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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2015, Vol. 9 Issue (4) : 383-396     https://doi.org/10.1007/s11709-015-0320-z
RESEARCH ARTICLE |
Computational model generation and RVE design of self-healing concrete
Md. Shahriar QUAYUM1,Xiaoying ZHUANG1,2,*(),Timon RABCZUK1
1. Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar 99425, Germany
2. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
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Abstract

Computational homogenization is a versatile tool that can extract effective properties of heterogeneous or composite material through averaging technique. Self-healing concrete (SHC) is a heterogeneous material which has different constituents as cement matrix, sand and healing agent carrying capsules. Computational homogenization tool is applied in this paper to evaluate the effective properties of self-healing concrete. With this technique, macro and micro scales are bridged together which forms the basis for multi-scale modeling. Representative volume element (RVE) is a small (microscopic) cell which contains all the microphases of the microstructure. This paper presents a technique for RVE design of SHC and shows the influence of volume fractions of different constituents, RVE size and mesh uniformity on the homogenization results.

Keywords homogenization      self-healing concrete (SHC)      representative volume element      multiscale modelling     
Corresponding Authors: Xiaoying ZHUANG   
Online First Date: 19 November 2015    Issue Date: 26 November 2015
 Cite this article:   
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.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-015-0320-z
http://journal.hep.com.cn/fsce/EN/Y2015/V9/I4/383
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Md. Shahriar QUAYUM
Xiaoying ZHUANG
Timon RABCZUK
Fig.1  The schematic representation of two-step homogenization [21]
Fig.2  Schematic illustration of Mori-Tanaka and effective interface micromechanics approaches [22]
Fig.3  (a) Microstructural cells of different sizes, (b) convergence of the apparent properties of effective values with increase of RVE size for different boundary conditions [33]
sieve No. sieve opening/mm mass of soil retained on each sieve, Wn/g percentage of mass retained on each sieve, Rn cumulative percent retained, ΣRn percent finer 100-ΣRn
4 4.75 154 18.7 18.7 81.3
8 2.36 72 8.7 27.4 72.6
16 1.18 72 8.7 36.1 63.9
30 0.6 141 17.1 53.2 46.8
40 0.425 85 10.3 63.5 36.5
50 0.3 80 9.7 73.2 26.8
100 0.15 149 18.1 91.3 8.7
200 0.075 45 5.5 96.8 3.2
Pan 24 2.9 99.7
∑ = 822 g= W1
Tab.1  A sample calculation of sieve analysis obtained from Sieve analysis test, the university of texas at Arlington (http://www.uta.edu/ce/geotech/lab/Main/sieve/index.htm, July, 2014)
sieve No. size range/mm avg. dia./mm weight distribu/gm weight/%
4 4.75-2.361 3.56 0
8 2.36-1.181 1.77 72 24.16
16 1.18-0.61 0.89 141 47.32
30 0.6-0.31 0.45 85 28.52
50 0.3-0.151 0.23 0 0.00
sieve No. asand area accord. to weight %/mm2 (area÷particle)/mm2 No. of particles reqd. considered No. of particles
4
8 483.22 2.46 196.39 196
16 946.31 0.62 1521.12 1520
30 570.47 0.16 3586.89 3585
50
Tab.2  Calculation of sand particles for a 100 mm×100 mm RVE
Fig.4  (a) Surface morphology of a capsule with UF wall, (b) cross-section of the shell wall [37]
material Young’s modulus, E/MPa Poisson’s ratio, v
cement matrix 14.848e3a(15e3 considered) 0.33
sand 10−28 (30 considered) 0.15−0.25 (0.2 considered)
capsule Shellb 3.60e3 0.3
capsule fluidc 1000 0.45
Tab.3  Material properties considered for the RVE
Fig.5  Error plots of elastic properties against seed difference on opposite boundaries of 2D RVE in 11 direction
