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Adaptive multi-scale beam lattice method for competitive trans-scale crack growth simulation of heterogeneous concrete-like materials

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Abstract

In order to overcome the shortcomings of traditional pure macro- and meso-scale crack growth simulation method, here an adaptive multi-scale beam lattice method (AMBLM) is developed to simulate trans-scale crack growth process from meso-scale to macro-scale for quasi-brittle heterogeneous concrete-like materials with low computation cost. In the trans-scale crack growth simulation, dangerous regions can be automatically found and the meso-scale model is then re-modeled in the found region, which can ensure continuous changes in the adaptive multi-scale modeling due to cracking. In this way, the meso-scale simulation is only implemented in the dangerous region of crack growth paths, and macro-scale simulation is implemented in other regions. This can improve computational efficiency of the developed method significantly. In order to verify the developed AMBLM, the trans-scale crack growth process of two concrete specimens are simulated. Then the simulation results are compared with experimental results, which show that the developed AMBLM is effective. In addition, the simulation results are also compared with the computation results obtained from pure meso-scale simulation. The results show that AMBLM has very high precision and superior computational efficiency on multi-scale crack growth simulation of quasi-brittle concrete-like materials.

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References

  • Azadi H, Khoei AR (2011) Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing. Int J Numer Meth Eng 85(8):1017–1048

    Article  Google Scholar 

  • Belytschko T, Chen H, Xu J et al (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Meth Eng 58(12):1873–1905

    Article  Google Scholar 

  • Cervera M, Chiumenti M (2006) Smeared crack approach: back to the original track. Int J Numer Anal Meth Geomech 30(12):1173–1199

    Article  Google Scholar 

  • Challamel N, Lanos C, Casandjian C (2005) Creep damage modelling for quasi-brittle materials. Eur J Mech A 24(4):593–613

    Article  Google Scholar 

  • Cook AC, Vel SS, Johnson SE (2018) Pervasive cracking of heterogeneous brittle materials using a multi-directional smeared crack band model. Int J Mech Sci 149:459–474

    Article  Google Scholar 

  • Deng J, Gu D (2011) On a statistical damage constitutive model for rock materials. Comput Geosci 37(2):122–128

    Article  Google Scholar 

  • Fish J, Shek K (2000) Multiscale analysis of composite materials and structures. Compos Sci Technol 60(12–13):2547–2556

    Article  Google Scholar 

  • Ghosh S, Paquet D (2013) Adaptive concurrent multi-level model for multi-scale analysis of ductile fracture in heterogeneous aluminum alloys. Mech Mater 65:12–34

    Article  Google Scholar 

  • Ghosh S, Lee K, Moorthy S (1995) Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. Int J Solids Struct 32(1):27–62

    Article  Google Scholar 

  • Ghosh S, Bai J, Raghavan P (2007) Concurrent multi-level model for damage evolution in microstructurally debonding composites. Mech Mater 39(3):241–266

    Article  Google Scholar 

  • Gitman IM, Askes H, Sluys LJ (2008) Coupled-volume multi-scale modelling of quasi-brittle material. Eur J Mech A 27(3):302–327

    Article  Google Scholar 

  • Gu Q, Wang L, Li Y et al (2019) Multi-scale response sensitivity analysis based on direct differentiation method for concrete structures. Compos B Eng 157:295–304

    Article  Google Scholar 

  • Hentz S, Daudeville L, Donzé FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719

    Google Scholar 

  • Jiangjiang Y, Guodong L, Zhengyi R et al (2019) Mixed-mode I–II mesoscale fracture behavior of concrete determined by the realistic aggregate numerical model. Constr Build Mater 226:802–817

    Article  Google Scholar 

  • Jin L, Wang T, Jiang X et al (2019) Size effect in shear failure of RC beams with stirrups: simulation and formulation. Eng Struct 199:109573

    Article  Google Scholar 

  • Johnson CV, Chen J, Hasparyk NP et al (2017) Fracture properties of the alkali silicate gel using microscopic scratch testing. Cement Concr Compos 79:71–75

