Skip to main content
SpringerLink
Log in

Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The non-ordinary state-based peridynamic (NOSB PD) model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics. In the present work, we first develop an NOSB PD model corresponding to the Johnson–Holmquist II (JH-2) constitutive damage model, which can describe the severe damage of concrete under intense impact compression. Besides, the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic (BA-NOSB PD) model is adopted to remove the oscillation. Then, the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation. Furthermore, concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated. The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis, illustrating the approach can well simulate and analyze the concrete spalling discontinuities.

Graphic Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31

Similar content being viewed by others

References

  1. Song, Y., Yan, J., Li, S., et al.: Peridynamic modeling and simulation of ice craters by impact. Comput. Model. Eng. Sci. 121, 465–492 (2019)

    Google Scholar 

  2. Ai, D., Zhao, Y., Wang, Q., et al.: Experimental and numerical investigation of crack propagation and dynamic properties of rock in SHPB indirect tension test. Int. J. Impact Eng 126, 135–146 (2019)

    Article  Google Scholar 

  3. Zhang, Y., Pan, G., Zhang, Y., et al.: A multi-physics peridynamics-DEM-IB-CLBM framework for the prediction of erosive impact of solid particles in viscous fluids. Comput. Methods Appl. Mech. Eng. 352, 675–690 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhou, G., Hillman, M.: A non-ordinary state-based Godunov-peridynamics formulation for strong shocks in solids. Comput. Part. Mech. 7, 365–375 (2020)

    Article  Google Scholar 

  5. Guo, J.S., Gao, W.C.: Study of the Kalthoff-Winkler experiment using an ordinary state-based peridynamic model under low velocity impact. Adv. Mech. Eng. 11, 168781401985256 (2019)

    Article  Google Scholar 

  6. Liu, R., Yan, J., Li, S.: Modeling and simulation of ice–water interactions by coupling peridynamics with updated Lagrangian particle hydrodynamics. Comput. Part. Mech. 7, 241–255 (2020)

    Article  Google Scholar 

  7. Lai, X., Ren, B., Fan, H., et al.: Peridynamics simulations of geomaterial fragmentation by impulse loads. Int. J. Numer. Anal. Meth. Geomech. 39, 1304–1330 (2015)

    Article  Google Scholar 

  8. Lai, X., Liu, L., Li, S., et al.: A non-ordinary state-based peridynamics modeling of fractures in quasi-brittle materials. Int. J. Impact Eng 111, 130–146 (2018)

    Article  Google Scholar 

  9. Silling, S.A., Parks, M.L., Kamm, J.R., et al.: Modeling shockwaves and impact phenomena with Eulerian peridynamics. Int. J. Impact Eng 107, 47–57 (2017)

    Article  Google Scholar 

  10. Gu, X., Zhang, Q., Huang, D., et al.: Wave dispersion analysis and simulation method for concrete SHPB test in peridynamics. Eng. Fract. Mech. 160, 124–137 (2016)

    Article  Google Scholar 

  11. Gu, X., Zhang, Q.: A modified conjugated bond-based peridynamic analysis for impact failure of concrete gravity dam. Meccanica 55, 547–566 (2020)

    Article  MathSciNet  Google Scholar 

  12. Chu, B., Liu, Q., Liu, L., et al.: A rate-dependent peridynamic model for the dynamic behavior of ceramic materials. Comput. Model. Eng. Sci. 124, 151–178 (2020)

    Google Scholar 

  13. Shen, F., Yu, Y., Zhang, Q., et al.: Hybrid model of peridynamics and finite element method for static elastic deformation and brittle fracture analysis. Eng. Anal. Bound. Elem. 113, 17–25 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu, L., Huang, D., Xu, Y., et al.: A non-ordinary state-based peridynamic formulation for failure of concrete subjected to impacting loads. Comput. Model. Eng. Sci. 118, 561–581 (2019)

    Google Scholar 

  15. Zhou, X., Wang, Y., Shou, Y., et al.: A novel conjugated bond linear elastic model in bond-based peridynamics for fracture problems under dynamic loads. Eng. Fract. Mech. (2017). https://doi.org/10.1016/j.engfracmech.2017.07.031

    Article  Google Scholar 

  16. Zhou, X., Wang, Y., Qian, Q.: Numerical simulation of crack curving and branching in brittle materials under dynamic loads using the extended non-ordinary state-based peridynamics. Eur. J. Mech. 60, 277–299 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Silling, S.A.: Stability of peridynamic correspondence material models and their particle discretizations. Comput. Methods Appl. Mech. Eng. 322, 42–57 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Li, P., Hao, Z.M., Zhen, W.Q.: A stabilized non-ordinary state-based peridynamic model. Comput. Methods Appl. Mech. Eng. 339, 262–280 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wan, J., Chen, Z., Chu, X., et al.: Improved method for zero-energy mode suppression in peridynamic correspondence model. Acta. Mech. Sin. 35, 1021–1032 (2019)

