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Clustering-enhanced Lattice discrete particle modeling for quasi-brittle fracture and fragmentation analysis

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Abstract

This study focuses on predicting and quantifying fragmentation phenomena under high impulsive dynamic loading, such as blast, impact, and penetration events, which induce plastic deformation, fracture, and fragmentation in materials. The research addresses the challenge of accurately quantifying fragmentation through individual fragment mass and velocities. To achieve this, the Lattice Discrete Particle Model (LDPM) is utilized to predict failure modes and crack patterns and analyze fragments in reinforced concrete protective structures subjected to dynamic loads. An innovative unsupervised learning clustering technique is developed to identify and characterize fragment mass and velocity. The study demonstrates that the proposed method efficiently and accurately quantifies fragmentation, offering significant speed and efficiency gains while maintaining high fidelity. By combining a high-fidelity physics-based model for fragment formation with advanced geometric algorithms and distance-based approximations, the method accurately characterizes fragment size, position, and velocity. This approach circumvents computational costs associated with simulations across various time scales of fragment generation, trajectory, and secondary impacts. Experimental validation confirms the effectiveness of the proposed method in simulating real-world fragmentation phenomena, making it a valuable tool for applications in materials science, engineering, and beyond. The integrated workflow of LDPM simulations with machine learning clustering also offers an efficient means for structural engineers and designers to develop protective structures for dynamic impulsive loads.

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References

  1. Alanbay B, Batra R (2022) Optimization of blast mitigating sandwich structures with fiber-reinforced face sheets and PVC foam layers as core. Thin-Walled Struct 179:109721

    Article  Google Scholar 

  2. Alloghani M, Al-Jumeily D, Mustafina J et al (2020) A systematic review on supervised and unsupervised machine learning algorithms for data science. In: Supervised and unsupervised learning for data science, pp 3–21

  3. Amoako R, Jha A, Zhong S (2022) Rock fragmentation prediction using an artificial neural network and support vector regression hybrid approach. Mining 2(2):233–247

    Article  Google Scholar 

  4. Bao X, Li B (2010) Residual strength of blast damaged reinforced concrete columns. Int J Impact Eng 37(3):295–308

    Article  Google Scholar 

  5. Beissel S, Gerlach C, Johnson G (2008) A quantitative analysis of computed hypervelocity debris clouds. Int J Impact Eng 35(12):1410–1418

    Article  Google Scholar 

  6. Børvik T, Hanssen A, Langseth M et al (2009) Response of structures to planar blast loads-a finite element engineering approach. Comput Struct 87(9–10):507–520

    Article  Google Scholar 

  7. Chowdhury A, Wilt T (2015) Characterizing explosive effects on underground structures. US Nuclear Regulatory Commission, Office of Nuclear Security and Incident

  8. Colo’ L, Ripepe M, Gurioli L et al (2020) Fragmentation processes during strombolian explosions revealed using particle size distribution mapping. Front Earth Sci 8:356

    Article  Google Scholar 

  9. Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 24(5):603–619

    Article  Google Scholar 

  10. Cullis I, Dunsmore P, Harrison A et al (2014) Numerical simulation of the natural fragmentation of explosively loaded thick walled cylinders. Def Technol 10(2):198–210

    Article  Google Scholar 

  11. Cusatis G (2011) Strain-rate effects on concrete behavior. Int J Impact Eng 38(4):162–170

    Article  Google Scholar 

  12. Cusatis G, Mencarelli A, Pelessone D et al (2011) Lattice discrete particle model (LDPM) for failure behavior of concrete. II: calibration and validation. Cem Concr Compos 33(9):891–905

    Article  Google Scholar 

  13. Cusatis G, Pelessone D, Mencarelli A (2011) Lattice discrete particle model (LDPM) for failure behavior of concrete. I: theory. Cem Concr Compos 33(9):881–890

    Article  Google Scholar 

  14. Cusatis G, Pelessone D, Mencarelli A (2011) Lattice discrete particle model (LDPM) for failure behavior of concrete. I: theory. Cement Concr Compos 33(9):881–890

    Article  Google Scholar 

  15. Day RW (2010) Foundation engineering handbook: design and construction with the 2009 international building code. McGraw-Hill

    Google Scholar 

  16. Dhari RS (2021) A numerical study on cross ply laminates subjected to stray fragments impact loading. Compos Struct 261:113563

