Baroghel-Bouny V, Nguyen TQ, Dangla P. Assessment and prediction of RC structure service life by means of durability indicators and physical/chemical models. Cement Concr Compos. 2009;31:522–34.
Schimmel EC, Remmers J. Development of a constitutive model for self-healing materials. Delft Aerospace Computational Science, Report DACS-06-003 2006.
Remmers J, de Borst R. Numerical modelling of self-healing mechanisms. In Self Healing Materials Springer. 2008. 365-380.
Abu Al-Rub R, Darabi MK, Little DN, Masad EA. A micro-damage healing model that improves the prediction of fatigue life in asphalt mixes. Int J Eng Sci. 2010;48:966–90.
Voyiadjis GZ, Shojaei A, Li G. A thermodynamic consistent damage and healing model for self healing materials. Int J Plast. 2011;27:1025–44.
Huang H, Ye G. Simulation of self-healing by further hydration in cementitious materials. Cement Concr Compos. 2012;34:460–7.
Mergheim J, Steinmann P. Phenomenological modelling of self-healing polymers based on integrated healing agents. Comput Mech. 2013;52:681–92.
Aliko-Benitez A, Doblare M, Sanz-Herrera JA. Chemical-diffusive modeling of the self-healing behaviour in concrete. Int J Solids Struct. 2015;69–70:392–402.
Chitez AS, Jefferson AD. A coupled thermo-hygro-chemical model for characterising autogenous healing in ordinary cementitious materials. Cem Concr Res. 2016;88:184–97.
Caggiano A, Etse G, Ferrara L, Krelani V. Zero-thickness interface constitutive theory for concrete self-healing effects. Comput Struct. 2017;186:22–34.
Davies R, Jefferson AD. Micromechanical modelling of self-healing cementitious materials. Int J Solids Struct. 2017;113–114:180–91.
Gilabert FA, Garoz D, Van Paepegem W. Macro- and micro-modeling of crack propagation in encapsulation-based self-healing materials: application of xfem and cohesive surface techniques. Mater Des. 2017;130:459–78.
Zhou S, Zhu H, Ju JW, Yan Z, Chen Q. Modeling microcapsule-enabled self-healing cementitious composite materials using discrete element method. Int J Damage Mech. 2017;26:340–57.
Di Luzio G, Ferrara L, Krelani V. Numerical modeling of mechanical regain due to self-healing in cement based composites. Cement Concr Compos. 2018;86:190–205.
Oucif C, Voyiadjis GZ, Rabczuk T. Modeling of damage-healing and nonlinear self-healing concrete behaviour: application to coupled and uncoupled self-healing mechanisms. Theoret Appl Fract Mech. 2018;96:216–30.
Ponnusami SA, Krishnasamy J, Turteltaub S, van der Zwaag S. A cohesive-zone crack healing model for self-healing materials. Int J Solids Struct. 2018;134:249–63.
Zhang Y, Zhuang X. A softening-healing law for self-healing quasi-brittle materials: analysing with strong discontinuity embedded approach. Eng Fract Mech. 2018;192:290–306.
Sanz-Herrera JA, Aliko-Benitez A, Fadrique-Contreras AM. Numerical investigation of the coupled mechanical behaviour of self-healing materials under cyclic loading. Int J Solids Struct. 2019;160:232–46.
Freeman BL, Jefferson AD. The simulation of transport processes in cementitious materials with embedded healing systems. Int J Numer Anal Meth Geomech. 2020;44:293–326.
Jefferson AD, Javierre E, Freeman B, Zaoui A, Koenders E, Ferrara L. Research progress on numerical models for self-healing cementitious materials. Adv Mater Interf. 2018;5:1701378.
Rots JG. Smeared and discrete representations of localized fracture. Int J Fract. 1991;51(1):45–59.
Noghabai K. Discrete versus smeared versus element-embedded crack models on ring problem. J Eng Mech. 1999;125(3):307–15.
de Borst R, Remmers JJC, Needleman A, Abellan M-A. Discrete vs smeared crack models for concrete fracture: bridging the gap. Int J Numer Anal Meth Geomech. 2004;28:583–607.
Dias-da-Costa D, Cervenka V, Graça-e-Costa R. Model uncertainty in discrete and smeared crack prediction in RC beams under flexural loads. Eng Fract Mech. 2018;199:532–43.
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng. 1999;45:601–20.
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth Eng. 1999;46:131–50.
Duarte CAM, Babuška I, Oden JT. Generalized finite element methods for three-dimensional structural mechanics problems. Comput Struct. 2000;77:215–32.
