A position-based FEM approach for modeling mixed-mode cracks in concrete
Bibliographic record
Abstract
No abstract is available for this record. The assistant can identify its topic from the title, but cannot infer the study’s results.
Source: Not provided · Quality: missing
Research context
OpenAlex topics: Numerical methods in engineering · Rock Mechanics and Modeling · Fluid Dynamics Simulations and Interactions
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (80)
Show source-provided references
1. Griffith AA (1921) Vi. the phenomena of rupture and flow in solids. Philosophical transactions of the royal society of london. Series A, containing papers of a mathematical or physical character 221(582–593):163–198. https://doi.org/10.1098/rsta.1921.000610.1098/rsta.1921.0006 ↗
2. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24(3):361–364. https://doi.org/10.1115/1.401154710.1115/1.4011547 ↗
3. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129. https://doi.org/10.1016/S0065-2156(08)70121-210.1016/S0065-2156(08)70121-2 ↗
4. Bažant ZP, Cedolin L (1979) Blunt crack band propagation in finite element analysis. J Eng Mech Div 105(2):297–315. https://doi.org/10.1061/JMCEA3.000246710.1061/JMCEA3.0002467 ↗
5. Rots JG, Nauta P, Kuster G, Blaauwendraad J (1985) Smeared crack approach and fracture localization in concrete. HERON 30(1):1985
6. Hillerborg A, Modéer M, Petersson P-E (1967) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6(6):773–781. https://doi.org/10.1016/0008-8846(76)90007-710.1016/0008-8846(76)90007-7 ↗
7. Elices M, Guinea G, Gomez J, Planas J (2002) The cohesive zone model: advantages, limitations and challenges. Eng Fract Mech 69(2):137–163. https://doi.org/10.1016/S0013-7944(01)00083-210.1016/S0013-7944(01)00083-2 ↗
8. Schlangen E, Mier JGM (1992) Experimental and numerical analysis of fracture processes in concrete. Heron 37(1):1–40
9. Bolander JE, Saito S (1998) Fracture analyses using spring networks with random geometry. Eng Fract Mech 61(5–6):569–591. https://doi.org/10.1016/S0013-7944(98)00069-110.1016/S0013-7944(98)00069-1 ↗
10. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45(5):601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5$$<$$601::AID-NME598$$>$$3.0.CO;2-S10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S ↗
11. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46(1):131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1$$<$$131::AID-NME726$$>$$3.0.CO;2-J10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J ↗
12. Francfort GA, Marigo J-J (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342. https://doi.org/10.1016/S0022-5096(98)00034-910.1016/S0022-5096(98)00034-9 ↗
13. Bourdin B, Francfort GA, Marigo J-J (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826. https://doi.org/10.1016/S0022-5096(99)00028-910.1016/S0022-5096(99)00028-9 ↗
14. Willam K, Pramono E, Sture S (1989) Fundamental issues of smeared crack models. In: Fracture of Concrete and Rock: SEM-RILEM International Conference June 17–19, 1987, Houston, Texas, USA, pp. 142–157. https://doi.org/10.1007/978-1-4612-3578-1_15 . Springer10.1007/978-1-4612-3578-1_15 ↗
15. Ožbolt J, Reinhardt H (2002) Numerical study of mixed-mode fracture in concrete. Int J Fract 118(2):145–162. https://doi.org/10.1023/A:102288612780610.1023/A:1022886127806 ↗
16. Jirásek M (2011) In: Hofstetter, G., Meschke, G. (eds.) Damage and smeared crack models, pp 1–49. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0897-0_110.1007/978-3-7091-0897-0_1 ↗