    Article  Google Scholar 

  17. Elek P, Jaramaz S (2009) Fragment mass distribution of naturally fragmenting warheads. FME Trans 37(3):129–135

    Google Scholar 

  18. Elshenawy T, Zaky MG, Elbeih A (2022) Experimental and numerical studies of fragmentation shells filled with advanced HMX-plastic explosive compared to various explosive charges. Braz J Chem Eng 1–12

  19. Esna Ashari S, Buscarnera G, Cusatis G (2016) Lattice discrete particle model (LDPM) for pressure-dependent inelasticity in granular rocks

  20. Fan H, Bergel GL, Li S (2016) A hybrid peridynamics–SPH simulation of soil fragmentation by blast loads of buried explosive. Int J Impact Eng 87:14–27

    Article  Google Scholar 

  21. Forquin P, Hild F (2010) A probabilistic damage model of the dynamic fragmentation process in brittle materials. Adv Appl Mech 44:1–72

    Article  Google Scholar 

  22. Grisaro H, Dancygier AN (2015) Numerical study of velocity distribution of fragments caused by explosion of a cylindrical cased charge. Int J Impact Eng 86:1–12

    Article  Google Scholar 

  23. Gubinelli G, Cozzani V (2009) Assessment of missile hazards: identification of reference fragmentation patterns. J Hazard Mater 163(2–3):1008–1018

    Article  Google Scholar 

  24. Guildenbecher DR, Dallman AR, Hall EM et al (2020) Advancing the science of explosive fragmentation and afterburn fireballs though experiments and simulations at the benchtop scale. Technical report, Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Georgia

  25. Han X, Gao J, Fleming M et al (2020) Efficient multiscale modeling for woven composites based on self-consistent clustering analysis. Comput Methods Appl Mech Eng 364:112929

    Article  MathSciNet  Google Scholar 

  26. Hang S (2015) TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):11

    MathSciNet  Google Scholar 

  27. Held M (1990) Fragment mass distribution of he projectiles. Propellants Explos Pyrotech 15(6):254–260

    Article  Google Scholar 

  28. Hirt CW, Amsden AA, Cook J (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253

    Article  Google Scholar 

  29. Kanagala HK, Krishnaiah VJR (2016) A comparative study of k-means, DBSCAN and optics. In: 2016 international conference on computer communication and informatics (ICCCI), IEEE, pp 1–6

  30. Kiakojouri F, Tavakoli HR, Sheidaii MR et al (2022) Numerical analysis of all-steel sandwich panel with drilled i-core subjected to air blast scenarios. Innov Infrastruct Solut 7(5):1–13

    Article  Google Scholar 

  31. Kim K, Kim W, Seo J et al (2022) The amount prediction of concrete fragments after impact using smoothed particle hydrodynamics. Eng Fail Anal 131:105882

    Article  Google Scholar 

  32. Kong X, Wu W, Li J et al (2013) A numerical investigation on explosive fragmentation of metal casing using smoothed particle hydrodynamic method. Mater Des 51:729–741

    Article  Google Scholar 

  33. Kong X, Fang Q, Chen L et al (2018) A new material model for concrete subjected to intense dynamic loadings. Int J Impact Eng 120:60–78

    Article  Google Scholar 

  34. Kumar KM, Reddy ARM (2016) A fast DBSCAN clustering algorithm by accelerating neighbor searching using groups method. Pattern Recognit 58:39–48

    Article  Google Scholar 

  35. Kumar V, Kartik K, Iqbal M (2020) Experimental and numerical investigation of reinforced concrete slabs under blast loading. Eng Struct 206:110125

    Article  Google Scholar 

  36. Lee H, Kim J, Jung C et al (2020) A deep learning-based fragment detection approach for the arena fragmentation test. Appl Sci 10(14):4744

    Article  Google Scholar 

  37. Lee J, Lacy TE Jr, Pittman CU Jr (2021) Lightning mechanical damage prediction in carbon/epoxy laminates using equivalent air blast overpressure. Compos B Eng 212:108649

    Article  Google Scholar 

  38. Leppänen J (2005) Experiments and numerical analyses of blast and fragment impacts on concrete. Int J Impact Eng 31(7):843–860

    Article  Google Scholar 

  39. Li E, Yang F, Ren M et al (2021) Prediction of blasting mean fragment size using support vector regression combined with five optimization algorithms. J Rock Mech Geotech Eng 13(6):1380–1397