Song JH, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Meth Eng. 2006;67:868–93.
Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng. 1996;139:289–314.
Bordas S, Nguyen PV, Dunant C, Guidoum A, Nguyen-Dang H. An extended finite element library. Int J Numer Meth Eng. 2007;71:703–32.
Karihallo BL, Xiao QZ. Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct. 2003;81:119–29.
Fries TP, Belytschko T. The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Meth Eng. 2010;84:253–304.
Yu T, Bui TQ. Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement. Comput Struct. 2018;196:112–33.
Strouboulis T, Babuška I, Copps K. The design and analysis of the generalized finite element method. Comput Methods Appl Mech Eng. 2000;181:43–69.
Strouboulis T, Copps A, Babuška I. The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Methods Eng. 2000;47:1401–17.
Strouboulis T, Copps K, Babuška I. The generalized finite element method. Comput Methods Appl Mech Eng. 2001;190:4081–193.
Babuška I, Caloz G, Osborn JE. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J Numer Anal. 1994;31:745–981.
Babuška I, Melenk JM. The partition of unity method. Int J Numer Meth Eng. 1997;40:727–58.
Oden JT, Duarte CAM, Zienkiewicz OC. A new cloud-based hp finite element method. Comput Methods Appl Mech Eng. 1998;153:117–26.
Belytschko T, Gracie R, Ventura G. A review of extended/generalized finite element methods for material modelling. Modell Simul Mater Sci Eng. 2009;17:043001.
Hansbo A, Hansbo P. An unfitted finite element method, based on Nitche’s method, for elliptic interface problems. Comput Methods Appl Mech Eng. 2002;191:5537–52.
Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng. 2004;193:3523–40.
Burman E, Claus S, Hansbo P, Larson MG, Massing A. CutFEM: discretizing geometry and partial differential equations. Int J Numer Meth Eng. 2015;104:472–501.
Schott B, Wall WA. A new face-oriented stabilized XFEM approach for 2D and 3D incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng. 2014;276:233–65.
Hansbo P, Larson MG, Massing A. A stabilized cut finite element method for the Darcy problem on surfaces. Comput Methods Appl Mech Eng. 2017;326:298–318.
Claus S, Kerfriden P. A stable and optimally convergent LaTIn-CutFEM algorithm for multiple unilateral contact problems. Int J Numer Meth Eng. 2017;113:938–66.
Burman E, Elfverson D, Hansbo P, Larson MG, Larsson K. Shape optimisation using the cut finite element method. Comput Methods Appl Mech Eng. 2018;328:242–61.
Claus S, Kerfriden P. A CutFEM method for two-phase flow problems. Comput Methods Appl Mech Eng. 2019;348:185–206.
Alfaiate J, Simone A, Sluys LJ. Non-homogeneous displacement jumps in strong embedded discontinuities. Int J Solids Struct. 2003;40(21):5799–817. https://doi.org/10.1016/S0020-7683(03)00372-X.
Oliver J, Huespe AE, Sanchez PJ. A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. Comput Methods Appl Mech Eng. 2006;195:4732–52.
Ortiz M, Leroy Y, Needleman A. A finite element method for localized failure analysis. Comput Methods Appl Mech Eng. 1987;61:189–214.
Dvorkin EN, Cuitino AM, Gioia G. Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions. Int J Numer Meth Eng. 1990;30:541–64.
Simo JC, Oliver J, Armero F. An analysis of strong discontinuities induced by strain softening in rate-independent inelastic solids. Comput Mech. 1993;12:277–96.
Lotfi HR, Shing PB. Embedded representation of fracture in concrete with mixed finite elements. Int J Numer Meth Eng. 1995;38:1307–25.
Oliver J. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng. 1996;39:3575–600.
Oliver J. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: numerical simulation. Int J Numer Methods Eng. 1996;39:3601–23.
Wells GN, Sluys LJ. Application of embedded discontinuities for softening solids. Eng Fract Mech. 2000;65:263–81.
Dias-da-Costa D, Alfaiate J, Sluys LJ, Julio E. A discrete strong discontinuity approach. Eng Fract Mech. 2009;76:1176–201.
Dias-da-Costa D, Alfaiate J, Sluys LJ, Julio E. Towards a generalization of a discrete discontinuity approach. Comput Methods Appl Mech Eng. 2009;198:3670–81.
Dias-da-Costa D, Alfaiate J, Sluys LJ, Areias P, Julio E. An embedded formulation with conforming finite elements to capture strong discontinuities. Int J Numer Meth Eng. 2013;93:224–44.
