Journal of Applied and Computational Mechanics
A FEM Multiscale Homogenization Procedure using Nanoindentation for High Performance Concrete
Document Type : Research Paper
Authors
1 GRESPI, University of Reims Champagne-Ardenne, UFR SEN, Campus Moulin de la Housse, Reims, 51687, France
2 LGC, Department of Civil Engineering, Djillali Liabès University, Rue Kadi Benkadi, Sidi-Bel-Abbès, 22000, Algeria
Abstract
This paper aims to develop a numerical multiscale homogenization method for prediction of elasto-viscoplastic properties of a high performance concrete (HPC). The homogenization procedure is separated into two-levels according to the microstructure of the HPC: the mortar or matrix level and the concrete level. The elasto-viscoplastic behavior of individual microstructural phases of the matrix are identified from nanoindentation data using an inverse identification method. The micromechanical results are then used as input parameters for numerical elasto-viscoplastic homogenization at microscale. The mortar level is analyzed with numerical homogenization by using the finite element simulation to predict the overall elasto-viscoplastic properties of HPC. The results are compared with macroscopic experimental and analytical results from the literature showing a good agreement.
Keywords
- Homogenization
- Nanoindentation
- Finite element simulation
- Elasto-viscoplastic model
- Multiscale modeling
- High performance concrete
Main Subjects
[1] Kanouté, P., Boso, D., Chaboche, J., Schrefler, B., Multiscale methods for composites: A review, Archives of Computational Methods in Engineering, 16, 2009, 31–75.
[2] Eshelby, J.D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London, A241(1226), 1957, 376–396.
[3] Hill, R., The elastic behavior of a crystalline aggregate, Proceedings of the Royal Society of London, A65, 1952, 349–354.
[4] Hashin, Z., and Shtrikman, S., A variational approach to the elastic behavior of multiphase minerals, Journal of the Mechanics and Physics of Solids, 11(2), 1963, 127–140.
[5] Hershey, A., The elasticity of an isotropic aggregate of anisotropic cubic crystals, Journal of Applied Mechanics – Transactions of the ASME, 21(3), 1954, 236–240.
[6] Zohdi, T. I., Oden, J., Rodin, G. J., Hierarchical modeling of heterogeneous bodies, Computer Methods in Applied Mechanics and Engineering, 138(1-4), 1996, 273 – 298.
[7] Fish, J., Shek, K., Pandheeradi, M., Shephard, M. S., Computational plasticity for composite structures based on mathematical homogenization: Theory and practice, Computer Methods in Applied Mechanics and Engineering, 148(1-2), 1997, 53–73.
[8] Feyel, F., Multiscale FE2 elasto-viscoplastic analysis of composite structures, Computational Materials Science, 16(1-4), 1999, 344–354.
[9] Levy, A. and Papazian, J., Elastoplastic finite element analysis of short-fiber-reinforced SiC/Al composites: effects of thermal treatment, Acta Metallurgica Materialia, 39(10), 1991, 2255 – 2266.
[10] Ghosh, S., Lee, K. and 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, 132(1-2), 1996, 63–116.
[11] Feyel, F. and Chaboche, J.-L., FE2 multiscale approach for modelling the elasto-viscoplastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, 183(3-4), 2000, 309–330.
[12] Sun, L. and Ju, J., Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part II: Applications, International Journal of Solids and Structures, 38(2), 2001, 203–225.
[13] Borges, D.C. and Pituba J.J.C., Analysis of quasi-brittle materials at mesoscopic level using homogenization model, Advances in Concrete Construction, 5(3), 2017, 221-240.
[14] Constantinides, G. and Ulm, F.J., The effect of two types of C–S–H on the elasticity of cement-based materials: results from nanoindentation and micromechanical modeling, Cement and Concrete Research, 34(1), 2004, 67–80.
[15] Sorelli, L., Constantinides, G., Ulm, F.J. and Toutlemonde, F., The nano-mechanical signature of ultra-high performance concrete by statistical nanoindentation techniques, Cement Concrete Research, 38(12), 2008, 1447–1456.
[16] Němeček, J., Králík, V. and Vondrejc, J., Micromechanical analysis of heterogeneous structural materials, Cement and Concrete Composites, 36, 2013, 85–92.
