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http://dx.doi.org/10.7234/composres.2020.33.2.081

A Review of Mean-Field Homogenization for Effective Physical Properties of Particle-Reinforced Composites  

Lee, Sangryun (Department of Mechanical Engineering, KAIST)
Ryu, Seunghwa (Department of Mechanical Engineering, KAIST)
Publication Information
Composites Research / v.33, no.2, 2020 , pp. 81-89 More about this Journal
Abstract
In this review paper, we introduce recent research studied effective physical properties of the reinforced composite using mean-field homogenization. We address homogenization for effective stiffness and expand it to effective thermal/electrical conductivity and dielectric constant. Multiphysics problems like piezoelectricity and thermoelectricity are considered by simplifying the constitutive equation into the linear equations like Hooke's law. We present a generalized theoretical formula for predicting effective physical properties of composite and validation by against finite element analysis.
Keywords
Homogenization; Micromechanics; Effective property; Multiphysics;
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1 Duschlbauer, D., Bohm, H.J., and Pettermann, H.E., "Computational Simulation of Composites Reinforced by Planar Random Fibers: Homogenization and Localization by Unit Cell and Mean Field Approaches," Journal of Composite Materials, Vol. 40, No. 24, 2006, pp. 2217-2234.   DOI
2 Obradovic, J., Boria, S., and Belingardi, G., "Lightweight Design and Crash Analysis of Composite Frontal Impact Energy Absorbing Structures," Composite Structures, Vol. 94, No. 2, 2012, pp. 423-430.   DOI
3 Immarigeon, J-P., Holt, R.T., Koul, A.K., Zhao, L., Wallace, W., and Beddoes, J.C., "Lightweight Materials for Aircraft Applications," Materials Characterization, Vol. 35, No. 1, 1995, pp. 41-67.   DOI
4 Imai, T., Sawa, F., Nakano, T., Shimizu, T., Kozako, M., and Tanaka, T., "Effects of Nano- and Micro-filler Mixture on Electrical Insulation Properties of Epoxy Based Composites," IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 13, No. 2, 2006, pp. 319-326.   DOI
5 Zheng, Y., Kim, C., Wang, G., Wei, P., and Jiang, P., "Epoxy/nano-silica Composites: Curing Kinetics, Glass Transition Temperatures, Dielectric, and Thermal-mechanical Performances," Journal of Applied Polymer Science, Vol. 111, No. 2, 2009, pp. 917-927.   DOI
6 Pan, Y., Igora, L., and Pelegri, A.A., "Numerical Generation of a Random Chopped Fiber Composite RVE and Its Elastic Properties," Composite Science and Technology, Vol. 68, No. 13, 2008, pp. 2792-2798.   DOI
7 Lee, S., Lee, J., Ryu, B., and Ryu, S., "A Micromechanics-based Analytical Solution for the Effective Thermal Conductivity of Composites with Orthotropic Matrices and Interfacial Thermal Resistance," Scientific Reports, Vol. 8, No. 1, 2018, 7266.
8 Wang, H.W., Zhou, H.W., Peng, R.D., and Mishnaevsky, L., "Nanoreinforced Polymer Composites: 3D FEM Modeling with Effective Interface Concept," Composite Science and Technology, Vol. 71, No. 7, 2011, pp. 980-988.   DOI
9 Doghri, I., and Ouaar, A., "Homogenization of Two-phase Elasto-plastic Composite Materials and Structures: Study of Tangent Operators, Cyclic Plasticity and Numerical Algorithms," International Journal of Solids and Structures, Vol. 40, No. 7, 2003, pp. 1681-1712.   DOI
10 Lee, S., Kim, Y., Lee, J., and Ryu, S., "Applicability of the Interface Spring Model for Micromechanical Analyses with Interfacial Imperfections to Predict the Modified Exterior Eshelby Tensor and Effective Modulus," Mathematics and Mechanics of Solids, Vol. 24, No. 9, 2019, pp. 2944-2960.   DOI
11 Huang, J.H., and Kuo, W-S., "Micromechanics Determination of the Effective Properties of Piezoelectric Composites Containing Spatially Oriented Short Fibers," Acta Materialia, Vol. 44, No. 12, 1996, pp. 4889-4898.   DOI
12 Mortazavi, B., Baniassadi, M., Bardon, J., and Ahzi, S., "Modeling of Two-phase Random Composite Materials by Finite Element, Mori-Tanaka and Strong Contrast Methods," Composite Part B: Engineering, Vol. 45, No. 1, 2013, pp. 1117-1125.   DOI
13 Giordano, S., and Palla, P.L., "Dielectric behavior of anisotropic inhomogeneities: interior and exterior Eshelby tensors," Journal of Physics A: Mathematical and Theoretical, Vol. 41, No. 41, 2008, 415205.   DOI
14 Bednarcyk, B.A., Aboudi, J., and Arnold, S.M., "Micromechanics of Composite Materials Governed by Vector Constitutive Laws," International Journal of Solids and Structures, Vol. 110-111, 2017, pp. 137-151.   DOI
15 Lee, S., Jung, J., and Ryu, S., "Micromechanics-based Prediction of the Effective Properties of Piezoelectric Composite Having Interfacial Imperfections," Composite Structures, Vol. 240, 2020, 112076.   DOI
16 Odegard, G.M., "Constitutive Modeling of Piezoelectric Polymer Composites," Acta Materialia, Vol. 52, No. 18, 2004, pp. 5315-5330.   DOI
17 Martínez-Ayuso, G., Friswell, M.I., Adhikari, S., Khodaparast, H.H., and Berger, H., "Homogenization of Porous Piezoelectric Materials," International Journal of Solids and Structures, Vol. 113-114, 2017, pp. 218-229.   DOI
18 Jung, J., Lee, S., Ryu, B., and Ryu, S., "Investigation of Effective Thermoelectric Properties of Composite with Interfacial Resistance Using Micromechanics-based Homogenisation," International Journal of Heat and Mass Transfer, Vol. 144, 2019, 118620.   DOI
19 Lee, D., and Suh, N., Axiomatic Design and Fabrication of Composite Structures Applications in Robots, Machine Tools, and Automobiles, NY Oxford University Press., New York, USA, 2005.
