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3D implementation of push-out test in ABAQUS using the phase-field method

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Abstract

The phase-field method (PFM) localizes the damaged and broken material in concrete with a phase-field order parameter d, successfully avoiding the description of nonsmooth crack surfaces, as well as the pre-setting and tracking of complex crack extension paths. However, most works have focused on 2D and simple 3D problems of non-reinforced concrete due to the high computational cost. A 3D PFM is implemented in the commercial finite element code ABAQUS to model damage and quasi-brittle fractures in composite beam concretes. The damage problem is implemented in the user subroutines UMAT and HETVAL on account of the similarity between the evolution law of the order parameter and the heat transfer law. In addition, a FORTRAN file is used to define the relationships among the material properties. Through this approach, modeling, computational task submission, and post-processing are completed in the GUI of ABAQUS, and the internal nonlinear algorithms are adopted directly. The accuracy of the modeling method is verified by comparing with two classical experimental data in the literature, and the maximum load data and load-displacement curve are well fitted. Moreover, a 3D numerical model for the push-out test of the composite beam is developed. Simulation results are consistent with the test results, such as the trend of the load-displacement curve, the damage pattern of the concrete, and the stress condition of the shear bolts. The parametric analysis shows that the compressive and tensile strengths of the shear bonds can significantly affect the load bearing capacity of composite beams, whereas the material parameters of concrete have a limited influence, consistent with the previous experience. The PFM has proven its ability to handle complex quasi-brittle fracture of concrete, and the present work can provide a reference for modeling concrete cracks in engineering structures.

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References

  1. G. Molnár and A. Gravouil, 2D and 3D ABAQUS implementation of a robust staggered phase-field solution for modeling brittle fracture, Finite Elements in Analysis and Design, 130 (2017) 27–38.

    Article  Google Scholar 

  2. J. C. Simo, J. Oliver and F. Armero, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Computational Mechanics, 12(5) (1993) 277–296.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Cervenka, Mixed mode discrete crack propagation in concrete structures, Ph.D. Thesis, University of Colorado, USA (1994).

    Google Scholar 

  4. N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, 46(1) (1999) 131–150.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. Benvenuti, A regularized XFEM framework for embedded cohesive interfaces, Computer Methods in Applied Mechanics and Engineering, 197(49–50) (2008) 4367–4378.

    Article  MATH  Google Scholar 

  6. I. Babuška and U. Banerjee, Stable generalized finite element method (SGFEM), Computer Methods in Applied Mechanics and Engineering, 201 (2012) 91–111.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Y. Wu and F. B. Li, An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks, Computer Methods in Applied Mechanics and Engineering, 295 (2015) 77–107.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. P. Bažant and B. H. Oh, Crack band theory for fracture of concrete, Matériaux et Construction, 16(3) (1983) 155–177.

    Article  Google Scholar 

  9. G. Pijaudier-Cabot and Z. P. Bažant, Nonlocal damage theory, Journal of Engineering Mechanics, 113(10) (1987) 1512–1533.

    Article  MATH  Google Scholar 

  10. R. H. J. Peerlings, R. De Borst, W. A. M. Brekelmans and J. H. P. De Vree, Gradient enhanced damage for quasi-brittle materials, International Journal for Numerical Methods in Engineering, 39(19) (1996) 3391–3403.

    Article  MATH  Google Scholar 

  11. V. L. Ginzburg and L. D. Landau, Towards the theory of superconductivity, Original in Journal of Experimental and Theoretical Physics, 20 (1950) 1064–1082.

    Google Scholar 

  12. C. Miehe, F. Welschinger and M. Hofacker, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83(10) (2010) 1273–1311.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Y. Wu, A unified phase-field theory for the mechanics of damage and quasi-brittle failure, Journal of the Mechanics and Physics of Solids, 103 (2017) 72–99.

    Article  MathSciNet  Google Scholar 

  14. B. Bourdin, G. A. Francfort and J. J. Marigo, The variational approach to fracture, Journal of Elasticity, 91(1) (2008) 5–148.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Navidtehrani, C. Betegón and E. Martínez-Pañeda, A simple and robust ABAQUS implementation of the phase field fracture method, Applications in Engineering Science, 6 (2021) 100050.

    Article  Google Scholar 

  16. P. Zhang, X. Hu, X. Wang and W. Yao, An iteration scheme for phase field model for cohesive fracture and its implementation in ABAQUS, Engineering Fracture Mechanics, 204 (2018) 268–287.

