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
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.
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