Frontiers of Structural and Civil Engineering

, Volume 13, Issue 2, pp 353–363 | Cite as

The effects of interfacial strength on fractured microcapsule

  • Luthfi Muhammad MauludinEmail author
  • Chahmi Oucif
Research Article


The effects of interfacial strength on fractured microcapsule are investigated numerically. The interaction between crack and microcapsule embedded in mortar matrix is modeled based on cohesive approach. The microcapsules are modelled with variation of core-shell thickness ratio and potential cracks are represented by pre-inserted cohesive elements along the element boundaries of the mortar matrix, microcapsules core, microcapsule shell, and at the interfaces between these phases. Special attention is given to the effects of cohesive fracture on the microcapsule interface, namely fracture strength, on the load carrying capacity and fracture probability of the microcapsule. The effect of fracture properties on microcapsule is found to be significant factor on the load carrying capacity and crack propagation characteristics. Regardless of core-shell thickness ratio of microcapsule, the load carrying capacity of self-healing material under tension increases as interfacial strength of microcapsule shell increases. In addition, given the fixed fracture strength of the interface of microcapsule shell, the higher the ratio core-shell thickness, the higher the probability of microcapsules being fractured.


interfacial strength cohesive elements microcapsule core-shell thickness ratio fracture properties 


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This work is supported and financed by RISTEKDIKTI (Directorate General of Resources for Science, Technology and Higher Education. Ministry of Research, Technology and Higher Education of Indonesia) under funding agreement No: 153.39/E4.4/2014, and the German Academic Exchange Program (DAAD). The supports are gratefully acknowledged.