    Article  CAS  Google Scholar 

  • Leong AFT, Robinson AK, Fezzaa K et al (2018) Quantitative in situ studies of dynamic fracture in brittle solids using dynamic X-ray phase contrast imaging. Exp Mech 58(9):1423–1437

    Article  Google Scholar 

  • Li G, Tang CA, Liang ZZ (2017) Development of a parallel FE simulator for modeling the whole trans-scale failure process of rock from meso-to engineering-scale. Comput Geosci 98:73–86

    Article  Google Scholar 

  • Li Q, Zhao G, Lian J et al (2019) Further development of the distinct lattice spring model for quasi-brittle crack propagation in concrete and its application in underground engineering. Tunn Undergr Space Technol 92:103061

    Article  Google Scholar 

  • Liu Z, Chen W, Zhang Y et al (2016) A three-dimensional multi-scale method to simulate the ion transport behavior of cement-based materials. Constr Build Mater 120:494–503

    Article  CAS  Google Scholar 

  • Lloberas-Valls O, Everdij F, Rixen D et al (2012) Concurrent multiscale analysis of heterogeneous materials. Delft Univ Technol 2:3mE

    Google Scholar 

  • Meng QX, Wang HL, Xu WY et al (2019) Multiscale strength reduction method for heterogeneous slope using hierarchical FEM/DEM modeling. Comput Geotech 115:103164

    Article  Google Scholar 

  • Mukherjee B, Dillard DA, Moore RB et al (2016) Debonding of confined elastomeric layer using cohesive zone model. Int J Adhes Adhes 66:114–127

    Article  CAS  Google Scholar 

  • Nader C, Rossi P, Tailhan JL (2019) Multi-scale strategy for modeling macrocracks propagation in reinforced concrete structures. Cement Concr Compos 99:262–274

    Article  CAS  Google Scholar 

  • Oden JT, Zohdi TI (1997) Analysis and adaptive modeling of highly heterogeneous elastic structures. Comput Methods Appl Mech Eng 148(3–4):367–391

    Article  Google Scholar 

  • Oliver-Leblond C (2019) Discontinuous crack growth and toughening mechanisms in concrete: a numerical study based on the beam-particle approach. Eng Fract Mech 207:1–22

    Article  Google Scholar 

  • Raghavan P, Ghosh S (2004) Concurrent multi-scale analysis of elastic composites by a multi-level computational model. Comput Methods Appl Mech Eng 193(6–8):497–538

    Article  Google Scholar 

  • Roca D, Lloberas-Valls O, Cante J et al (2018) A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling. Comput Methods Appl Mech Eng 330:415–446

    Article  Google Scholar 

  • Slobbe AT, Hendriks MAN, Rots JG (2014) Smoothing the propagation of smeared cracks. Eng Fract Mech 132:147–168

    Article  Google Scholar 

  • Stoxreiter T, Gehwolf P, Galler R (2019) Alternative approaches for the determination of unconfined rock deformation and strength properties. Rock Mech Rock Eng 53:1–23

    Google Scholar 

  • Suchorzewski J, Tejchman J, Nitka M (2018) Experimental and numerical investigations of concrete behaviour at meso-level during quasi-static splitting tension. Theoret Appl Fract Mech 96:720–739

    Article  Google Scholar 

  • Sun B (2020) A computational method for two/three dimensional competitive fracture process simulation of rock-like materials due to cracking. Arab J Geosci 13:1031

    Article  Google Scholar 

  • Sun B, Li Z (2015) Adaptive image-based method for integrated multi-scale modeling of damage evolution in heterogeneous concrete. Comput Struct 152:66–81

    Article  Google Scholar 

  • Sun B, Li Z (2015) Adaptive concurrent multi-scale FEM for trans-scale damage evolution in heterogeneous concrete. Comput Mater Sci 99:262–273

    Article  Google Scholar 

  • Sun B, Li Z (2016) Multi-scale modeling and trans-level simulation from material meso-damage to structural failure of reinforced concrete frame structures under seismic loading. J Comput Scie 12:38–50

    Article  Google Scholar 

  • Sun B, Li Z (2016) Adaptive concurrent three-level multiscale simulation for trans-scale process from material mesodamage to structural failure of concrete structures. Int J Damage Mech 25(5):750–769

