow.
  55. Rossi, P. (1991), "A physical phenomenon which can explain the mechanical behaviour of concrete under high strain rates", Mater. Struct., 24, 422-424. https://doi.org/10.1007/BF02472015
  56. Roth, S., Oudry, J., El-Rich, M. and Shakourzadeh, H. (2009), "Influence of mesh density on a finite element model's response under dynamic loading", J. Biol. Phys. Chem., 9, 210-219. https://doi.org/10.4024/39RO09C.jbpc.09.04
  57. Rousseau, J., Frangin, E., Marin, P. and Daudeville, L. (2009), "Multidomain finite and discrete elements method for impact analysis of a concrete structure", Eng. Struct., 31(11), 2735-2743. https://doi.org/10.1016/j.engstruct.2009.07.001
  58. Sercombe, J., Ulm, F.J. and Mang, H.A. (2000), "Consistent return mapping algorithm for chemoplastic constitutive laws with internal couplings", Int. J. Numer. Meth. Eng., 47, 75-100. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<75::AID-NME762>3.0.CO;2-Y
  59. Simone, A. (2003), "Continuous-discontinuous modelling of failure", Ph.D. Dissertation, TU Delft, Delft.
  60. Skarzynski, L. and Tejchman, J. (2010), "Calculations of fracture process zones on meso-scale in notched concrete beams subjected to three-point bending", European J. Mech. A Solid, 29, 746-760. https://doi.org/10.1016/j.euromechsol.2010.02.008
  61. Skarzynski, L., Syroka, E. and Tejchman, J. (2011), "Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams", Strain, 47, e319-e332. https://doi.org/10.1111/j.1475-1305.2008.00605.x
  62. Sluys, L.J. and de Borst R. (1992), "Wave propagation and localization in a rate-dependent cracked mediummodel formulation and one-dimensional examples", Int. J. Solid Struct., 29, 2945-58. https://doi.org/10.1016/0020-7683(92)90151-I
  63. Stromberg, L. and Ristinmaa, M. (1996), "FE-formulation of nonlocal plasticity theory", Comput. Method. Appl. M., 136, 127-144. https://doi.org/10.1016/0045-7825(96)00997-8
  64. Suaris, W. and Shah, S.P. (1984), "Rate-sensitive damage theory for brittle materials", J. Eng. Mech., 110, 985-997. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:6(985)
  65. Syroka, E., Tejchman, J. and Mroz, Z. (2013), "FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening", Eng. Struct., 48, 205-219. https://doi.org/10.1016/j.engstruct.2012.09.013
  66. Syroka-Korol, E. and Tejchman, J. (2013), "Experimental investigations of size effect in reinforced concrete beams failing by shear", Eng. Struct., http://dx.doi.org/10.1016/j.engstruct.2013.10.012.
  67. Tejchman, J. and Bobinski, J. (2013), Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM, Springer, Berlin-Heidelberg, Germany.
  68. Vermeer, P.A. and Brinkgreve, R.B.J. (1994), "A new effective non-local strain-measure for softening plasticity", Localisation and Bifurcation Theory for Soils and Rocks (edited by: Chambon, R., Desrues, J. and Vardoulakis, I.), Balkema, 89-100.
  69. Wang, W.M., Sluys, L.J. and de Borst, R. (1997), "Viscoplasticity for instabilities due to strain softening and strain-rate softening", Int. J. Numer. Meth. Eng., 40, 3839-64. https://doi.org/10.1002/(SICI)1097-0207(19971030)40:20<3839::AID-NME245>3.0.CO;2-6
  70. Werner, S. and Thienel, K.-Ch. (2011), "Influence of impact velocity on the fragment formation of concrete specimens", Int. Conference Particles, 211-221, Barcelona.
  71. Winnicki, A. (2007), "Viscoplastic and internal discontinuity models in analysis of structural concrete", Habilitation Monograph, Cracow University of Technology, Cracow.
  72. Winnicki, A., Pearce, C.J., Bicanic, N. (2001), "Viscoplastic Hoffman consistency model for concrete", Comput. Struct., 79, 7-19. https://doi.org/10.1016/S0045-7949(00)00110-3
  73. Zheng, D. and Li, Q. (2004), "An explanation for rate effect of concrete strength based on fracture toughness including free water viscosity", Eng. Fract. Mech., 71, 2319-2327. https://doi.org/10.1016/j.engfracmech.2004.01.012
  74. Zhang, X.X., Ruiz, G., Yu, G.R.C. and Tarifa, M. (2009), "Fracture behaviour of high strength concrete at a wide range of loading rates", Int. J. Impact. Eng., 36, 1204-1209. https://doi.org/10.1016/j.ijimpeng.2009.04.007
  75. Yan, D. and Lin, G. (2006), "Dynamic properties of concrete in direct tension", Cement Concrete Res., 36, 1371-1378. https://doi.org/10.1016/j.cemconres.2006.03.003

피인용 문헌

  1. 3D modelling of reinforced concrete slab with yielding supports subject to impact load vol.21, pp.7-8, 2017, https://doi.org/10.1080/19648189.2016.1194330
  2. Performance of double reinforced concrete panel against blast hazard vol.18, pp.6, 2016, https://doi.org/10.12989/cac.2016.18.6.807
  3. Performance of double reinforced concrete panel against blast hazard vol.18, pp.4, 2015, https://doi.org/10.12989/cac.2016.18.4.807
  4. Rate-Dependent Characteristic of Relaxation Time of Concrete vol.32, pp.1, 2015, https://doi.org/10.1007/s10338-018-0065-z
  5. On Some Problems in Determining Tensile Parameters of Concrete Model from Size Effect Tests vol.26, pp.2, 2019, https://doi.org/10.2478/pomr-2019-0031
  6. Crack propagation in flexural fatigue of concrete using rheological-dynamical theory vol.27, pp.1, 2015, https://doi.org/10.12989/cac.2021.27.1.055