17. Cendón D, Gálvez J, Elices M, Planas J (2000) Modelling the fracture of concrete under mixed loading. Int J Fract 103(3):293–310. https://doi.org/10.1023/A:100768702557510.1023/A:1007687025575 ↗
18. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Engineering with Computers 18(2):148–159. https://doi.org/10.1007/s00366020001310.1007/s003660200013 ↗
19. Gálvez J, Červenka J, Cendón D, Saouma V (2002) A discrete crack approach to normal/shear cracking of concrete. Cem Concr Res 32(10):1567–1585. https://doi.org/10.1016/S0008-8846(02)00825-610.1016/S0008-8846(02)00825-6 ↗
20. Yang Z, Chen J (2004) Fully automatic modelling of cohesive discrete crack propagation in concrete beams using local arc-length methods. Int J Solids Struct 41(3–4):801–826. https://doi.org/10.1016/j.ijsolstr.2003.09.03310.1016/j.ijsolstr.2003.09.033 ↗
21. Sancho J, Planas J, Gálvez J, Reyes E, Cendón D (2006) An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete. Fatigue Fract Eng Mater Struct 29(12):1056–1065. https://doi.org/10.1111/j.1460-2695.2006.01076.x10.1111/j.1460-2695.2006.01076.x ↗
22. Park K, Paulino GH, Roesler JR (2009) A unified potential-based cohesive model of mixed-mode fracture. J Mech Phys Solids 57(6):891–908. https://doi.org/10.1016/j.jmps.2008.10.00310.1016/j.jmps.2008.10.003 ↗
23. Bourdin B, Francfort GA, Marigo J-J (2008) The variational approach to fracture. J Elast 91:5–148. https://doi.org/10.1007/s10659-007-9107-310.1007/s10659-007-9107-3 ↗
24. Borden MJ, Verhoosel CV, Scott MA, Hughes TJ, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95. https://doi.org/10.1016/j.cma.2012.01.00810.1016/j.cma.2012.01.008 ↗
25. Patil R, Mishra B, Singh I (2018) An adaptive multiscale phase field method for brittle fracture. Comput Methods Appl Mech Eng 329:254–288. https://doi.org/10.1016/j.cma.2017.09.02110.1016/j.cma.2017.09.021 ↗
26. Bilgen C, Homberger S, Weinberg K (2019) Phase-field fracture simulations of the brazilian splitting test: C. bilgen et al. Int J Fract 220(1):85–98. https://doi.org/10.1007/s10704-019-00401-w10.1007/s10704-019-00401-w ↗
27. Spetz A, Denzer R, Tudisco E, Dahlblom O (2020) Phase-field fracture modelling of crack nucleation and propagation in porous rock. Int J Fract 224(1):31–46. https://doi.org/10.1007/s10704-020-00444-410.1007/s10704-020-00444-4 ↗
28. Rao Q, Zhao C, Yi W (2023) A new mixed-mode phase-field model for crack propagation of brittle rock. Journal of Rock Mechanics and Geotechnical Engineering 15(5):1186–1199. https://doi.org/10.1016/j.jrmge.2022.10.01910.1016/j.jrmge.2022.10.019 ↗
29. Pandolfi A, Ortiz M (1998) Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 14(4):287–308. https://doi.org/10.1007/BF0120176110.1007/BF01201761 ↗
30. Trädegård A, Nilsson F, Östlund S (1998) Fem-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160(1–2):115–131. https://doi.org/10.1016/S0045-7825(97)00287-910.1016/S0045-7825(97)00287-9 ↗
31. Bouchard P-O, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189(3):723–742. https://doi.org/10.1016/S0045-7825(99)00324-210.1016/S0045-7825(99)00324-2 ↗
32. Bouchard P-O, Bay F, Chastel Y (2003) Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Methods Appl Mech Eng 192(35–36):3887–3908. https://doi.org/10.1016/S0045-7825(03)00391-810.1016/S0045-7825(03)00391-8 ↗
33. Paulino GH, Celes W, Espinha R, Zhang Z (2008) A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes. Engineering with Computers 24(1):59–78. https://doi.org/10.1007/s00366-007-0069-710.1007/s00366-007-0069-7 ↗
34. Day R, Potts D (1994) Zero thickness interface elements-numerical stability and application. Int J Numer Anal Meth Geomech 18(10):689–708. https://doi.org/10.1002/nag.161018100310.1002/nag.1610181003 ↗