  1. 1.
    Rabczuk T. Computational methods for fracture in brittle and quasibrittle solids: state-of-the-art review and future perspectives. ISRN Applied Mathematics, 2013, 2013(2013): 849231zbMATHGoogle Scholar
  2. 2.
    Rabczuk T, Belytschko T. Cracking particles: a simplied meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343CrossRefzbMATHGoogle Scholar
  3. 3.
    Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29‒30): 2777–2799MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760CrossRefzbMATHGoogle Scholar
  5. 5.
    Areias P, Rabczuk T. Quasi-static crack propagation in plane and plate structures using set-valued traction-separation laws. International Journal for Numerical Methods in Engineering, 2008, 74(3): 475–505CrossRefzbMATHGoogle Scholar
  6. 6.
    Chen L, Rabczuk T, Bordas S P A, Liu G, Zeng K, Kerfriden P. Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209–212: 250–265MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Nguyen-Vinh H, Bakar I, Msekh M, Song J H, Muthu J, Zi G, Le P, Bordas S, Simpson R, Natarajan S, Lahmer T, Rabczuk T. Extended finite element method for dynamic fracture of piezo-electric materials. Engineering Fracture Mechanics, 2012, 92: 19–31CrossRefGoogle Scholar
  8. 8.
    Zhang C, Wang C, Lahmer T, He P, Rabczuk T. A dynamic xfem formulation for crack identification. International Journal of Mechanics and Materials in Design, 2016, 12(4): 427–448CrossRefGoogle Scholar
  9. 9.
    Vu-Bac N, Nguyen-Xuan H, Chen L, Bordas S, Kerfriden P, Simpson R, Liu G, Rabczuk T. A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. Computer Modeling in Engineering & Sciences, 2011, 73(4): 331–356MathSciNetzbMATHGoogle Scholar
  10. 10.
    Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109CrossRefGoogle Scholar
  11. 11.
    Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gui Y L, Bui H H, Kodikara J, Zhang Q B, Zhao J, Rabczuk T. Modelling the dynamic failure of brittle rocks using a hybrid continuum-discrete element method with a mixed-mode cohesive fracture model. International Journal of Impact Engineering, 2016, 87: 146–155CrossRefGoogle Scholar
  13. 13.
    Nguyen V P, Lian H, Rabczuk T, Bordas S. Modelling hydraulic fractures in porous media using flow cohesive interface elements. Engineering Geology, 2017, 225: 68–82CrossRefGoogle Scholar
  14. 14.
    Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137CrossRefGoogle Scholar
  15. 15.
    Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Areias P, Rabczuk T, Camanho P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63CrossRefGoogle Scholar
  17. 17.
    Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350MathSciNetCrossRefGoogle Scholar
  18. 18.
    Areias P, Msekh M, Rabczuk T. Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143CrossRefGoogle Scholar
  19. 19.
    Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41CrossRefGoogle Scholar
  20. 20.
    Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476MathSciNetCrossRefGoogle Scholar
  21. 21.
    Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: a stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782MathSciNetCrossRefGoogle Scholar
  22. 22.
    Hamdia K M, Lahmer T, Nguyen-Thoi T, Rabczuk T. Predicting the fracture toughness of pncs: a stochastic approach based on ANN and ANFIS. Computational Materials Science, 2015, 102: 304–313CrossRefGoogle Scholar
  23. 23.
    Hamdia K M, Zhuang X, He P, Rabczuk T. Fracture toughness of polymeric particle nanocomposites: evaluation of models performance using bayesian method. Composites Science and Technology, 2016, 126: 122–129CrossRefGoogle Scholar
  24. 24.
    Talebi H, Silani M, Bordas S P, Kerfriden P, Rabczuk T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071MathSciNetCrossRefGoogle Scholar
  25. 25.
    Talebi H, Silani M, Rabczuk T. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92CrossRefGoogle Scholar
  26. 26.
    Budarapu P R, Gracie R, Bordas S P, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148CrossRefGoogle Scholar
  27. 27.
    Yang S W, Budarapu P R, Mahapatra D R, Bordas S P, Zi G, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015, 96: 382–395CrossRefGoogle Scholar
  28. 28.
    Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143CrossRefGoogle Scholar
  29. 29.
    Arash B, Park H S, Rabczuk T. Tensile fracture behavior of short carbon nanotube reinforced polymer composites: a coarse-grained model. Composite Structures, 2015, 134: 981–988CrossRefGoogle Scholar
  30. 30.
    Arash B, Park H S, Rabczuk T. Coarse-grained model of the Jintegral of carbon nanotube reinforced polymer composites. Carbon, 2016, 96: 1084–1092CrossRefGoogle Scholar
  31. 31.
    Yang Z, Hollar J, He X, Shi X. A self-healing cementitious composite using oil core/silica gel shell microcapsules. Cement and Concrete Composites, 2011, 33(4): 506–512CrossRefGoogle Scholar
  32. 32.
    Huang H, Ye G. Simulation of self-healing by further hydration in cementitious materials. Cement and Concrete Composites, 2012, 34 (4): 460–467CrossRefGoogle Scholar
  33. 33.
    Van Tittelboom K, Adesanya K, Dubruel P, Van Puyvelde P, De Belie N. Methyl methacrylate as a healing agent for self-healing cementitious materials. Smart Materials and Structures, 2011, 20 (12): 125016CrossRefGoogle Scholar
  34. 34.
    Van Tittelboom K, De Belie N. Self-healing in cementitious materials- A review. Materials (Basel), 2013, 6(6): 2182–2217CrossRefGoogle Scholar
  35. 35.
    White S, Maiti S, Jones A, Brown E, Sottos N, Geubelle P. Fatigue of self-healing polymers: multiscale analysis and experiments. In: ICF11, Italy, 2005Google Scholar
  36. 36.
    Gilabert F, Garoz D, Van Paepegem W. Stress concentrations and bonding strength in encapsulation-based self-healing materials. Materials & Design, 2015, 67: 28–41CrossRefGoogle Scholar
  37. 37.
    Kaltzakorta E, Erkizia I. Silica microcapsules encapsulating epoxy compounds for self-healing cementitiousmaterials. In: Proceedings of 3rd International Conference on Self-Healing Materials, Bath, UK, 2011Google Scholar
  38. 38.
    Alexeev A, Verberg R, Balazs A C. Patterned surfaces segregate compliant microcapsules. Langmuir, 2007, 23(3): 983–987CrossRefGoogle Scholar
  39. 39.
    Hilloulin B, Van Tittelboom K, Gruyaert E, De Belie N, Loukili A. Design of polymeric capsules for self-healing concrete. Cement and Concrete Composites, 2015, 55: 298–307CrossRefGoogle Scholar
  40. 40.
    Simulia A V. Abaqus 6.13 documentation. Dassault systemes, 2013Google Scholar
  41. 41.
    Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455CrossRefzbMATHGoogle Scholar
  42. 42.
    Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71MathSciNetzbMATHGoogle Scholar
  43. 43.
    Rabczuk T, Song J H, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Engineering Fracture Mechanics, 2009, 76(6): 730–741CrossRefGoogle Scholar
  44. 44.
    Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically nonlinear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758CrossRefGoogle Scholar
  45. 45.
    Rabczuk T, Zi G, Gerstenberger A, Wall W. A new crack tip element for the phantom-node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599CrossRefzbMATHGoogle Scholar
  46. 46.
    Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6–8): 641–658MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Rabczuk T, Areias P, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495CrossRefzbMATHGoogle Scholar
  49. 49.
    Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411CrossRefGoogle Scholar
  50. 50.
    Belytschko T, Lu Y Y, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Nguyen V, Rabczuk T, Bordas S, Duflot M. Meshless methods: a review and computer implementation aspects. Mathematics and Computers in Simulation, 2008, 79(3): 763–813MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Hughes T J, Cottrell J A, Bazilevs Y. Isogeometric analysis: CAD, finite elements, nurbs, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39–41): 4135–4195MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Nguyen V, Anitescu C, Bordas S, Rabczuk T. Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116MathSciNetCrossRefGoogle Scholar
  54. 54.
    Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based xiga for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146CrossRefGoogle Scholar
  55. 55.
    Nguyen-Thanh N, Valizadeh N, Nguyen M, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on kirchhofflove theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Nguyen-Thanh N, Nguyen-Xuan H, Bordas S, Rabczuk T. Isogeometric analysis using polynomial splines over hierarchical T-meshes for two dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering, 2011, 200(21–22): 1892–1908MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger K, Bazilevs Y, Rabczuk T. Rotation free isogeometric thin shell analysis using pht-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Ghasemi H, Park H, Rabczuk T. A level-set based iga formulation for topology optimization of exoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258MathSciNetCrossRefGoogle Scholar
  59. 59.
    Quayum M S, Zhuang X, Rabczuk T. Computational model generation and RVE design of self-healing concrete. Frontiers of Structural and Civil Engineering, 2015, 9(4): 383–396CrossRefGoogle Scholar
  60. 60.
    Wang X, Jivkov A P. Combined numerical-statistical analyses of damage and failure of 2D and 3D mesoscale heterogeneous concrete. Mathematical Problems in Engineering, 2015, 501: 702563Google Scholar
  61. 61.
    Hamdia K M, Msekh M A, Silani M, Vu-Bac N, Zhuang X, Nguyen-Thoi T, Rabczuk T. Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190CrossRefGoogle Scholar
  62. 62.
    Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Structural MechanicsBauhaus University of WeimarWeimarGermany
  2. 2.Department of Civil EngineeringPoliteknik Negeri Bandung (POLBAN)BandungIndonesia
  3. 3.Département de Génie CivilUniversité des Sciences et de la TechnologieOranAlgérie

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