Please wait a minute...

Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (3) : 792-801
The effects of mismatch fracture properties in encapsulation-based self-healing concrete using cohesive-zone model
Luthfi Muhammad MAULUDIN1,2, Chahmi OUCIF1, Timon RABCZUK3,4()
1. Institute of Structural Mechanics, Bauhaus University of Weimar, Weimar 99423, Germany
2. Department of Civil Engineering, Politeknik Negeri Bandung (POLBAN), Bandung 40012, Indonesia
3. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4. Faculty of Civil Engineering,Ton Duc Thang University, Ho Chi Minh City, Vietnam
Download: PDF(3172 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Finite element analysis is developed to simulate the breakage of capsule in capsule-based self-healing concrete. A 2D circular capsule with different core-shell thickness ratios embedded in the mortar matrix is analyzed numerically along with their interfacial transition zone. Zero-thickness cohesive elements are pre-inserted into solid elements to represent potential cracks. This study focuses on the effects of mismatch fracture properties, namely fracture strength and energy, between capsule and mortar matrix into the breakage likelihood of the capsule. The extensive simulations of 2D specimens under uniaxial tension were carried out to investigate the key features on the fracture patterns of the capsule and produce the fracture maps as the results. The developed fracture maps of capsules present a simple but valuable tool to assist the experimentalists in designing appropriate capsule materials for self-healing concrete.

Keywords self-healing concrete      interfacial zone      capsule materials      cohesive elements      fracture maps     
Corresponding Author(s): Timon RABCZUK   
Just Accepted Date: 13 May 2020   Online First Date: 17 June 2020    Issue Date: 13 July 2020
 Cite this article:   
Luthfi Muhammad MAULUDIN,Chahmi OUCIF,Timon RABCZUK. The effects of mismatch fracture properties in encapsulation-based self-healing concrete using cohesive-zone model[J]. Front. Struct. Civ. Eng., 2020, 14(3): 792-801.
E-mail this article
E-mail Alert
Articles by authors
Luthfi Muhammad MAULUDIN
Chahmi OUCIF
Fig.1  Geometry of the model, loadings, and boundary conditions.
Fig.2  Traction-separation law for cohesive elements.
Fig.3  Mesh discretization of the model. (a) Initial mesh; (b) inserted cohesive elements around the model.
parameter value
elastic modulus (Ec/Em = 2, 1, 1/7) nm = 0.2
fracture strength (0.1<tc/tm<10) nc = 0.3
fracture toughness (0.01<Gc/Gm<50)
Tab.1  Ratio of material properties used in this simulation
Fig.4  Failure path of an incoming crack through capsule based on mismatch in elastic and fracture properties. (a) Ec/Em=2, tc/tm= 0.5, Gc/Gm=1.5; (b) Ec/Em=1, tc/tm= 0.5, Gc/Gm=1; (c) Ec/Em=1, tc/tm= 1.5, Gc/Gm=2; (d) Ec/Em=1/7, tc/tm= 1, Gc/Gm=0.5; (e) Ec/Em=2, tc/tm= 2, Gc/Gm=0.02; (f) Ec/Em=1/7, tc/tm=3, Gc/Gm=1.5.
Fig.5  Effect of mismatch in elastic properties on fractured capsule. (a) Ec/Em = 1; (b) Ec/Em = 1/7; (c) Ec/Em = 2.
Fig.6  Fracture map: effect of mismatch in fracture properties with different elastic ratios.
Fig.7  Capsule samples with different shell thickness. (a) R11; (b) R51; (c) R101; (d) R151.
Fig.8  Failure path of an incoming crack through capsule with different core-shell thickness ratios. (a) Rcore/Rshell =1, tc/tm=1, Gc/Gm=1; (b) Rcore/Rshell=1, tc/tm= 2.4, Gc/Gm=0.02; (c) Rcore/Rshell =5, tc/tm= 1.5, Gc/Gm=0.02; (d) Rcore/Rshell =5, tc/tm= 2.5, Gc/Gm=1; (e) Rcore/Rshell =10, tc/tm= 1, Gc/Gm=2; (f) Rcore/Rshell =10, tc/tm=4, Gc/Gm=2; (g) Rcore/Rshell =15, tc/tm= 1, Gc/Gm=1; (h) Rcore/Rshell =15, tc/tm= 5, Gc/Gm=2.
