Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Porosities exist as pores of different sizes within a structure to fabricate lightweight materials and the sintering process. The porous structure gives a lower loading capacity than the perfect design. Crack propagation is also a complicated behavior in this structure. The hybrid phase-field approach is suitable to provide an effective computational tool to model the crack propagation of functionally graded materials with porosity effects. We show the influence of porosity on both the critical force and crack path of the FGM structure. In the framework of isogeometric analysis (IGA), a local refinement multi-patch algorithm based on the Virtual Uncommon-Knot-Inserted Master–Slave (VUKIMS) technique allows us to reduce the computational cost of the phase-field model significantly. The study revealed that cubic NURBS elements with the effective element size of half length-scale parameter could be used to achieve the desired accuracy while maintaining a reasonable computational cost.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Alessi R, Freddi F (2017) Phase-field modelling of failure in hybrid laminates. Compos Struct 181:9–25

    Article  Google Scholar 

  2. Ambati M, Gerasimov T, De Lorenzis L (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405. https://doi.org/10.1007/s00466-014-1109-y

    Article  MathSciNet  MATH  Google Scholar 

  3. Badnava H, Msekh MA, Etemadi E, Rabczuk T (2018) An h-adaptive thermo-mechanical phase field model for fracture. Finite Elem Anal Des 138:31–47. https://doi.org/10.1016/j.finel.2017.09.003

    Article  Google Scholar 

  4. Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ (2016) A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng 312:130–166. https://doi.org/10.1016/j.cma.2016.09.005

    Article  MathSciNet  MATH  Google Scholar 

  5. Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118. https://doi.org/10.1016/j.cma.2014.01.016

    Article  MathSciNet  MATH  Google Scholar 

  6. Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217–220:77–95. https://doi.org/10.1016/j.cma.2012.01.008

    Article  MathSciNet  MATH  Google Scholar 

  7. Bouhala L, Makradi A, Belouettar S (2012) Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method. Eng Fract Mech 88:35–48

    Article  Google Scholar 

  8. Bourdin B, Francfort GA (2008) Marigo J-JJJoe. The variational approach to fracture 91:5–148

    Google Scholar 

  9. Buliga MJJoE (1998) Energy minimizing brittle crack propagation. 52:201

  10. Chafi M, Boulenouar A (2019) A numerical modelling of mixed mode crack initiation and growth in functionally graded materials. Mater Res. https://doi.org/10.1590/1980-5373-mr-2018-0701

    Article  Google Scholar 

  11. Chen X, Luo T, Ooi ET, Ooi EH, Song C (2018) A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials. Theor Appl Fract Mech 94:120–133. https://doi.org/10.1016/j.tafmec.2018.01.008

    Article  Google Scholar 

  12. Cheng Z, Liu Y, Zhao J, Feng H, Wu Y (2018) Numerical simulation of crack propagation and branching in functionally graded materials using peridynamic modeling. Eng Fract Mech 191:13–32. https://doi.org/10.1016/j.engfracmech.2018.01.016

    Article  Google Scholar 

  13. Coox L, Greco F, Atak O, Vandepitte D, Desmet W (2017) A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces. Comput Methods Appl Mech Eng 316:235–260. https://doi.org/10.1016/j.cma.2016.06.022

    Article  MathSciNet  MATH  Google Scholar 

  14. Costantini M, Jaroszewicz J, Kozon L, Szlazak K, Swieszkowski W, Garstecki P, Stubenrauch C, Barbetta A, Guzowski J (2019) 3D-printing of functionally graded porous materials using on-demand reconfigurable microfluidics. Angew Chem Int Ed Engl 58:7620–7625. https://doi.org/10.1002/anie.201900530

    Article  Google Scholar 

  15. Craveiro F, Nazarian S, Bartolo H, Bartolo PJ, Pinto Duarte J (2020) An automated system for 3D printing functionally graded concrete-based materials. Addit Manuf. https://doi.org/10.1016/j.addma.2020.101146

    Article  Google Scholar 

  16. Dal Maso G (2002) Toader RJAfRM, Analysis A model for the quasi-static growth of brittle fractures: existence and approximation. Results 162:101–135

    MATH  Google Scholar 

  17. Dastjerdi S, Malikan M, Dimitri R, Tornabene F (2020) Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment. Compos Struct 255:112925