    Article  MathSciNet  Google Scholar 

  20. Chowdhury, S.R., Roy, P., Roy, D., et al.: A modified peridynamics correspondence principle: removal of zero-energy deformation and other implications. Comput. Methods Appl. Mech. Eng. 346, 530–549 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  21. Madenci, E., Dorduncu, M., Phan, N., et al.: Weak form of bond-associated non-ordinary state-based peridynamics free of zero energy modes with uniform or non-uniform discretization. Eng. Fract. Mech. 218, 106613 (2019)

    Article  Google Scholar 

  22. Gu, X., Zhang, Q., Madenci, E., et al.: Possible causes of numerical oscillations in non-ordinary state-based peridynamics and a bond-associated higher-order stabilized model. Comput. Methods Appl. Mech. Eng. 357, 112592 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yaghoobi, A., Chorzepa, M.G.: Higher-order approximation to suppress the zero-energy mode in non-ordinary state-based peridynamics. Comput. Struct. 188, 63–79 (2017)

    Article  Google Scholar 

  24. Cui, H., Li, C., Zheng, H.: The generation of non-ordinary state-based peridynamics by the weak form of the peridynamic method. Math. Mech. Solids 25, 1544–1567 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  25. Luo, J., Sundararaghavan, V.: Stress-point method for stabilizing zero-energy modes in non-ordinary state-based peridynamics. Int. J. Solids Struct. 150, 197–207 (2018)

    Article  Google Scholar 

  26. Gu, X., Zhang, Q., Madenci, E.: Non-ordinary state-based peridynamic simulation of elastoplastic deformation and dynamic cracking of polycrystal. Eng. Fract. Mech. 218, 106568 (2019)

    Article  Google Scholar 

  27. Gu, X., Zhang, Q., Yu, Y.: An effective way to control numerical instability of a nonordinary state-based peridynamic elastic model. Math. Probl. Eng. Theory Methods Appl. (2017). https://doi.org/10.1155/2017/1750876

    Article  MATH  Google Scholar 

  28. Gu, X., Madenci, E., Zhang, Q.: Revisit of non-ordinary state-based peridynamics. Eng. Fract. Mech. 190, 31–52 (2018)

    Article  Google Scholar 

  29. Li, H., Zheng, Y.G., Zhang, Y.X., et al.: Large deformation and wrinkling analyses of bimodular structures and membranes based on a peridynamic computational framework. Acta. Mech. Sin. 35, 1226–1240 (2019)

    Article  MathSciNet  Google Scholar 

  30. Wang, L.: Stress Wave Foundation (In Chinese). National Defense Industry Press, Beijing (2005)

    Google Scholar 

  31. Zhang, L., Hu, S., Chen, D.X., et al.: An experimental technique for spalling of concrete. Exp. Mech. 49, 523–532 (2009)

    Article  Google Scholar 

  32. Hu, S.S., Zhang, L., Wu, H.J., et al.: Experimental study on spalling strength of concrete. Eng. Mech. 21, 128–132 (2004)

    Google Scholar 

  33. Klepaczko, J.R., Brara, A.: An experimental method for dynamic tensile testing of concrete by spalling. Int. J. Impact Eng 25, 387–409 (2001)

    Article  Google Scholar 

  34. Lu, Z., Wang, Z.: Dispersion characteristics of peridynamics method and its application to spalling analysis of rock (in chinese). J. Harbin Inst. Technol. (2016)

  35. Xue, D.: Preliminary Investigation on Spall Fracture (In Chinese). Wuhan University of Technology, Wuhan (2016)

    Google Scholar 

  36. Liao, L.: The Numerical Simulation of Dynamic Indirect Tensile and Spalling Test About Concrete (In Chinese). Hefei University of Technology, Hefei (2016)

    Google Scholar 

  37. Forquin, P., Erzar, B.: Dynamic fragmentation process in concrete under impact and spalling tests. Int. J. Fract. 163, 193–215 (2010)

    Article  MATH  Google Scholar 

  38. Khosravani, M.R., Wagner, P., Frohlich, D., et al.: Dynamic fracture investigations of ultra-high performance concrete by spalling tests. Eng. Struct. 201, 109844 (2019)

    Article  Google Scholar 

  39. Piscesa, B., Attard, M.M., Prasetya, D., et al.: Modeling cover spalling behavior in high strength reinforced concrete columns using a plasticity-fracture model. Eng. Struct. 196, 109336 (2019)

    Article  Google Scholar 

  40. Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  41. Silling, S.A., Epton, M.A., Weckner, O., et al.: Peridynamic states and constitutive modeling. J. Elast. 88, 151–184 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. Madenci, E., Oterkus, E.: Peridynamic theory and its applications to diffusion equation. Peridyn. Theory Appl. (2014). https://doi.org/10.1007/978-1-4614-8465-3