    Article  Google Scholar 

  17. P. Zhang, X. Hu, S. Yang and W. Yao, Modelling progressive failure in multi-phase materials using a phase field method, Engineering Fracture Mechanics, 209 (2019) 105–124.

    Article  Google Scholar 

  18. S. Natarajan, R. K. Annabattula and E. Martínez-Pañeda, Phase field modelling of crack propagation in functionally graded materials, Composites Part B: Engineering, 169 (2019) 239–248.

    Article  Google Scholar 

  19. Y. Shao, Q. Duan and S. Qiu, Adaptive analysis for phase-field model of brittle fracture of functionally graded materials, Engineering Fracture Mechanics, 251 (2021) 107783.

    Article  Google Scholar 

  20. T. T. Nguyen, J. Réthoré and M. C. Baietto, Phase field modelling of anisotropic crack propagation, European Journal of Mechanics-A/Solids, 65 (2017) 279–288.

    Article  MathSciNet  MATH  Google Scholar 

  21. J.-Y. Wu, V. P. Nguyen, H. Zhou and Y. Huang, A variationally consistent phase-field anisotropic damage model for fracture, Computer Methods in Applied Mechanics and Engineering, 358 (2020) 112629.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Rojas, T. Takaki and M. Ohno, A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection, Journal of Computational Physics, 298 (2015) 29–40.

    Article  MathSciNet  MATH  Google Scholar 

  23. A. J. Clarke, D. Tourret, Y. Song, S. D. Imhoff, P. J. Gibbs, J. W. Gibbs, K. Fezzaa and A. Karma, Microstructure selection in thin-sample directional solidification of an Al−Cu alloy: in situ X-ray imaging and phase-field simulations, Acta Materialia, 129 (2017) 203–216.

    Article  Google Scholar 

  24. D. C. Feng and J. Y. Wu, Phase-field regularized cohesive zone model (CZM) and size effect of concrete, Engineering Fracture Mechanics, 197 (2018) 66–79.

    Article  Google Scholar 

  25. J. Wang, X. Guo and N. Zhang, Study of the progressive failure of concrete by phase field modeling and experiments, International Journal of Damage Mechanics, 30(9) (2021) 1377–1399.

    Article  Google Scholar 

  26. E. Martínez-Pañeda, A. Golahmar and C. F. Niordson, A phase field formulation for hydrogen assisted cracking, Computer Methods in Applied Mechanics and Engineering, 342 (2018) 742–761.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Y. Wu, T. K. Mandal and V. P. Nguyen, A phase-field regularized cohesive zone model for hydrogen assisted cracking, Computer Methods in Applied Mechanics and Engineering, 358 (2020) 112614.

    Article  MathSciNet  MATH  Google Scholar 

  28. B. Bourdin, G. A. Francfort and J. J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, 48(4) (2000) 797–826.

    Article  MathSciNet  MATH  Google Scholar 

  29. J. Y. Wu and Y. Huang, Comprehensive implementations of phase-field damage models in ABAQUS, Theoretical and Applied Fracture Mechanics, 106 (2020) 102440.

    Article  Google Scholar 

  30. J. Y. Wu, Y. Huang and V. P. Nguyen, On the BFGS monolithic algorithm for the unified phase field damage theory, Computer Methods in Applied Mechanics and Engineering, 360 (2020) 112704.

    Article  MathSciNet  MATH  Google Scholar 

  31. J. Y. Wu and V. P. Nguyen, A length scale insensitive phase-field damage model for brittle fracture, Journal of the Mechanics and Physics of Solids, 119 (2018) 20–42.

    Article  MathSciNet  Google Scholar 

  32. J.-Y. Wu, Y. Huang, H. Zhou and V. P. Nguyen, Three-dimensional phase-field modeling of mode I+II/III failure in solids, Computer Methods in Applied Mechanics and Engineering, 373 (2021) 113537.

    Article  MathSciNet  MATH  Google Scholar 

  33. K. Pham, H. Amor, J.-J. Marigo and C. Maurini, Gradient damage models and their use to approximate brittle fracture, International Journal of Damage Mechanics, 20(4) (2011) 618–652.

    Article  Google Scholar 

  34. B. Bourdin, J.-J. Marigo, C. Maurini and P. Sicsic, Morphogenesis and propagation of complex cracks induced by thermal shocks, Physical Review Letters, 112(1) (2014) 014301.

    Article  Google Scholar 

  35. B. Bourdin, C. J. Larsen and C. L. Richardson, A time-discrete model for dynamic fracture based on crack regularization, International Journal of Fracture, 168(2) (2011) 133–143.