    Article  Google Scholar 

  18. Demirhan PA, Taskin V (2019) Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Compos B Eng 160:661–676

    Article  Google Scholar 

  19. Deogekar S, Vemaganti K (2017) A computational study of the dynamic propagation of two offset cracks using the phase field method. Eng Fract Mech 182:303–321. https://doi.org/10.1016/j.engfracmech.2017.08.003

    Article  Google Scholar 

  20. Francfort GA, Marigo J-J (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46:1319–1342. https://doi.org/10.1016/S0022-5096(98)00034-9

    Article  MathSciNet  MATH  Google Scholar 

  21. Gayen D, Tiwari R, Chakraborty D (2019) Static and dynamic analyses of cracked functionally graded structural components: a review. Compos B Eng. https://doi.org/10.1016/j.compositesb.2019.106982

    Article  Google Scholar 

  22. Gerstle WH, Martha LF, Ingraffea AR (1987) Finite and boundary element modeling of crack propagation in two and three dimensions. Eng Comput 2:167–183

    Article  Google Scholar 

  23. Gharehdash S, Shen L, Gan Y (2020) Numerical study on mechanical and hydraulic behaviour of blast-induced fractured rock. Eng Comput 36:915–929

    Article  Google Scholar 

  24. Goswami S, Anitescu C, Chakraborty S, Rabczuk T (2020) Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. Theor Appl Fract Mech 106:102447

    Article  Google Scholar 

  25. Goswami S, Anitescu C, Rabczuk T (2020) Adaptive fourth-order phase field analysis for brittle fracture. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2019.112808

    Article  MathSciNet  MATH  Google Scholar 

  26. Griffith AA (1921) VI. The phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A 221:163–198

    Article  MATH  Google Scholar 

  27. Hadraba H, Maca K, Cihlar J (2004) Electrophoretic deposition of alumina and zirconia. Ceram Int 30:853–863. https://doi.org/10.1016/j.ceramint.2003.09.020

    Article  Google Scholar 

  28. Hirshikesh NS, Annabattula RK, Martínez-Pañeda E (2019) Phase field modelling of crack propagation in functionally graded materials. Compos B Eng 169:239–248. https://doi.org/10.1016/j.compositesb.2019.04.003

    Article  Google Scholar 

  29. Hosseini S, Bagheri R, Monfared M (2020) Transient response of several cracks in a nonhomogeneous half-layer bonded to a magneto-electro-elastic coating. Theor Appl Fract Mech 110:102821

    Article  Google Scholar 

  30. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195. https://doi.org/10.1016/j.cma.2004.10.008

    Article  MathSciNet  MATH  Google Scholar 

  31. Irwin GR (1957) Analysis of stresses and strains near the end of a crack transversing a plate. Trans ASME Ser E J Appl Mech 24:361–364

    Article  Google Scholar 

  32. Jin X, Wu L, Guo L, Yu H, Sun Y (2009) Experimental investigation of the mixed-mode crack propagation in ZrO2/NiCr functionally graded materials. Eng Fract Mech 76:1800–1810. https://doi.org/10.1016/j.engfracmech.2009.04.003

    Article  Google Scholar 

  33. Karami B, Janghorban M, Li L (2018) On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronaut 143:380–390

    Article  Google Scholar 

  34. Kim J-H, Paulino GH (2004) Simulation of crack propagation in functionally graded materials under mixed-mode and non-proportional loading. Mech Mater Des 1:63–94

    Google Scholar 

  35. Le Thanh C, Nguyen TN, Vu TH, Khatir S, Wahab MA (2020) A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate. Eng Comput 1–12

  36. Liu G, Li Q, Msekh MA, Zuo Z (2016) Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model. Comput Mater Sci 121:35–47. https://doi.org/10.1016/j.commatsci.2016.04.009

    Article  Google Scholar 

  37. Liu Y, Su S, Huang H, Liang Y (2019) Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Compos B Eng 168:236–242

    Article  Google Scholar 

  38. Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199:2765–2778. https://doi.org/10.1016/j.cma.2010.04.011

    Article  MathSciNet  MATH  Google Scholar 

  39. Miehe C, Schänzel L-M, Ulmer H (2015) Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Comput Methods Appl Mech Eng 294:449–485. https://doi.org/10.1016/j.cma.2014.11.016

    Article  MathSciNet  MATH  Google Scholar 

  40. Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Meth Eng 83:1273–1311. https://doi.org/10.1002/nme.2861