Fig.9  Fracture map: effect of different capsule shell thickness ratios.
1 J Li, B Zong, Y Wang, W Zhuang. Experiment and modeling of mechanical properties on iron matrix composites reinforced by different types of ceramic particles. Materials Science and Engineering A, 2010, 527(29–30): 7545–7551
2 T Srivatsan. Microstructure, tensile properties and fracture behaviour of Al2O3 particulate-reinforced aluminium alloy metal matrix composites. Journal of Materials Science, 1996, 31(5): 1375–1388
3 L S Sigl, P Mataga, B Dalgleish, R McMeeking, A Evans. On the toughness of brittle materials reinforced with a ductile phase. Acta Metallurgica, 1988, 36(4): 945–953
4 P Areias, T Rabczuk, D Dias-da Costa. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137
5 P Areias, T Rabczuk. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122
6 P Areias, T Rabczuk, P Camanho. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
7 C Oucif, L M Mauludin. Numerical modeling of high velocity impact applied to reinforced concrete panel. Underground Space, 2019, 4(1): 1–9
8 C Oucif, K Ouzaa, L M Mauludin. Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns. Journal of Applied and Computational Mechanics, 2019, 5: 517–525
9 L Chen, T Rabczuk, S P A Bordas, G Liu, K Zeng, P Kerfriden. 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: 250–265
10 H Nguyen-Vinh, I Bakar, M Msekh, J H Song, J Muthu, G Zi, P Le, S Bordas, R Simpson, S Natarajan, T Lahmer, T Rabczuk. Extended finite element method for dynamic fracture of piezo-electric materials. Engineering Fracture Mechanics, 2012, 92: 19–31
11 C Zhang, C Wang, T Lahmer, P He, T Rabczuk. A dynamic XFEM formulation for crack identification. International Journal of Mechanics and Materials in Design, 2016, 12(4): 427–448
12 N Vu-Bac, H Nguyen-Xuan, L Chen, S Bordas, P Kerfriden, R Simpson, G Liu, T Rabczuk. A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. Computer Modeling in Engineering & Sciences, 2011, 73(4): 331–356
13 Y Zhang, X Zhuang. Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics, 2019, 102: 1–9
14 Y Zhang, R Lackner, M Zeiml, H A Mang. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 335–366
15 Y Zhang, X Zhuang. Cracking elements: A self-propagating strong discontinuity embedded approach for quasi-brittle fracture. Finite Elements in Analysis and Design, 2018, 144: 84–100
16 Y Zhang, X Zhuang. A softening-healing law for self-healing quasi-brittle materials: Analyzing with strong discontinuity embedded approach. Engineering Fracture Mechanics, 2018, 192: 290–306
17 X Zhuang, Q Wang, H Zhu. Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials. International Journal of Fracture, 2017, 204(1): 1–27
18 T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
19 T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
20 T Rabczuk, G Zi. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760
21 X Zhuang, C Augarde, S Bordas. Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling. International Journal for Numerical Methods in Engineering, 2011, 86(2): 249–268
22 X Zhuang, C Augarde, K Mathisen. Fracture modeling using meshless methods and level sets in 3D: Framework and modeling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998
23 P Areias, T Rabczuk, M Msekh. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350
24 F Amiri, D Millán, Y Shen, T Rabczuk, M Arroyo. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109
25 F Amiri, C Anitescu, M Arroyo, S P A Bordas, T Rabczuk. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
26 S Zhou, T Rabczuk, X Zhuang. Phase field modeling of quasi-static and dynamic crack propagation: Comsol implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49
27 S Zhou, X Zhuang, T Rabczuk. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203
