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Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics


In this paper, a semi-discrete model based on peridynamics (PD) for engineered cementitious composites (ECCs) is applied to simulate the fracture behavior of functionally graded ECC (FGECC) beams. This is a new application of PD in ECC. Prior to simulating the crack behavior, the convergence of the PD model for ECC is discussed and the appropriate horizon size \(\delta \) and nonlocal ratio m are obtained, i.e., \(\delta = 1.6\,\hbox {mm}\) and \(m = 4\). In addition, when the bond strain exceeds the elastic limit, a damage variable is introduced into the model, and the model is validated using a simple numerical algorithm. Finally, the dynamic fracture behavior of a two-dimensional FGECC beam under four-point bending is investigated, and the effect of the initial crack location on the fracture behavior is analyzed. Simulation results show that the initial crack location can affect the crack propagation pattern, thereby enabling one to understand the dynamic fracture behavior of ECC structures and guide the engineering practice.

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  1. 1.

    Koizumi M. FGM activities in Japan. Compos B Eng. 1997;28(1–2):1–4.

    Article  Google Scholar 

  2. 2.

    Bobaru F. Designing optimal volume fractions for functionally graded materials with temperature-dependent material properties. J Appl Mech. 2008;74(4):861–74.

    Google Scholar 

  3. 3.

    Li VC, Leung CKY. Steady-state and multiple cracking of short random fiber composites. J Eng Mech. 1992;118(11):2246–64.

    Article  Google Scholar 

  4. 4.

    Li VC. On engineered cementitious composites (ECC): A review of the material and its applications. J Adv Concr Technol. 2003;1(3):215–30.

    Article  Google Scholar 

  5. 5.

    Li VC, Wang S, Wu C. Tensile strain-hardening behavior of polyvinyl alcohol engineered cementitious composite (PVA-ECC). ACI Mater J. 2001;98(5):483–92.

    Google Scholar 

  6. 6.

    Dias CMR Jr, Savastano H, John VM. The FGM concept in the development of fiber cement components. In: AIP Conference Proceedings 2008. vol. 973(1), p. 525–31.

  7. 7.

    Shen B, Hubler M, Paulino GH, et al. Functionally-graded fiber-reinforced cement composite: Processing, microstructure, and properties. Cem Concr Compos. 2008;30(8):663–73.

    Article  Google Scholar 

  8. 8.

    Roesler J, Bordelon A, Gaedicke C, et al. Fracture behavior and properties of functionally graded fiber-reinforced concrete. In: AIP Conference Proceedings 2008. vol. 973(1), p. 513–8.

  9. 9.

    Xu SL, Li QH. Theoretical analysis on bending behavior of functionally graded composite beam crack-controlled by ultrahigh toughness cementitious composites. Sci China Ser E-Technol Sci. 2009;52(2):363–78.

    Article  Google Scholar 

  10. 10.

    Li QH, Xu SL. Experimental investigation and analysis on flexural performance of functionally graded composite beam crack-controlled by ultrahigh toughness cementitious composites. Sci China Ser E-Technol Sci. 2009;52(5):1648–64.

    Article  Google Scholar 

  11. 11.

    Chen ZR. A new enriched finite element method with application to static fracture problems with internal fluid pressure. Int J Appl Mech. 2015;7(3):1550037.

    Article  Google Scholar 

  12. 12.

    Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids. 2000;48(1):175–209.

    MathSciNet  Article  Google Scholar 

  13. 13.

    Silling SA, Askari E. A meshfree method based on the peridynamic model of solid mechanics. Comput Struct. 2005;83(17–18):1526–35.

    Article  Google Scholar 

  14. 14.

    Silling SA. Dynamic fracture modeling with a meshfree peridynamic code. Comput Fluid Solid Mech. 2003;1:641–4.

  15. 15.

    Silling SA, Weckner O, Askari E, et al. Crack nucleation in a peridynamic solid. Int J Fract. 2010;162(1–2):219–27.

    Article  Google Scholar 

  16. 16.

    Foster JT. Dynamic Crack Initiation Toughness: Experiments and peridynamic modeling. Office of Scientific and Technical Information Technical Reports. 2009.

  17. 17.

    Gerstle W, Sau N, Silling SA. Peridynamic modeling of concrete structures. Nucl Eng Des. 2007;237(12–13):1250–8.

    Article  Google Scholar 

  18. 18.

    Huang D, Zhang Q, Qiao PZ. Damage and progressive failure of concrete structures using non-local peridynamic modeling. Sci China Technol Sci. 2011;54(3):591–6.

    Article  Google Scholar 

  19. 19.

    Wang YT, Zhou XP, Shou YD. The modeling of crack propagation and coalescence in rocks under uniaxial compression using the novel conjugated bond-based peridynamics. Int J Mech Sci. 2017;128–129:614–43.

    Article  Google Scholar 

  20. 20.

    Wang YT, Zhou XP, Wang Y, Shou Y. A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids. Int J Solids Struct. 2018;134:89–115.

    Article  Google Scholar 

  21. 21.

    Kou MM, Bi J, Yuan BH, Wang YT. Peridynamic analysis of dynamic fracture behaviors in FGMs with different gradient directions. Struct Eng Mech. 2020;75(3):339–56.

    Google Scholar 

  22. 22.

    Mehrmashhadi J, Chen ZG, Zhao JM, Bobaru F. A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites. Compos Sci Technol. 2019;182:107770.

    Article  Google Scholar 

  23. 23.

    Zhao JM, Chen ZG, Mehrmashhadi J, Bobaru F. A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete. Eng Fract Mech. 2020;229:106969.

    Article  Google Scholar 

  24. 24.

    Zhang Y, Cheng ZQ, Feng H. Dynamic fracture analysis of functional gradient material coating based on the peridynamic method. Coatings. 2019;9(1):62.

    Article  Google Scholar 

  25. 25.

    Huang D, Lu GD, Zhang Q. A peridynamic study on quasi-static deformation and failure. Chin J Comput Mech. 2016;5:657–62.

    Google Scholar 

  26. 26.

    Radtke FKF, Simone A, Sluys LJ. A computational model for failure analysis of fiber reinforced concrete with discrete treatment of fibers. Eng Fract Mech. 2010;77(4):597–620.

    Article  Google Scholar 

  27. 27.

    Kang J, Kim K, Lim YM, Bolander JE. Modeling of fiber-reinforced cement composites: Discrete representation of fiber pullout. Int J Solids Struct. 2014;51(10):1970–9.

    Article  Google Scholar 

  28. 28.

    Delale F, Erdogan F. The crack problem for a non-homogeneous plane, Transactions of the ASME. J Appl Mech. 1983;50(3):609–14.

    Article  Google Scholar 

  29. 29.

    Cai XR. The Basic Mechanical Performance and Strain Hardening Process Theoretical Analysis of Ultra High Toughness Cementitious Composites; 2010.

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This work was supported by the Natural Science Foundation of China (Nos. 11872339, 11472248) and the Natural Science Foundation of Henan Province (No. 182300410221).

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Correspondence to Hu Feng.

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Cheng, Z., Wu, Y., Chu, L. et al. Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics. Acta Mech. Solida Sin. (2021).

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  • Peridynamics
  • Functionally graded ECC structures
  • Semi-discrete models
  • Dynamic fracture