Linder C, Armero F. Finite elements with embedded branching. Finite Elem Anal Des. 2009;45:280–93.
Armero F, Linder C. Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int J Fract. 2009;160:119–41.
Djuc A, Brank B, Ibrahimbegovic A. Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids. Int J Numer Meth Eng. 2013;94:1075–98.
Saksala T, Brancherie D, Harari I, Ibrahimbegovic A. Combined continuum damage-embedded discontinuity model for explicit dynamic fracture analyses of quasi-brittle materials. Int J Numer Meth Eng. 2015;101:230–50.
Saksala T, Brancherie D, Ibrahimbegovic A. Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage-embedded discontinuity model. Int J Numer Anal Meth Geomech. 2016;40:1339–57.
Lu M, Zhang H, Zheng Y, Zhang L. A multiscale finite element method with embedded strong discontinuity model for the simulation of cohesive cracks in solids. Comput Methods Appl Mech Eng. 2016;311:576–98.
Lu M, Zhang H, Zheng Y, Zhang L. A multiscale finite element method for the localization analysis of homogeneous and heterogeneous saturated porous media with embedded strong discontinuity model. Int J Numer Meth Eng. 2017;112:1439–72.
Jirasek M. Comparative study on finite elements with embedded discontinuities. Comput Methods Appl Mech Eng. 2000;188:307–30.
Hou TY, Wu XH. A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys. 1997;134(1):169–89.
Jefferson AD, Selvarajoo T, Freeman BL, Davies R. An experimental and numerical study on vascular self-healing cementitious materials. MATEC Web Conf. Concrete solutions 2019—7th international conference on concrete repair. 2019.
Jefferson AD, Mihai IC, Tenchev R, Alnaas WF, Cole G, Lyons P. A plastic-damage-contact constitutive model for concrete with smoothed evolution functions. Comput Struct. 2016;169:40–56.
Gardner D, Jefferson AD, Hoffman A. Investigation of capillary flow in discrete cracks in cementitious materials. Cem Concr Res. 2012;42(7):972–81. https://doi.org/10.1016/j.cemconres.2012.03.017.
Gardner D, Jefferson AD, Hoffman A, Lark R. Simulation of the capillary flow of an autonomic healing agent in discrete cracks in cementitious materials. Cem Concr Res. 2014;58:35–44. https://doi.org/10.1016/j.cemconres.2014.01.005.
Gardner D, Herbert D, Jayaprakash M, Jefferson AD, Paul A. Capillary flow characteristics of an autogenic and autonomic healing agent for self-healing concrete. J Mater Civ Eng. 2017;29(11):4017228. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002092.
Selvarajoo T, Davies RE, Gardner DR, Freeman BL, Jefferson AD. Characterisation of a vascular self-healing cementitious materials system: flow and curing properties. Constr Build Mater. 2020;245:118332.
Jiang T-S, Soo-Gun OH, Slattery JC. Correlation for dynamic contact angle. J Colloid Interface Sci. 1979;69(1):74–7. https://doi.org/10.1016/0021-9797(79)90081-X.
Comyn J. Moisture cure of adhesives and sealants. Int J Adhes Adhes. 1998;18(4):247–53. https://doi.org/10.1016/S0143-7496(97)00031-6.
Li YJ, Barthès-Biesel D, Salsac AV. Polymerization kinetics of n-butyl cyanoacrylate glues used for vascular embolization. J Mech Behav Biomed Mater. 2017;69(January):307–17. https://doi.org/10.1016/j.jmbbm.2017.01.003.
Alfaiate J, Wells GN, Sluys LJ. On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture. Eng Fract Mech. 2002;69(6):661–86. https://doi.org/10.1016/S0013-7944(01)00108-4.
Cervera M, Pelà L, Clemente R, Roca P. A crack-tracking technique for localized damage in quasi-brittle materials. Eng Fract Mech. 2010;77:2431–50.
Selvarajoo T, Characterisation of a vascular self-healing cementitious material system (PhD thesis), Cardiff University, UK, 2019.
Selvarajoo T, Davies RE, Freeman BL, Jefferson AD. Mechanical response of a vascular self-healing cementitious material system under varying loading conditions. Constr Build Mater. 2020;254:119245.
Winkler B, Hofstetter G, Niederwanger G. Experimental verification of a constitutive model for concrete cracking. Proc Instit Mech Eng Part L J Mater Design Appl. 2001;215(2):75–86.