[17] Da Silva, W.R.L., Němeček, J. and Štemberk, P., Application of multiscale elastic homogenization based on nanoindentation for high performance concrete, Advances in Engineering Software, 62–63, 2013, 109–118.
[18] Fakhari Tehrani, F., Absi, J., Allou, F. and Petit, Ch., Heterogeneous numerical modeling of asphalt concrete through use of a biphasic approach: Porous matrix/inclusions, Computational Materials Science, 69, 2013, 186–196.
[19] Zhou, C., Li, K. and Ma, F., Numerical and statistical analysis of elastic modulus of concrete as a three-phase heterogeneous composite, Computers and Structures, 139, 2014, 33–42.
[20] Caballero, A., Lopez, C.M. and Carol, I., 3D meso-structural analysis of concrete specimens, Computer Methods in Applied Mechanics and Engineering, 195, 2006, 7182–7195.
[21] Shahbeyk, S., Hosseini, M. and Yaghoobi, M., Mesoscale finite element prediction of concrete failure, Computational Materials Science, 50, 2011, 1973–1990.
Shim, S., Oliver, W.C. and Pharr, G.M., A critical examination of the Berkovich vs. conical indentation based on 3D finite element calculation, MRS Proceedings, 841, 2004, R9.5.
[22] Sun, B. and Li, Z., Adaptive concurrent multi-scale FEM for trans-scale damage evolution in heterogeneous concrete, Computational Materials Science, 99, 2015, 262–273.
[23] Tedesco, J.W., Hughes, M.L. and Ross, C.A., Numerical simulation of high strain rate concrete compression tests, Computers & Structures, 51(1), 1994, 65–77.
[24] Tedesco, J.W., Powell, J.C., Ross, C.A. and Hughes, M.L., A strain-rate-dependent concrete material model for ADINA, Computers & Structures, 64(5-6), 1997, 1053–1067.
[25] Beshara, F. and Virdi, K., Prediction of dynamic response of blast-loaded reinforced concrete structures, Computers & Structures, 44(1-2), 1992, 297–313.
[26] Cela, J.J.L., Analysis of reinforced concrete structures subjected to dynamic loads with a viscoplastic Drucker–Prager model, Applied Mathematical Modelling, 22(7), 1998, 495–515.
[27] Shirai, K., Ito, C. and Onuma, H., Numerical studies of impact on reinforced concrete beam of hard missile, Nuclear Engineering and Design, 150, 1994, 483–489.
[28] Park, S.W., Xia, Q. and Zhou, M., Dynamic behavior of concrete at high strain rates and pressures: II. Numerical simulation, International Journal of Impact Engineering, 25, 2001, 887–910.
[29] Buck, J. J., McDowell, D.L. and Zhou, M., Effect of microstructure on load-carrying and energy-dissipation capacities of UHPC, Cement and Concrete Research, 43, 2013, 34-50.
[30] Häfner, S., Eckardt, S., Luther, T. and Könke, C., Mesoscale modeling of concrete: Geometry and numerics, Computers & Structures, 84(7), 2006, 450–461.
[31] Dupray, F., Malecot, Y., Daudeville and L., Buzaud, E., A mesoscopic model for the behaviour of concrete under high confinement, International Journal for Numerical and Analytical Methods in Geomechanics, 33(11), 2009, 1407–1423.
[32] Comby-Peyrot, I., Bernard, F., Bouchard, P., Bay, F. and Garcia-Diaz, E., Development and validation of a 3D computational tool to describe concrete behaviour at mesoscale. Application to the alkali-silica reaction, Computational Materials Science, 46, 2009, 1163–1177.
[33] Aydin, A.C., Arslan, A. and Gül, R., Mesoscale simulation of cement based materials’ time-dependent behavior, Computational Materials Science, 41, 2007, 20–26.
[34] Setiawan, Y., Gan, B.S. and Han, A.L., Modeling of the ITZ zone in concrete: Experiment and numerical simulation, Computers and Concrete, 19(6), 2017, 647-655.
[35] Xu, W., Wu, F., Jiao, Y., Liu, M., A general micromechanical framework of effective moduli for the design of nonspherical nano- and micro-particle reinforced composites with interface properties, Materials & Design, 127, 2017, 162–172.
