The effects of interfacial strength on fractured microcapsule

Abstract

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.

Keywords

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

References

[1] Rabczuk T. Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives. ISRN Applied Mathematics, 2013, 2013(2013): 849231

[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): 2316–2343

[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): 2777–2799

[4] Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

[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): 475–505

[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: 250–265

[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: 19–31

[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): 427–448

[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): 331–356

[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: 102–109

[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): 45–57

[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: 146–155

[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: 68–82

[14] Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

[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): 1099–1122

[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: 50–63

[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: 322–350

[18] Areias P, Msekh M, Rabczuk T. Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

[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: 27–41

[20] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[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: 762–782

[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: 304–313

[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: 122–129

[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): 1047–1071

[25] Talebi H, Silani M, Rabczuk T. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92

[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): 1129–1148

[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: 382–395

[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: 126–143

[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: 981–988

[30] Arash B, Park H S, Rabczuk T. Coarse-grained model of the J-integral of carbon nanotube reinforced polymer composites. Carbon, 2016, 96: 1084–1092

[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): 506–512

[32] Huang H, Ye G. Simulation of self-healing by further hydration in cementitious materials. Cement and Concrete Composites, 2012, 34(4): 460–467

[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): 125016

[34] Van Tittelboom K, De Belie N. Self-healing in cementitious materials- A review. Materials (Basel), 2013, 6(6): 2182–2217

[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, 2005

[36] Gilabert F, Garoz D, Van Paepegem W. Stress concentrations and bonding strength in encapsulation-based self-healing materials. Materials & Design, 2015, 67: 28–41

[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, 2011

[38] Alexeev A, Verberg R, Balazs A C. Patterned surfaces segregate compliant microcapsules. Langmuir, 2007, 23(3): 983–987

[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: 298–307

[40] Simulia A V. Abaqus 6.13 documentation. Dassault systemes, 2013

[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): 2437–2455

[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): 48–71

[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): 730–741

[44] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[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): 577–599

[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): 641–658

[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): 524–548

[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): 473–495

[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): 1391–1411

[50] Belytschko T, Lu Y Y, Gu L. Element-free galerkin methods, International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256 doi:10.1002/nme.1620370205

[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): 763–813

[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): 4135–4195

[53] Nguyen V, Anitescu C, Bordas S, Rabczuk T. Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116

[54] Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based xiga for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146

[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 kirchhoff-love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291

[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): 1892–1908

[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): 3410–3424

[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: 239–258

[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): 383–396

[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: 702563

[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: 1177–1190

[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: 19–31

RIGHTS & PERMISSIONS

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