    Article  MathSciNet  MATH  Google Scholar 

  41. Mishra R, Burela RG (2019) Thermo-electro-mechanical fatigue crack growth simulation in piezoelectric solids using XFEM approach. Theor Appl Fract Mech 104:102388

    Article  Google Scholar 

  42. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. J Numer Methods Eng 46:131–150

    Article  MathSciNet  MATH  Google Scholar 

  43. Molnár G, Gravouil A (2017) 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture. Finite Elem Anal Des 130:27–38. https://doi.org/10.1016/j.finel.2017.03.002

    Article  Google Scholar 

  44. Nguyen KD, E. Augarde C, Coombs WM, Nguyen-Xuan H, Abdel-Wahab M, (2020) Non-conforming multipatches for NURBS-based finite element analysis of higher-order phase-field models for brittle fracture. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2020.107133

    Article  Google Scholar 

  45. Nguyen KD, Nguyen-Xuan H (2015) An isogeometric finite element approach for three-dimensional static and dynamic analysis of functionally graded material plate structures. Compos Struct 132:423–439. https://doi.org/10.1016/j.compstruct.2015.04.063

    Article  Google Scholar 

  46. Nguyen NT, Bui TQ, Zhang C, Truong TT (2014) Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method. Eng Anal Bound Elem 44:87–97

    Article  MathSciNet  MATH  Google Scholar 

  47. Nha NT, Bang TK, Tinh BQ, Thien TT (2013) Elastostatic analysis of isotropic and orthotropic functionally graded structures by meshfree radial point interpolation method

  48. Parthasarathy J, Starly B, Raman S (2011) A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications. J Manuf Process 13:160–170

    Article  Google Scholar 

  49. Patil RU, Mishra BK, Singh IV (2018) A local moving extended phase field method (LMXPFM) for failure analysis of brittle materials. Comput Methods Appl Mech Eng 342:674–709. https://doi.org/10.1016/j.cma.2018.08.018

    Article  MathSciNet  MATH  Google Scholar 

  50. Patil RU, Mishra BK, Singh IV, Bui TQ (2018) A new multiscale phase field method to simulate failure in composites. Adv Eng Softw 126:9–33. https://doi.org/10.1016/j.advengsoft.2018.08.010

    Article  Google Scholar 

  51. Peake MJ, Trevelyan J, Coates G (2013) Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems. Comput Methods Appl Mech Eng 259:93–102. https://doi.org/10.1016/j.cma.2013.03.016

    Article  MathSciNet  MATH  Google Scholar 

  52. Phung-Van P, Thai CH, Nguyen-Xuan H, Abdel-Wahab M (2019) An isogeometric approach of static and free vibration analyses for porous FG nanoplates. Eur J Mech A Solids. https://doi.org/10.1016/j.euromechsol.2019.103851

    Article  MathSciNet  MATH  Google Scholar 

  53. Phung-Van P, Thai CH, Nguyen-Xuan H, Wahab MA (2019) Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis. Compos B Eng 164:215–225

    Article  Google Scholar 

  54. Piegl L, Tiller W (1997) The NURBS Book. Springer

    Book  MATH  Google Scholar 

  55. Rabczuk T, Areias P, Belytschko T (2007) A meshfree thin shell method for non-linear dynamic fracture. Int J Numer Meth Eng 72:524–548

    Article  MathSciNet  MATH  Google Scholar 

  56. Ren HL, Zhuang XY, Anitescu C, Rabczuk T (2019) An explicit phase field method for brittle dynamic fracture. Comput Struct 217:45–56. https://doi.org/10.1016/j.compstruc.2019.03.005

    Article  Google Scholar 

  57. Rezaei A, Saidi A, Abrishamdari M, Mohammadi MP (2017) Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach. Thin-Walled Struct 120:366–377

    Article  Google Scholar 

  58. Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh VM, Guo H, Hamdia K, Zhuang X, Rabczuk T (2020) An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2019.112790

    Article  MathSciNet  MATH  Google Scholar 

  59. Sargado JM, Keilegavlen E, Berre I, Nordbotten JM (2017) High-accuracy phase-field models for brittle fracture based on a new family of degradation functions. J Mech Phys Solids. https://doi.org/10.1016/j.jmps.2017.10.015

    Article  MATH  Google Scholar 

  60. Schillinger D, Borden MJ, Stolarski HK (2015) Isogeometric collocation for phase-field fracture models. Comput Methods Appl Mech Eng 284:583–610. https://doi.org/10.1016/j.cma.2014.09.032