Fig.6  Elastic properties against different volume fraction of sand in same RVE length
model RVE size/mm matrix sand cap core cap shell
FE1 100 78.73% 18.67% 2.23% 0.37%
FE2 50 78.17% 18.15% 3.16% 0.51%
FE3 40 77.27% 19.01% 3.19% 0.53%
FE4 30 76.23% 20.53% 2.79% 0.45%
FE5 20 75.20% 21.67% 2.72% 0.41%
FE6 10 73.39% 22.01% 4.00% 0.60%
Tab.4  RVE sizes and different constituents’ volume fraction
Fig.7  Different RVE sizes with random sand and capsule distributions. (a) FE6:size 10 mm; (b) FE5:size 20 mm; (c) FE4:size 30 mm; (d) FE3:size 40 mm; (e) FE2:size 50 mm; (f) FE1:size 100 mm
Fig.8  Variation of elastic properties against different length of RVE with random distribution of capsules and sands; and comparison with analytical solution
Fig.9  3D RVEs with different RVE size. (a) “REV” size 5 mm; (b) “REV” size 8 mm; (c) “REV” size 10 mm; (d) “REV” size 15 mm; (e) “REV” size 20 mm; (f) “REV” size 25 mm (Color legend: gray= matrix, yellow= sand, green= cap. shell, red= cap.core)
RVE size/mm volume fraction/%
matrix sand cap shell cap core
5 93.57 6.41 0.02 8.00E-06
8 89.89 6.22 0.73 3.16
10 88.03 10.24 0.34 1.39
15 83.02 13.38 0.74 2.86
20 83.01 12.74 0.84 3.41
25 86.8 9.86 0.67 2.67
Tab.5  Volume fractions of different constituents of 3D RVEs
Fig.10  The homogenized elastic properties against the RVE size obtained from FEA and analytical solution
Fig.11  Error plot of different elastic properties against RVE size
Fig.12  L2 error norm of elasticity tensor against RVE size
1 Van Tittelboom  K, De Belie  N. Self-healing in cementitious materials—a review. Materials, 2013, 6(6): 2182–2217
2 Dry  C. Matrix cracking repair and filling using active and passive modes for smart timed release of chemicals from fibers into cement matrices. Smart Materials and Structures, 1994, 3(2): 118
3 White  S R, Sottos  N R, Geubelle  P H, Moore  J S, Kessler  M, Sriram  S R, Brown  E N, Viswanathan  S. Autonomic healing of polymer composites. Nature, 2001, 409(6822): 794–797
4 Dry  C. Procedures developed for self-repair of polymer matrix composite  materials.  Composite  Structures,  1996,  35(3):  263–269
5 Li  V C, Lim  Y M, Chan  Y W. Feasibility study of a passive smart self-healing cementitious composite. Composites. Part B, Engineering, 1998, 29(6): 819–827
6 Lee  J Y, Buxton  G A, Balazs  A C. Using nanoparticles to create self-healing composites. The Journal of chemical physics, 2004, 121(11): 5531–5540
7 Li  V C, Yang  E H. Self Healing in Concrete Materials. Self Healing Materials. Netherlands: Springer, 2007, 161–193
8 Gumbsch  P, Pippan  R, eds. Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics. Springer Science & Business Media, 2011, 522
9 Suquet  P M. Local and global aspects in the mathematical theory of plasticity. Plasticity today: Modelling, methods and applications, 1985, 279–310
10 Guedes  J M, Kikuchi  N. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Computer Methods in Applied Mechanics and Engineering, 1990, 83(2): 143–198
11 Terada  K, Kikuchi  N. Nonlinear homogenization method for practical applications. ASME Applied Mechanics Division-Publications-AMD, 1995, 212: 1–16
12 Ghosh  S, Lee  K, Moorthy  S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. International Journal of Solids and Structures, 1995, 32(1): 27–62
13 Ghosh  S, Lee  K, Moorthy  S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Computer Methods in Applied Mechanics and Engineering, 1996, 132(1): 63–116
14 Kouznetsova  V, Geers M G D, Brekelmans W A M. Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. International Journal for Numerical Methods in Engineering, 2002, 54(8): 1235–1260
15 Yuan  Z, Fish  J. Toward realization of computational homogenization in practice. International Journal for Numerical Methods in Engineering, 2008, 73(3): 361–380