    Article  Google Scholar 

  40. Li F, Yuan H, Liu H (2021) Implementation of metal ductile damage criteria in Abaqus Fea. J Phys Conf Ser 012058

  41. Li W, Zhou X, Carey JW et al (2018) Multiphysics lattice discrete particle modeling (m-LDPM) for the simulation of shale fracture permeability. Rock Mech Rock Eng 51(12):3963–3981

    Article  Google Scholar 

  42. Liang SC, Li Y, Chen H et al (2013) Research on the technique of identifying debris and obtaining characteristic parameters of large-scale 3D point set. Int J Impact Eng 56:27–31

    Article  Google Scholar 

  43. Lin X, Zhang Y, Hazell PJ (2014) Modelling the response of reinforced concrete panels under blast loading. Mater Des 1980–2015(56):620–628

    Article  Google Scholar 

  44. Liu Z, Bessa M, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319–341

    Article  MathSciNet  Google Scholar 

  45. Luccioni B, Isla F, Codina R et al (2018) Experimental and numerical analysis of blast response of high strength fiber reinforced concrete slabs. Eng Struct 175:113–122

    Article  Google Scholar 

  46. Lyu Y, Pathirage M, Nguyen HT et al (2023) Dissipation mechanisms of crack-parallel stress effects on fracture process zone in concrete. J Mech Phys Solids 181:105439

    Article  MathSciNet  Google Scholar 

  47. Lyu Y, Pathirage M, Ramyar E et al (2023) Machine learning meta-models for fast parameter identification of the lattice discrete particle model. Comput Mech 1–20

  48. Morales-Alonso G, Cendón DA, Gálvez F et al (2011) Blast response analysis of reinforced concrete slabs: experimental procedure and numerical simulation. J Appl Mech 78(5)

  49. Nyström U, Gylltoft K (2009) Numerical studies of the combined effects of blast and fragment loading. Int J Impact Eng 36(8):995–1005

    Article  Google Scholar 

  50. Pioli L, Harris AJ (2019) Real-time geophysical monitoring of particle size distribution during volcanic explosions at Stromboli volcano (Italy). Front Earth Sci 7:52

    Article  Google Scholar 

  51. Raj C (2017) Comparison of k means k medoids DBSCAN algorithms using DNA microarray dataset. Int J Comput Appl Math 12(1):1819–4966

    Google Scholar 

  52. Randles P, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139(1–4):375–408

    Article  MathSciNet  Google Scholar 

  53. Ren B, Fan H, Bergel GL et al (2015) A peridynamics-SPH coupling approach to simulate soil fragmentation induced by shock waves. Comput Mech 55:287–302

    Article  MathSciNet  Google Scholar 

  54. Rigby S, Fuller B, Tyas A (2018) Validation of near-field blast loading in ls-dyna. In: Proceedings of the 5th international conference on protective structures (ICPS5), Poznan, Poland

  55. Sakong J, Woo SC, Kim TW (2019) Determination of impact fragments from particle analysis via smoothed particle hydrodynamics and k-means clustering. Int J Impact Eng 134:103387

    Article  Google Scholar 

  56. Schauffert EA, Cusatis G (2012) Lattice discrete particle model for fiber-reinforced concrete. I: theory. J Eng Mech 138(7):826–833

    Article  Google Scholar 

  57. Schauffert EA, Cusatis G, Pelessone D et al (2012) Lattice discrete particle model for fiber-reinforced concrete. II: tensile fracture and multiaxial loading behavior. J Eng Mech 138(7):834–841

    Article  Google Scholar 

  58. Schubert E, Sander J, Ester M et al (2017) DBSCAN revisited, revisited: why and how you should (still) use DBSCAN. ACM Trans Database Syst TODS 42(3):1–21

    Article  MathSciNet  Google Scholar 

  59. Starczewski A, Goetzen P, Er MJ (2020) A new method for automatic determining of the DBSCAN parameters. J Artif Intell Soft Comput Res 10(3):209–221

    Article  Google Scholar 

  60. Systèmes D (2009) Abaqus analysis user’s manual v6. 9. Simulia Corp, Providence, RI

  61. Tong K, Wu Y (2022) Deep learning-based detection from the perspective of small or tiny objects: a survey. Image Vis Comput 104471