35. Caggiano A, Etse G, Martinelli E (2012) Zero-thickness interface model formulation for failure behavior of fiber-reinforced cementitious composites. Comput Struct 98:23–32. https://doi.org/10.1016/j.compstruc.2012.01.01310.1016/j.compstruc.2012.01.013 ↗
36. Etse G, Caggiano A, Vrech S (2012) Multiscale failure analysis of fiber reinforced concrete based on a discrete crack model. Int J Fract 178(1):131–146. https://doi.org/10.1007/s10704-012-9733-z10.1007/s10704-012-9733-z ↗
37. Cannizzaro F, Pantò B, Caddemi S, Caliò I (2018) A discrete macro-element method (dmem) for the nonlinear structural assessment of masonry arches. Eng Struct 168:243–256. https://doi.org/10.1016/j.engstruct.2018.04.00610.1016/j.engstruct.2018.04.006 ↗
38. Sharma H, Singh A (2025) Combined phase-field and cohesive zone modeling for mixed-mode fracture in polymer composites. Engineering with Computers 1–29. https://doi.org/10.1007/s00366-025-02134-y10.1007/s00366-025-02134-y ↗
39. Grassl P (2009) A lattice approach to model flow in cracked concrete. Cement Concr Compos 31(7):454–460. https://doi.org/10.1016/j.cemconcomp.2009.05.00110.1016/j.cemconcomp.2009.05.001 ↗
40. Cusatis G, Pelessone D, Mencarelli A (2011) Lattice discrete particle model (LDPM) for failure behavior of concrete. i: Theory. Cement and Concrete Composites 33(9):881–890. https://doi.org/10.1016/j.cemconcomp.2011.02.01110.1016/j.cemconcomp.2011.02.011 ↗
41. Grassl P, Bolander JE (2016) Three-dimensional network model for coupling of fracture and mass transport in quasi-brittle geomaterials. Materials 9(9):782. https://doi.org/10.3390/ma909078210.3390/ma9090782 ↗
42. Chang Z, Zhang H, Schlangen E, Šavija B (2020) Lattice fracture model for concrete fracture revisited: Calibration and validation. Appl Sci 10(14):4822. https://doi.org/10.3390/app1014482210.3390/app10144822 ↗
43. Cusatis G, Mencarelli A, Pelessone D, Baylot J (2011) Lattice discrete particle model (ldpm) for failure behavior of concrete. ii: Calibration and validation. Cement and Concrete composites 33(9):891–905. https://doi.org/10.1016/j.cemconcomp.2011.02.01010.1016/j.cemconcomp.2011.02.010 ↗
44. Bomfim DS, Coda HB, Paccola RR (2025) Intermediate flexural crack debonding of externally bonded frp in rc beams through a fem formulation based on positions. Comput Methods Appl Mech Eng 436:117716. https://doi.org/10.1016/j.cma.2024.11771610.1016/j.cma.2024.117716 ↗
45. Manzoli OL, Maedo MA, Bitencourt LA Jr, Rodrigues EA (2016) On the use of finite elements with a high aspect ratio for modeling cracks in quasi-brittle materials. Eng Fract Mech 153:151–170. https://doi.org/10.1016/j.engfracmech.2015.12.02610.1016/j.engfracmech.2015.12.026 ↗
46. Teng JG, Chen JF, Smith ST, Lam L (2003) Behaviour and strength of frp-strengthened rc structures: a state-of-the-art review. Proc Inst Civ Eng Struct Build 156(1):51–62. https://doi.org/10.1680/stbu.2003.156.1.5110.1680/stbu.2003.156.1.51 ↗
47. Pham H, Al-Mahaidi R (2004) Experimental investigation into flexural retrofitting of reinforced concrete bridge beams using frp composites. Compos Struct 66(1–4):617–625. https://doi.org/10.1016/j.compstruct.2004.05.01010.1016/j.compstruct.2004.05.010 ↗
48. Majorana CE, Salomoni VA, Mazzucco G, Khoury G (2010) An approach for modelling concrete spalling in finite strains. Math Comput Simul 80(8):1694–1712. https://doi.org/10.1016/j.matcom.2009.05.01110.1016/j.matcom.2009.05.011 ↗