20 Xu, Y., and Yagi, K., "Automatic FEM Model Generation for Evaluating Thermal Conductivity of Composite with Random Materials Arrangement," Computational Materials Science, Vol. 30, No. 3-4, 2004, pp. 242-250.   DOI
21 Kim, Y., Kim, Y., Lee, T-I., Kim, T-S., and Ryu, S., "An Extended Analytic Model for the Elastic Properties of Platelet-staggered Composites and Its Application to 3D Printed Structures," Composite Structures, Vol. 189, 2018, pp. 27-36.   DOI
22 Mura, T., Micromechanics of Defects in Solids, Kluwer Academic Publishers, Netherlands, 1982.
23 Wu, L., Noels, L., Adam, L., and Doghri, I., "A Combined Incremental-secant Mean-field Homogenization Scheme with Per-phase Residual Strains for Elasto-plastic Composites," International Journal of Plasticity, Vol. 51, 2013, pp. 80-102.   DOI
24 Benveniste, Y., "A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials," Mechanics and Materials, Vol. 6, No. 2, 1987, pp. 147-157.   DOI
25 Hill, R., "A Self-consistent Mechanics of Composite Materials," Journal of the Mechanics and Physics of Solids, Vol. 13, No. 4, 1965, pp. 213-222.   DOI
26 Castaneda, P.P., and Tiberio, E., "A Second-order Homogenization Method in Finite Elasticity and Applications to Black-filled Elastomers," Journal of the Mechanics and Physics of Solids, Vol. 48, No. 6-7, 2000, pp. 1389-1411.   DOI
27 Castaneda, P.P., "The Effective Mechanical Properties of Nonlinear Isotropic Composites," Journal of the Mechanics and Physics of Solids, Vol. 39, No. 1, 1991, pp. 45-71.   DOI
28 Chiu, Y.P., "On the Stress Field due to Initial Strains in a Cuboid Surrounded by an Infinite Elastic Space," Journal of Applied Mechanics, Vol. 44, No. 4, 1977, pp. 587-590.   DOI
29 Eshelby, J.D., "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proceedings of the Royal Society A, Vol. 241, No. 1226, 1957, pp. 376-396.
30 Jun, T-S., and Korsunsky, A.M., "Evaluation of Residual Stresses and Strains Using the Eigenstrain Reconstruction Method," International Journal of Solids and Structures, Vol. 47, No. 13, 2010, pp. 1678-1686.   DOI
31 Ryu, S., Lee, S., Jung, J., Lee, J., and Kim, Y., "Micromechanics-based Homogenization of the Effective Physical Properties of Composites with an Anisotropic Matrix and Interfacial Imperfections," Frontiers in Materials, Vol. 6, No. 21, 2019, pp. 1-17.   DOI
32 Dvorak, G.J., and Benveniste, Y., "On Transformation Strain and Uniform Fields In Multiphase Elastic Media," Proceedings of the Royal Society A, Vol. 437, No. 1900, 1992, pp. 291-310.
33 Lee, S., Lee, J., and Ryu, S., "Modified Eshelby Tensor for an Anisotropic Matrix with Interfacial Damage," Mathematics and Mechanics of Solids, Vol. 24, No. 6, 2019, pp. 1749-1762.   DOI
34 Lee, S., and Ryu, S., "Theoretical Study of the Effective Modulus of a Composite Considering the Orientation Distribution of the Fillers and the Interfacial Damage," European Journal of Mechanics - A Solids, Vol. 72, 2018, pp. 79-87.   DOI
35 Dunn, M.L., and Taya, M., "Micromechanics Predictions of the Effective Electroelastic Moduli of Piezoelectric Composites," International Journal of Solids and Structures, Vol. 30, No. 2, 1993, pp. 161-175.   DOI
36 Fu, H., and Cohen, R.E., "Polarization Rotation Mechanism for Ultrahigh Electromechanical Response in Single-crystal Piezoelectrics," Nature, No. 403, No. 6767, 2000, pp. 281-283.   DOI
37 Barnett, D.M., and Lothe, J., "Dislocation and Line Charges in Anisotropic Piezoelectric Insulators," Physics Status Solidi (b), Vol. 67, No. 1, 1975, pp. 105-111.   DOI
38 Zhao, L-D., Lo, S-H., Zhang, Y., Sun, H., Tan, G., Uher, C., Wolverton, C., Dravid, V.P., and Kanatzidis, M.G., "Ultralow Thermal Conductivity and High Thermoelectric Figure of Merit in SnSe Crystals," Nature, No. 508, No. 7496, 2014, pp. 373-377.   DOI