    Article  MathSciNet  MATH  Google Scholar 

  61. Schlüter A, Willenbücher A, Kuhn C, Müller R (2014) Phase field approximation of dynamic brittle fracture. Comput Mech 54:1141–1161. https://doi.org/10.1007/s00466-014-1045-x

    Article  MathSciNet  MATH  Google Scholar 

  62. Shahverdi H, Barati MR (2017) Vibration analysis of porous functionally graded nanoplates. Int J Eng Sci 120:82–99

    Article  MathSciNet  MATH  Google Scholar 

  63. Shang C, Wang C, Li C, Yang G, Xu G, You J (2020) Eliminating the crack of laser 3D printed functionally graded material from TA15 to Inconel718 by base preheating. Opt Laser Technol. https://doi.org/10.1016/j.optlastec.2020.106100

    Article  Google Scholar 

  64. Singh N, Verhoosel CV, de Borst R, van Brummelen EH (2016) A fracture-controlled path-following technique for phase-field modeling of brittle fracture. Finite Elem Anal Des 113:14–29. https://doi.org/10.1016/j.finel.2015.12.005

    Article  MathSciNet  Google Scholar 

  65. Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng Fract Mech 55:321–334

    Article  Google Scholar 

  66. Torabi J, Ansari R (2020) Crack propagation in functionally graded 2D structures: a finite element phase-field study. Thin-Walled Struct. https://doi.org/10.1016/j.tws.2020.106734

    Article  Google Scholar 

  67. Trinh M-C, Kim S-E (2019) A three variable refined shear deformation theory for porous functionally graded doubly curved shell analysis. Aerosp Sci Technol 94:105356

    Article  Google Scholar 

  68. Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp Sci Technol 32:111–120. https://doi.org/10.1016/j.ast.2013.12.002

    Article  Google Scholar 

  69. Wu J-Y, Huang Y, Nguyen VP (2020) On the BFGS monolithic algorithm for the unified phase field damage theory. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2019.112704

    Article  MathSciNet  MATH  Google Scholar 

  70. Yadav A, Godara R, Bhardwaj G (2020) A review on XIGA method for computational fracture mechanics applications. Eng Fract Mech 107001

  71. Yin BB, Zhang LW (2019) Phase field method for simulating the brittle fracture of fiber reinforced composites. Eng Fract Mech 211:321–340. https://doi.org/10.1016/j.engfracmech.2019.02.033

    Article  Google Scholar 

  72. Zhang J, Yu T, Bui TQ (2021) An adaptive XIGA with locally refined NURBS for modeling cracked composite FG Mindlin–Reissner plates. Eng Comput 1–23

  73. Zhang P, Feng Y, Bui TQ, Hu X, Yao W (2020) Modelling distinct failure mechanisms in composite materials by a combined phase field method. Compos Struct 232:111551

    Article  Google Scholar 

  74. Zhang P, Hu X, Bui TQ, Yao W (2019) Phase field modeling of fracture in fiber reinforced composite laminate. Int J Mech Sci 161:105008

    Article  Google Scholar 

  75. Zhou S, Zhuang X, Rabczuk T (2019) Phase-field modeling of fluid-driven dynamic cracking in porous media. Comput Methods Appl Mech Eng 350:169–198. https://doi.org/10.1016/j.cma.2019.03.001

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge VLIR-UOS TEAM Project's financial support, VN2017TEA454A103, "An innovative solution to protect Vietnamese coastal riverbanks from floods and erosion", funded by the Flemish Government.

Author information

Authors and Affiliations

  1. Soete Laboratory, Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium

    Khuong D. Nguyen & M. Abdel-Wahab

  2. Department of Engineering Mechanics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam

    Khuong D. Nguyen

  3. Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Khuong D. Nguyen

  4. Faculty of Civil Engineering, Ho Chi Minh City Open University, Ho Chi Minh City, Vietnam

    Cuong-Le Thanh

  5. CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam

    H. Nguyen-Xuan

  6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    H. Nguyen-Xuan

Authors
  1. Khuong D. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cuong-Le Thanh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Nguyen-Xuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Abdel-Wahab
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to H. Nguyen-Xuan or M. Abdel-Wahab.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nguyen, K.D., Thanh, CL., Nguyen-Xuan, H. et al. A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures. Engineering with Computers 39, 129–149 (2023). https://doi.org/10.1007/s00366-021-01518-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01518-0

Keywords

Search

Navigation