49. Li J, Hao H (2014) Numerical study of concrete spall damage to blast loads. Int J Impact Eng 68:41–55. https://doi.org/10.1016/j.ijimpeng.2014.02.00110.1016/j.ijimpeng.2014.02.001 ↗
50. Min G, Fukuda D, Cho S (2022) 3d numerical analysis method for simulating collapse behavior of rc structures by hybrid fem/dem. Appl Sci 12(6):3073. https://doi.org/10.3390/app1206307310.3390/app12063073 ↗
51. Yuzbasi J (2025) Debris simulation in controlled demolition of tall building structures: Solid model-based approach. Buildings 15(18):3396. https://doi.org/10.3390/buildings1518339610.3390/buildings15183396 ↗
52. Manzoli O, Gamino A, Rodrigues E, Claro G (2012) Modeling of interfaces in two-dimensional problems using solid finite elements with high aspect ratio. Computers & Structures 94:70–82. https://doi.org/10.1016/j.compstruc.2011.12.00110.1016/j.compstruc.2011.12.001 ↗
53. Sánchez M, Manzoli OL, Guimarães LJ (2014) Modeling 3-d desiccation soil crack networks using a mesh fragmentation technique. Comput Geotech 62:27–39. https://doi.org/10.1016/j.compgeo.2014.06.00910.1016/j.compgeo.2014.06.009 ↗
54. Zhan Y, Meschke G (2016) Multilevel computational model for failure analysis of steel-fiber-reinforced concrete structures. J Eng Mech 142(11):04016090. https://doi.org/10.1061/(ASCE)EM.1943-7889.000115410.1061/(ASCE)EM.1943-7889.0001154 ↗
55. Rodrigues EA, Manzoli OL, Bitencourt LA Jr, Bittencourt TN (2016) 2d mesoscale model for concrete based on the use of interface element with a high aspect ratio. Int J Solids Struct 94:112–124. https://doi.org/10.1016/j.ijsolstr.2016.05.00410.1016/j.ijsolstr.2016.05.004 ↗
56. Zhan Y, Meschke G (2017) Adaptive crack modeling with interface solid elements for plain and fiber reinforced concrete structures. Materials 10(7):771. https://doi.org/10.3390/ma1007077110.3390/ma10070771 ↗
57. Manzoli OL, Sánchez M, Maedo M, Hajjat J, Guimaraes LJ (2018) An orthotropic interface damage model for simulating drying processes in soils. Acta Geotech 13:1171–1186. https://doi.org/10.1007/s11440-017-0608-310.1007/s11440-017-0608-3 ↗
58. Cleto PR, Camargo M, Maedo MA, Rodrigues EA, Manzoli OL (2023) Three-dimensional high aspect ratio interface elements for simulating 3d hydraulic fracturing in deformable porous media. Computers & Structures 283:107057. https://doi.org/10.1016/j.compstruc.2023.10705710.1016/j.compstruc.2023.107057 ↗
59. Gimenes M, Rodrigues EA, Bitencourt LA Jr, Manzoli OL (2023) 2d mesoscale modeling of compressive fracture in concrete using a mesh fragmentation technique. Int J Solids Struct 260:112031. https://doi.org/10.1016/j.ijsolstr.2022.11203110.1016/j.ijsolstr.2022.112031 ↗
60. Bonet J, Wood R, Mahaney J, Heywood P (2000) Finite element analysis of air supported membrane structures. Comput Methods Appl Mech Eng 190(5–7):579–595. https://doi.org/10.1016/S0045-7825(99)00428-410.1016/S0045-7825(99)00428-4 ↗
61. Coda HB, Greco M (2004) A simple fem formulation for large deflection 2d frame analysis based on position description. Comput Methods Appl Mech Eng 193(33–35):3541–3557. https://doi.org/10.1016/j.cma.2004.01.00510.1016/j.cma.2004.01.005 ↗
62. Coda HB, Paccola RR (2007) An alternative positional fem formulation for geometrically non-linear analysis of shells: curved triangular isoparametric elements. Comput Mech 40(1):185–200. https://doi.org/10.1007/s00466-006-0094-110.1007/s00466-006-0094-1 ↗
63. Coda HB, Paccola RR (2011) A fem procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3d frames. Finite Elem Anal Des 47(4):319–333. https://doi.org/10.1016/j.finel.2010.11.00110.1016/j.finel.2010.11.001 ↗