    Article  MATH  Google Scholar 

  43. Bobaru, F., Foster, J.T., Geubelle, P.H., et al.: Handbook of Peridynamic Modeling. CRC Press, Boca Raton (2016)

    Book  MATH  Google Scholar 

  44. Silling, S.A., Askari, E.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83, 1526–1535 (2005)

    Article  Google Scholar 

  45. Warren, T.L., Silling, S.A., Askari, A., et al.: A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Int. J. Solids Struct. 46, 1186–1195 (2009)

    Article  MATH  Google Scholar 

  46. Breitenfeld, M.S., Geubelle, P.H., Weckner, O., et al.: Non-ordinary state-based peridynamic analysis of stationary crack problems. Comput. Methods Appl. Mech. Eng. 272, 233–250 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  47. Chen, H.: Bond-associated deformation gradients for peridynamic correspondence model. Mech. Res. Commun. 90, 34–41 (2018)

    Article  Google Scholar 

  48. Chen, H., Spencer, B.W.: Peridynamic bond-associated correspondence model: stability and convergence properties. Int. J. Numer. Methods Eng. 117, 713–727 (2019)

    Article  MathSciNet  Google Scholar 

  49. Foster, J.T., Silling, S.A., Chen, W.: An energy based failure criterion for use with peridynamic states. Int. J. Multiscale Comput. Eng. 9, 675–688 (2015)

    Article  Google Scholar 

  50. Underwood, P.: Dynamic Relaxation; Computational Method for Transient Analysis. North Holland, Amsterdam (1983)

    MATH  Google Scholar 

  51. Parks, M.L., Lehoucq, R.B., Plimpton, S.J., et al.: Implementing peridynamics within a molecular dynamics code. Comput. Phys. Commun. 179, 777–783 (2008)

    Article  MATH  Google Scholar 

  52. Parks, M.L., Seleson, P., Plimpton, S.J. et al.: Peridynamics with LAMMPS: A User Guide. Version 0.3 Beta (2011)

  53. Johnson, G.R., Holmquist, T.J.: An improved computational constitutive model for brittle materials. AIP Conference Proceedings, pp. 981–984 (1994)

  54. Chen, Z., Bakenhus, D., Bobaru, F.: A constructive peridynamic kernel for elasticity. Comput. Methods Appl. Mech. Eng. 311, 356–373 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  55. Huang, Z.: Revisiting the peridynamic motion equation due to characterization of boundary conditions. Acta. Mech. Sin. 35, 972–980 (2019)

    Article  MathSciNet  Google Scholar 

  56. Gu, X., Zhang, Q., Madenci, E.: Refined bond-based peridynamics for thermal diffusion. Eng. Comput. 36, 2557–2587 (2019)

    Article  Google Scholar 

  57. Hiermaier, S.: Improvements to the Prototype Micro-brittle Model of Peridynamics. Springer, Berlin (2015)

    MATH  Google Scholar 

  58. Shojaei, A., Mossaiby, F., Zaccariotto, M., et al.: An adaptive multi-grid peridynamic method for dynamic fracture analysis. Int. J. Mech. Sci. 144, 600–617 (2018)

    Article  Google Scholar 

  59. Gu, X., Zhang, Q., Xia, X.: Voronoi-based peridynamics and cracking analysis with adaptive refinement. Int. J. Numer. Meth. Eng. 112, 2087–2109 (2017)

    Article  MathSciNet  Google Scholar 

  60. Wang, G.: Dynamic Response and Damage Mechanism of Concrete Gravity Dams Under Extreme Loadings (In Chinese). Tianjin University, Tianjin (2014)

    Google Scholar 

  61. Chai, C.: Study on the Mechanism of Penetration into Concrete of Nose Headed Projectile (In Chinese). Beijing Institute of Technology, Beijing (2014)

    Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Fundamental Research Funds for the Central Universities (Grant B200202231), the National Natural Science Foundation of China (Grants 11932006, 11672101, U1934206, and 12002118), the National Key Research & Development Plan of China (Grants 2018YFC0406703 and 2017YFC1502603), and the China Postdoctoral Science Foundation (Grant 2019M651667).

Author information

Author notes

  1. Siyang Yang and Xin Gu shared the First authorship.

Authors and Affiliations

  1. Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

    Siyang Yang, Xin Gu, Qing Zhang & Xiaozhou Xia

Authors
  1. Siyang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xin Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaozhou Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qing Zhang.

Additional information

Executive Editor: Jian-Xiang Wang

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, S., Gu, X., Zhang, Q. et al. Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete. Acta Mech. Sin. 37, 1104–1135 (2021). https://doi.org/10.1007/s10409-021-01055-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-021-01055-5

Keywords

Search

Navigation