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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2015, Vol. 9 Issue (4) : 383-396
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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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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Md. Shahriar QUAYUM
Xiaoying ZHUANG
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 (, 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
8 483.22 2.46 196.39 196
16 946.31 0.62 1521.12 1520
30 570.47 0.16 3586.89 3585
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
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