64. Coda HB, Paccola RR (2014) A total-lagrangian position-based fem applied to physical and geometrical nonlinear dynamics of plane frames including semi-rigid connections and progressive collapse. Finite Elem Anal Des 91:1–15. https://doi.org/10.1016/j.finel.2014.07.00110.1016/j.finel.2014.07.001 ↗
65. Teodoro CP, Carrazedo R (2024) Nonlinear numerical analysis of corroded reinforced concrete structures using laminated frame elements. Mater Struct 57(5):109. https://doi.org/10.1617/s11527-024-02386-y10.1617/s11527-024-02386-y ↗
66. Oliver J, Cervera M, Manzoli O (1999) Strong discontinuities and continuum plasticity models: the strong discontinuity approach. Int J Plast 15(3):319–351. https://doi.org/10.1016/S0749-6419(98)00073-410.1016/S0749-6419(98)00073-4 ↗
67. Oliver J (2000) On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations. Int J Solids Struct 37(48–50):7207–7229. https://doi.org/10.1016/S0020-7683(00)00196-710.1016/S0020-7683(00)00196-7 ↗
68. Camanho PP, Davila CG, De Moura M (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Compos Mater 37(16):1415–1438. https://doi.org/10.1177/002199830303450510.1177/0021998303034505 ↗
69. Camanho, P.P., Dávila, C.G.: Mixed-mode decohesion finite elements for the simulation of delamination in composite materials. Technical report (2002)
70. Wu EM, Reuter R Jr (1965) Crack extension in fiberglass reinforced plastics. TAM R 27510.21236/AD0613576 ↗
71. Cui W, Wisnom M, Jones M (1992) A comparison of failure criteria to predict delamination of unidirectional glass/epoxy specimens waisted through the thickness. Composites 23(3):158–166. https://doi.org/10.1016/0010-4361(92)90436-X10.1016/0010-4361(92)90436-X ↗
72. Simo JC, Ju J (1987) Strain-and stress-based continuum damage models-i. formulation. Int J Solids Structures 23(7):821–840. https://doi.org/10.1016/0020-7683(87)90083-710.1016/0020-7683(87)90083-7 ↗
73. Chaboche J-L (1992) Damage induced anisotropy: on the difficulties associated with the active/passive unilateral condition. Int J Damage Mech 1(2):148–171. https://doi.org/10.1177/10567895920010020110.1177/105678959200100201 ↗
74. Fichant S, La Borderie C, Pijaudier-Cabot G (1999) Isotropic and anisotropic descriptions of damage in concrete structures. Mechanics of Cohesive-frictional Materials An International Journal on Experiments Modelling and Computation of Materials and Structures 4(4):339–359. https://doi.org/10.1002/(SICI)1099-1484(199907)4:4$$<$$339::AID-CFM65$$>$$3.0.CO;2-J10.1002/(SICI)1099-1484(199907)4:4<339::AID-CFM65>3.3.CO;2-A ↗
75. Hamiel Y, Lyakhovsky V, Agnon A (2004) Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks. Geophys J Int 156(3):701–713. https://doi.org/10.1111/j.1365-246X.2004.02172.x10.1111/j.1365-246X.2004.02172.x ↗
76. Béton CE-I (1993) CEB-FIP Model Code 1990: Design Code. Thomas Telford Publishing, London, UK
77. Winkler BJ (2001) Traglastuntersuchungen von unbewehrten und bewehrten betonstrukturen auf der grundlage eines objektiven werkstoffgesetzes für beton. PhD thesis, Innsbruck University Press
78. Grégoire D, Rojas-Solano LB, Pijaudier-Cabot G (2013) Failure and size effect for notched and unnotched concrete beams. Int J Numer Anal Meth Geomech 37(10):1434–1452. https://doi.org/10.1002/nag.218010.1002/nag.2180 ↗
79. Nooru-Mohamed MB (1993) Mixed-mode fracture of concrete: An experimental approach. PhD thesis, Technische Universiteit Delft - The Netherlands
80. Ballatore E, Carpinteri A, Ferrara G, Melchiorri G (1990) Mixed mode fracture energy of concrete. Eng Fract Mech 35(1–3):145–157. https://doi.org/10.1016/0013-7944(90)90192-J10.1016/0013-7944(90)90192-J ↗