28 S Zhou, X Zhuang, H Zhu, T Rabczuk. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192
29 S Zhou, X Zhuang, T Rabczuk. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198
30 P Areias, M Msekh, T Rabczuk. Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143
31 H Ren, X Zhuang, Y Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
32 H Ren, X Zhuang, T Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
33 P Areias, T Rabczuk. 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): 475–505
34 V P Nguyen, H Lian, T Rabczuk, S Bordas. Modelling hydraulic fractures in porous media using flow cohesive interface elements. Engineering Geology, 2017, 225: 68–82
35 C Anitescu, E Atroshchenko, N Alajlan, T Rabczuk. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359
36 T Rabczuk, H Ren, X Zhuang. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem, Computers. Materials and Continua, 2019, 59(1): 31–55
37 H Guo, X Zhuang, T Rabczuk. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456
38 C Atkinson. The interaction between a crack and an inclusion. International Journal of Engineering Science, 1972, 10(2): 127–136
39 F Erdogan, G Gupta, M Ratwani. Interaction between a circular inclusion and an arbitrarily oriented crack. Journal of Applied Mechanics, 1974, 41(4): 1007–1013
40 E Patton, M Santare. The effect of a rigid elliptical inclusion on a straight crack. International Journal of Fracture, 1990, 46(1): 71–79
41 Z Li, Q Chen. Crack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method. International Journal of Fracture, 2002, 118(1): 29–40
42 A Ayyar, N Chawla. Microstructure-based modeling of crack growth in particle reinforced composites. Composites Science and Technology, 2006, 66(13): 1980–1994
43 V A Romanova, R R Balokhonov, S Schmauder. The influence of the reinforcing particle shape and interface strength on the fracture behavior of a metal matrix composite. Acta Materialia, 2009, 57(1): 97–107
44 M Knight, L Wrobel, J Henshall, L De Lacerda. A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. International Journal of Fracture, 2002, 114(1): 47–61
45 M Bush. The interaction between a crack and a particle cluster. International Journal of Fracture, 1997, 88(3): 215–232
46 J Leggoe, X Hu, M Bush. Crack tip damage development and crack growth resistance in particulate reinforced metal matrix composites. Engineering Fracture Mechanics, 1996, 53(6): 873–895
47 J N Hall, J Wayne Jones, A K Sachdev. Particle size, volume fraction and matrix strength effects on fatigue behavior and particle fracture in 2124 aluminum-SiCp composites. Materials Science and Engineering A, 1994, 183(1–2): 69–80
48 S Y Fu, X Q Feng, B Lauke, Y W Mai. Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate-polymer composites. Composites. Part B, Engineering, 2008, 39(6): 933–961
49 K V Rao, W Soboyejo, R Ritchie. Ductile-phase toughening and fatigue-crack growth in Nb-reinforced molybdenum disilicide intermetallic composites. Metallurgical Transactions. A, Physical Metallurgy and Materials Science, 1992, 23(8): 2249–2257
50 X Sun, J Yeomans. Optimization of a ductile-particle-toughened ceramic. Journal of the American Ceramic Society, 1996, 79(10): 2705–2717
51 J Yang, S Jeng. Interface and mechanical behavior of MoSi 2-based composites. Journal of Materials Research, 1991, 6(3): 505–513
52 M Maes, K Van Tittelboom, N De Belie. The efficiency of self-healing cementitious materials by means of encapsulated polyurethane in chloride containing environments. Construction & Building Materials, 2014, 71: 528–537
53 B Dong, Y Wang, G Fang, N Han, F Xing, Y Lu. Smart releasing behavior of a chemical self-healing microcapsule in the stimulated concrete pore solution. Cement and Concrete Composites, 2015, 56: 46–50