    Article  CAS  Google Scholar 

  • Sun B, Wang X, Li Z (2015) Meso-scale image-based modeling of reinforced concrete and adaptive multi-scale analyses on damage evolution in concrete structures. Comput Mater Sci 110:39–53

    Article  Google Scholar 

  • Sun X, Gao Z, Cao P et al (2019) Fracture performance and numerical simulation of basalt fiber concrete using three-point bending test on notched beam. Constr Build Mater 225:788–800

    Article  Google Scholar 

  • Sun B, Zheng Y, Li Z et al (2020) Random beam lattice modeling method for catastrophic crack growth simulation of brittle-like materials. Constr Build Mater 244:118396

    Article  Google Scholar 

  • Sun B, Huang X, Zheng Y et al (2020) Multi-scale lattice method for mesoscopic crack growth simulation of concrete structures. Theor Appl Fract Mech 106:102475

    Article  Google Scholar 

  • Terada K, Hori M, Kyoya T et al (2000) Simulation of the multi-scale convergence in computational homogenization approaches. Int J Solids Struct 37(16):2285–2311

    Article  Google Scholar 

  • Thomas DL, Wilson JM, Wilson RR (1973) Timoshenko beam finite elements. J Sound Vib 31(3):315–330

    Article  Google Scholar 

  • Unger JF, Eckardt S (2011) Multiscale modeling of concrete. Arch Comput Methods Eng 18(3):341

    Article  Google Scholar 

  • Vernerey FJ, Kabiri M (2012) An adaptive concurrent multiscale method for microstructured elastic solids. Comput Methods Appl Mech Eng 241:52–64

    Article  Google Scholar 

  • Winkler B, Hofstetter G, Niederwanger G (2001) Experimental verification of a constitutive model for concrete cracking. Proc Insti Mech Eng Part L 215(2):75–86

    Google Scholar 

  • Wohlmuth BI (2000) A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J Num Anal 38(3):989–1012

    Article  Google Scholar 

  • Xu Z, Zhang G, Chen Z et al (2018) Elastic vortices and thermally-driven cracks in brittle materials with peridynamics. Int J Fract 209(1–2):203–222

    Article  Google Scholar 

  • Yang D, He X, Yi S et al (2019) An improved ordinary state-based peridynamic model for cohesive crack growth in quasi-brittle materials. Int J Mech Sci 153:402–415

    Article  Google Scholar 

  • Yang ZJ, Li BB, Wu JY (2019) X-ray computed tomography images based phase-field modeling of mesoscopic failure in concrete. Eng Fract Mech 208:151–170

    Article  Google Scholar 

  • Yun K, Wang Z, Chang M et al (2019) A computational methodology for simulating quasi-brittle fracture problems. Comput Struct 215:65–79

    Article  Google Scholar 

  • Zhang X, Bui TQ (2015) A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures. Eng Comput 32(2):473–497

    Article  Google Scholar 

  • Zhou J, Wei J, Yang T et al (2018) Damage analysis of rock mass coupling joints, water and microseismicity. Tunn Undergr Space Technol 71:366–381

    Article  Google Scholar 

  • Zohdi T, Wriggers P (1999) A domain decomposition method for bodies with heterogeneous microstructure based on material regularization. Int J Solids Struct 36(17):2507–2525

    Article  Google Scholar 

Download references

Acknowledgements

The works described in this paper are financially supported by National Natural Science Foundation of China (Grant No. 52008104) and National Program on Key R&D Project of China (Grant No. 2020YFB2103500-3). The authors are very grateful to the reviewers and editor for their constructive comments and suggestions, which helped the authors to improve their paper significantly.

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  1. Jiangsu Key Laboratory of Engineering Mechanics, Department of Engineering Mechanics, Southeast University, Nanjing, 210096, China

    Bin Sun

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Sun, B. Adaptive multi-scale beam lattice method for competitive trans-scale crack growth simulation of heterogeneous concrete-like materials . Int J Fract 228, 85–101 (2021). https://doi.org/10.1007/s10704-021-00519-w

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