[36] Xu, W., Jia, M., Zhu, Z., Liu, M., Lei, D., Gou, X., n-Phase micromechanical framework for the conductivity and elastic modulus of particulate composites: Design to microencapsulated phase change materials (MPCMs)-cementitious composites, Materials & Design, 145, 2018, 108–115.
[37] Xu, W., Wu, Y., Gou, X., Effective elastic moduli of nonspherical particle-reinforced composites with inhomogeneous interphase considering graded evolutions of elastic modulus and porosity, Computer Methods in Applied Mechanics and Engineering, 350, 2019, 535–553.
[38] Xu, W., Zhang, D., Lan, P., Jiao, Y., Multiple-inclusion model for the transport properties of porous composites considering coupled effects of pores and interphase around spheroidal particles, International Journal of Mechanical Sciences, 150, 2019, 610–616.
[39] Xu, W., Xu, B., Guo, F., Elastic properties of particle-reinforced composites containing nonspherical particles of high packing density and interphase: DEM–FEM simulation and micromechanical theory, Computer Methods in Applied Mechanics and Engineering, 326, 2017, 122–143.
[40] Xu, W., Sun, H., Chen, W., Chen, H., Transport properties of concrete-like granular materials interacted by their microstructures and particle components, International Journal of Modern Physics B, 32(18), 2018, 1840011.
[41] Perzyna, P., Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9, 1966, 243–377.
[42] Oliver, W.C and Pharr, G.M., An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, Journal of Material Research, 7(6), 1992, 1564–1583.
[43] Guessasma, S., Sehaki, M., Lourdin, D. and Bourmaud, A., Viscoelasticity properties of biopolymer composite materials determined using finite element calculation and nanoindentation, Computational Materials Science, 44, 2008, 371–377.
[44] Chen, Z., Diebels, S., Peter, N.J. and Schneider, A.S., Identification of finite viscoelasticity and adhesion effects in nanoindentation of a soft polymer by inverse method, Computational Materials Science, 72, 2013, 127–139.
[45] Benkabou, R., Abbès, B., Abbès, F., Asroun, A. and Li, Y. (), Contribution of 3D numerical simulation of instrumented indentation testing in the identification of elastic-viscoplastic behaviour law of a high-performance concrete, Matériaux & Techniques, 105, 2017, 102.
[46] Abaqus Version 6.13, Dassault Systèmes Simulia Corp., Providence, RI, USA, 2013.
[47] Wang, X.F., Wang, X.W., Zhou, G.M. and Zhou, C.Z., Multi-scale analysis of 3D woven composite based on periodicity boundary conditions, Journal of Composite Materials, 41(14), 2007, 1773-1788.
[48] Melro, A.R., Camanho, P.P., Andrade Pires, F.M. and Pinho, S.T., Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses, International Journal of Solids and Structures, 50(11-12), 2013, 1906–1915.
[49] Bocciarelli, M., Bolzon, G. and Maier, G., Parameter identification in anisotropic elastoplasticity by indentation and imprint mapping, Mechanics of Materials, 37, 2005, 855–868.
[50] Nakamura, T. and Gu, Y., Identification of elastic-plastic anisotropic parameters using instrumented indentation and inverse analysis, Mechanics of Materials, 39, 2007, 340–356.
[51] Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2), 2002, 182–197.
[52] Trofimov, A., Abaimov, S. G., Akhatov, I., Sevostianov, I., On the bounds of applicability of two-step homogenization technique for porous materials, International Journal of Engineering Science, 123, 2018, 117–126.
[53] Trofimov, A., Markov, A., Abaimov, S. G., Akhatov, I., Sevostianov, I., Overall elastic properties of a material containing inhomogeneities of concave shape, International Journal of Engineering Science, 132, 2018, 30–44.
[54] Xu, W., Jia, M., Gong, Z., Thermal conductivity and tortuosity of porous composites considering percolation of porous network: From spherical to polyhedral pores, Composites Science and Technology, 167, 2018, 134–140.
[55] Xu, W., Jiao, Y., Theoretical framework for percolation threshold, tortuosity and transport properties of porous materials containing 3D non-spherical pores, International Journal of Engineering Science, 134, 2019, 31–46.
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