54 Gruyaert E, Van Tittelboom K, Sucaet J, Anrijs J, Van Vlierberghe S, Dubruel P, De Geest B, Remon J, De Belie N. Capsules with evolving brittleness to resist the preparation of self-healing concrete. Materiales de Construcciόn, 2016, 66(323): 092
55 Z Yang, J Hollar, X He, X Shi. A self-healing cementitious composite using oil core/silica gel shell microcapsules. Cement and Concrete Composites, 2011, 33(4): 506–512
56 H Huang, G Ye. Simulation of self-healing by further hydration in cementitious materials. Cement and Concrete Composites, 2012, 34(4): 460–467
57 K Van Tittelboom, K Adesanya, P Dubruel, P Van Puyvelde, N De Belie. Methyl methacrylate as a healing agent for self-healing cementitious materials. Smart Materials and Structures, 2011, 20(12): 125016
58 K Van Tittelboom, N De Belie. Self-healing in cementitious materials-a review. Materials (Basel), 2013, 6(6): 2182–2217
59 S White, S Maiti, A Jones, E Brown, N Sottos, P Geubelle. Fatigue of self-healing polymers: Multiscale analysis and experiments. In: ICF11. Italy, 2013
60 L M Mauludin, C Oucif. Modeling of self-healing concrete: A review. Journal of Applied and Computational Mechanics, 2019, 5: 526–539
61 C Oucif, L Mauludin. Continuum damage-healing and super healing mechanics in brittle materials: A state-of-the-art review. Applied Sciences (Basel, Switzerland), 2018, 8(12): 2350
62 L M Mauludin, X Zhuang, T Rabczuk. Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements. Composite Structures, 2018, 196: 63–75
63 F Gilabert, D Garoz, W Van Paepegem. Stress concentrations and bonding strength in encapsulation-based self-healing materials. Materials & Design, 2015, 67: 28–41
64 A Alexeev, R Verberg, A C Balazs. Patterned surfaces segregate compliant microcapsules. Langmuir, 2007, 23(3): 983–987
65 E Kaltzakorta, I Erkizia. Silica microcapsules encapsulating epoxy compounds for self-healing cementitious materials. In: Proceedings of the 3rd International Conference on Self-Healing Materials. Bath, 2011
66 J Parmigiani, M Thouless. The roles of toughness and cohesive strength on crack deflection at interfaces. Journal of the Mechanics and Physics of Solids, 2006, 54(2): 266–287
67 W Wang, K Sadeghipour, G Baran. Finite element analysis of the effect of an interphase on toughening of a particle-reinforced polymer composite. Composites. Part A, Applied Science and Manufacturing, 2008, 39(6): 956–964
68 M V Cid Alfaro, A S J Suiker, C V Verhoosel, R de Borst. Numerical homogenization of cracking processes in thin fibre-epoxy layers. European Journal of Mechanics. A, Solids, 2010, 29(2): 119–131
69 S A Ponnusami, S Turteltaub, S van der Zwaag. Cohesive-zone modelling of crack nucleation and propagation in particulate composites. Engineering Fracture Mechanics, 2015, 149: 170–190
70 L M Mauludin, C Oucif. The effects of interfacial strength on fractured microcapsule. Frontiers of Structural and Civil Engineering, 2019, 13(2): 353–363
71 L M Mauludin, C Oucif. Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete. Underground Space, 2018, 3(3): 181–189
72 B Hilloulin, K Van Tittelboom, E Gruyaert, N De Belie, A Loukili. Design of polymeric capsules for self-healing concrete. Cement and Concrete Composites, 2015, 55: 298–307
73 M Keller, N Sottos. Mechanical properties of microcapsules used in a self-healing polymer. Experimental Mechanics, 2006, 46(6): 725–733
Related articles from Frontiers Journals
[1] Luthfi Muhammad MAULUDIN, Chahmi OUCIF. The effects of interfacial strength on fractured microcapsule[J]. Front. Struct. Civ. Eng., 2019, 13(2): 353-363.
[2] Md. Shahriar QUAYUM,Xiaoying ZHUANG,Timon RABCZUK. Computational model generation and RVE design of self-healing concrete[J]. Front. Struct. Civ. Eng., 2015, 9(4): 383-396.
Full text