    Article  MATH  Google Scholar 

  36. C. Kuhn, A. Schlüter and R. Müller, On degradation functions in phase field fracture models, Computational Materials Science, 108 (2015) 374–384.

    Article  Google Scholar 

  37. E. Lorentz and V. Godard, Gradient damage models: toward full-scale computations, Computer Methods in Applied Mechanics and Engineering, 200(21–22) (2011) 1927–1944.

    Article  MathSciNet  MATH  Google Scholar 

  38. H. Cornelissen, D. Hordijk and H. Reinhardt, Experimental determination of crack softening characteristics of normalweight and lightweight, Heron, 31(2) (1986) 45–46.

    Google Scholar 

  39. J. Y. Wu et al., Chapter one-phase-field modeling of fracture, Advances in Applied Mechanices, 53 (2020) 1–183.

    Article  Google Scholar 

  40. P. E. Petersson, Crack growth and development of fracture zones in plain concrete and similar materials, Doctoral Dissertation, Lund Institute of Technology, Sweden (1981).

    Google Scholar 

  41. B. J. Winkler, Traglastuntersuchungen von Unbewehrten und Bewehrten Betonstrukturen auf der Grundlage eines Objektiven Werkstoffgesetzes für Beton, Innsbruck University Press (2001).

  42. F. Ding et al., Experimental study on slip behavior and calculation of shear bearing capacity for shear stud connectors, Journal of Building Structures, 35(9) (2014) 98–106 (in Chinese).

    Google Scholar 

  43. D. A. Hordijk, Tensile and tensile fatigue behaviour of concrete; experiments, modelling and analyses, Heron, 37(1) (1992) (79 pages).

    Google Scholar 

  44. D. A. Hordijk, Local approach to fatigue of concrete, Doctoral Dissertation, Delft University of Technology, Netherlands (1991).

    Google Scholar 

  45. P. Lacki, J. Nawrot, A. Derlatka and J. Winowiecka, Numerical and experimental tests of steel-concrete composite beam with the connector made of top-hat profile, Composite Structures, 211 (2019) 244–253.

    Article  Google Scholar 

  46. H. T. Nguyen and S. E. Kim, Finite element modeling of push-out tests for large stud shear connectors, Journal of Constructional Steel Research, 65(10–11) (2009) 1909–1920.

    Article  Google Scholar 

  47. C. Xu, K. Sugiura, C. Wu and Q. Su, Parametrical static analysis on group studs with typical push-out tests, Journal of Constructional Steel Research, 72 (2012) 84–96.

    Article  Google Scholar 

  48. L. An and K. Cederwall, Push-out tests on studs in high strength and normal strength concrete, Journal of Constructional Steel Research, 36(1) (1996) 15–29.

    Article  Google Scholar 

  49. C. S. Shim, P. G. Lee and T. Y. Yoon, Static behavior of large stud shear connectors, Engineering Structures, 26(12) (2004) 1853–1860.

    Article  Google Scholar 

  50. J. C. Gálvez, M. Elices, G. V. Guinea and J. Planas, Mixed mode fracture of concrete under proportional and nonproportional loading, International Journal of Fracture, 94(3) (1998) 267–284.

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (52178138), the Natural Science Foundation of Guangdong Province (2021A1515012064).

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Authors and Affiliations

  1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510640, China

    Xianbin Yu, Ronghui Wang, Jianyi Ji & Xiaoxia Zhen

  2. Poly ChangDa Engineering Co., Ltd., Guangzhou, 510230, China

    Chunguang Dong

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  1. Xianbin Yu
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  2. Ronghui Wang
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  3. Chunguang Dong
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  4. Jianyi Ji
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  5. Xiaoxia Zhen
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Correspondence to Xiaoxia Zhen.

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Xianbin Yu is a doctoral candidate pursuing a Ph.D. degree in Bridge and Tunnel Engineering at South China University of Technology, China. He received his Bachelor degree in Engineering Mechanics at Central South University. His current research area is mainly on the mechanics analysis of long-span bridges.

Xiaoxia Zhen is an Associate Professor in the School of Civil Engineering and Transportation, South China University of Technology, China. She received her Ph.D. in Structural Engineering from South China University of Technology. Her current research area is mainly on the structural stability and vibration of long-span bridges.

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Yu, X., Wang, R., Dong, C. et al. 3D implementation of push-out test in ABAQUS using the phase-field method. J Mech Sci Technol 37, 1731–1745 (2023). https://doi.org/10.1007/s12206-023-0314-z

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  • DOI: https://doi.org/10.1007/s12206-023-0314-z

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