  62. Troemner MA (2022) Multiscale lattice discrete particle modeling of concrete: micromechanics, scaling, dynamics. Ph.D. thesis, Northwestern University

  63. Tu Z, Lu Y (2009) Evaluation of typical concrete material models used in hydrocodes for high dynamic response simulations. Int J Impact Eng 36(1):132–146

    Article  Google Scholar 

  64. Vaghefi M, Mobaraki B (2021) Evaluation of the effect of explosion on the concrete bridge deck using LS-DYNA. Int Rev Civ Eng 12:135

    Google Scholar 

  65. Vargas L, Hokanson J, Rindner R (1981) Explosive fragmentation of dividing walls. Technical report, Southwest Research Inst San Antonio TX

  66. Wang W, Zhang D, Lu F et al (2013) Experimental study and numerical simulation of the damage mode of a square reinforced concrete slab under close-in explosion. Eng Fail Anal 27:41–51

    Article  Google Scholar 

  67. Wu J, Zhou Y, Zhang R et al (2020) Numerical simulation of reinforced concrete slab subjected to blast loading and the structural damage assessment. Eng Fail Anal 118:104926

    Article  Google Scholar 

  68. Yang F, Veljkovic M, Liu Y (2020) Ductile damage model calibration for high-strength structural steels. Constr Build Mater 263:120632

    Article  Google Scholar 

  69. Yang T, Ma H, Weng L et al (2022) Fragmentation analyses of rocks under high-velocity impacts using the combined finite-discrete element simulation. Front Earth Sci 10:998521

    Article  Google Scholar 

  70. Yeom GS (2022) Numerical simulation of conical and linear-shaped charges using an Eulerian elasto-plastic multi-material multi-phase flow model with detonation. Materials 15(5):1700

    Article  Google Scholar 

  71. Yi C, Nordlund E, Zhang P et al (2021) Numerical modeling for a simulated rockburst experiment using LS-DYNA. Undergr Space 6(2):153–162

    Article  Google Scholar 

  72. Zaker T (1975) Fragment and debris hazards. Technical report, Department of Defense Explosives Safety Board Alexandria VA

  73. Zecevic B, Terzic J, Catovic A et al (2011) Characterization of distribution parameters of fragment mass and number for conventional projectiles. NTREM, Czech Republic, pp 1026–1039

  74. Zhang T, Ramakrishnan R, Livny M (1996) Birch: an efficient data clustering method for very large databases. ACM SIGMOD Rec 25(2):103–114

    Article  Google Scholar 

  75. Zhang X, Guanghui J, Huang H (2011) Fragment identification and statistics method of hypervelocity impact SPH simulation. Chin J Aeronaut 24(1):18–24

    Article  Google Scholar 

  76. Zhao C, Chen J (2013) Damage mechanism and mode of square reinforced concrete slab subjected to blast loading. Theoret Appl Fract Mech 63:54–62

    Article  Google Scholar 

  77. Zhao H, Bi Z, Ceng X et al (2021) Machine learning-based design of software to calculate the fragmentation power of the combat section of an explosive killing shell. In: ICMLCA 2021; 2nd international conference on machine learning and computer application, VDE, pp 1–5

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, 60208, USA

    Yuhui Lyu, Matthew Troemner, Erol Lale, Elham Ramyar, Wing Kam Liu & Gianluca Cusatis

  2. Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

    Wing Kam Liu

  3. Co-Founder of HIDENN-AI, LLC, Evanston, IL, USA

    Wing Kam Liu

  4. Cusatis Computational Services, Inc, Wilmette, IL, USA

    Matthew Troemner

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  1. Yuhui Lyu
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  2. Matthew Troemner
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  3. Erol Lale
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  4. Elham Ramyar
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  5. Wing Kam Liu
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  6. Gianluca Cusatis
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Correspondence to Gianluca Cusatis.

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LDPM geometry parameters and material parameters

LDPM geometry parameters and material parameters

See Tables 3 and 4.

Table 3 Values of parameters governing the generation of concrete mesostructure
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Table 4 LDPM material parameters used in simulations
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Lyu, Y., Troemner, M., Lale, E. et al. Clustering-enhanced Lattice discrete particle modeling for quasi-brittle fracture and fragmentation analysis. Comput Mech (2024). https://doi.org/10.1007/s00466-024-02485-1

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