16 Weinan  E. Principles of Multiscale Modeling. Cambridge University Press, 2011
17 THAO  T D P. Quasi-Brittle Self-Healing Materials: Numerical Modelling and Applications in Civil Engineering. Dissertation for the Doctoral Degree. Singapore: National University of Singapore, 2011
18 Bakis  C, ed. American Society of Composites-28th Technical Conference. DEStech Publications, Inc, 2013
19 Talebi  H, Silani  M, Bordas  S P A, Kerfriden  P, Rabczuk  T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071
20 Li  G. Self-healing Composites: Shape Memory Polymer Based Structures. Chichester, West Sussex, UK: John Wiley & Sons, 2014
21 Pierard  O, Friebel  C, Doghri  I. Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation. Composites Science and Technology, 2004, 64(10): 1587–1603
22 Odegard  G M, Clancy  T C, Gates  T S. Modeling of the mechanical properties of nanoparticle/polymer composites. Polymer, 2005, 46(2): 553–562
23 Drugan, W J, Willis  J R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. Journal of the Mechanics and Physics of Solids, 1996, 44(4): 497–524
24 De Bellis  M L, Ciampi  V, Oller  S, Addessi  D. First order computational homogenization. Multi-scale techniques for masonry structures (pp. 27–74). Barcelona: International Center for Numerical Methods in Engineering, 2010
25 Hill  R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids, 1963, 11(5): 357–372
26 Van der Sluis  O, Schreurs  P J G, Brekelmans  W A M, Meijer  H E H. Overall behaviour of heterogeneous elastoviscoplastic materials: Effect of microstructural modelling. Mechanics of Materials, 2000, 32(8): 449–462
27 Terada  K, Hori  M, Kyoya  T, Kikuchi  N. Simulation of the multi-scale convergence in computational homogenization approaches. International Journal of Solids and Structures, 2000, 37(16): 2285–2311
28 Huet  C. Application of variational concepts to size effects in elastic heterogeneous bodies. Journal of the Mechanics and Physics of Solids, 1990, 38(6): 813–841
29 Huet  C. Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies. Mechanics of Materials, 1999, 31(12): 787–829
30 Ostoja-Starzewski  M. Random field models of heterogeneous materials. International Journal of Solids and Structures, 1998, 35(19): 2429–2455
31 Ostoja-Starzewski  M. Scale effects in materials with random distributions of needles and cracks. Mechanics of Materials, 1999, 31(12): 883–893
32 Pecullan  S, Gibiansky  L V, Torquato  S. Scale effects on the elastic behavior of periodic and hierarchical two-dimensional composites. Journal of the Mechanics and Physics of Solids, 1999, 47(7): 1509–1542
33 Gumbsch  P, Pippan  R, eds. Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics. Springer Science & Business Media, 2011, 522
34 Övez  B, Citak  B, Oztemel  D, Balbas  A, Peker  S, Cakir  S. Variation of droplet sizes during the formation of microcapsules from emulsions. Journal of Microencapsulation, 1997, 14(4): 489–499
35 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
36 Wang  X, Xing  F, Zhang  M, Han  N, Qian  Z. Experimental study on cementitious composites embedded with organic microcapsules. Materials (Basel), 2013, 6(9): 4064–4081
37 Keller  M W, Sottos  N R. Mechanical properties of microcapsules used in a self-healing polymer. Experimental Mechanics, 2006, 46(6): 725–733
38 Mindess  S, Young  J F, Darwin  D. Response of concrete to stress. In: Concrete, 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2003, 303–362
39 Powers  T C, Brownyard  T L. Studies of the physical properties of hardened Portland cement paste. ACI Journal Proceedings, ACI, 1947, 43(9): 845–880
40 Gilford  III J. Microencapsulation of Self-healing Concrete Properties. Master’s thesis, Louisiana State Univ Baton Rouge, 2012
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