Composites Research

The Korean Society for Composite Materials (한국복합재료학회)
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A Review of Mean-Field Homogenization for Effective Physical Properties of Particle-Reinforced Composites

평균장 균질화를 이용한 입자 강화 복합재의 유효 물성치 예측 연구 동향

  • Received : 2020.03.03
  • Accepted : 2020.04.09
  • Published : 2020.04.30
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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.

본 리뷰 논문에서는 최근에 연구된 평균장 균질화법을 이용한 다양한 물성치 예측 연구의 동향에 대해 소개한다. 유효 강성 예측에 사용되는 기존의 균질화법을 소개하고 이를 확장하여 유효 열/전기 전도성 및 유전 상수를 예측하는 방법을 소개한다. 압전 및 열전과 같이 2개의 물리현상이 중첩된 다중 물리 현상의 구성방정식은 훅 법칙과 같이 단순한 선형 형태로 변환하여 복합재의 유효 물성치를 예측하는 연구를 소개하고 마지막으로 복합 재료의 유효 물성치를 예측하기 위한 일반화된 식을 제시하고 유한 요소 해석과 비교한 검증/연구를 소개한다.

Keywords

References

  1. 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. https://doi.org/10.1016/j.compstruct.2011.08.005
  2. 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. https://doi.org/10.1016/1044-5803(95)00066-6
  3. 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. https://doi.org/10.1109/TDEI.2006.1624276
  4. 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. https://doi.org/10.1002/app.28875
  5. 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. https://doi.org/10.1016/j.compscitech.2008.06.007
  6. 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. https://doi.org/10.1016/j.compscitech.2011.03.003
  7. 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. https://doi.org/10.1016/S0020-7683(03)00013-1
  8. 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. https://doi.org/10.1177/1081286519826343
  9. 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.
  10. 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. https://doi.org/10.1016/j.compositesb.2012.05.015
  11. 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. https://doi.org/10.1088/1751-8113/41/41/415205
  12. 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. https://doi.org/10.1016/j.ijsolstr.2017.01.033
  13. 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. https://doi.org/10.1016/j.compstruct.2020.112076
  14. Odegard, G.M., "Constitutive Modeling of Piezoelectric Polymer Composites," Acta Materialia, Vol. 52, No. 18, 2004, pp. 5315-5330. https://doi.org/10.1016/j.actamat.2004.07.037
  15. 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. https://doi.org/10.1016/S1359-6454(96)00090-0
  16. 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. https://doi.org/10.1016/j.ijsolstr.2017.03.003
  17. 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. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118620
  18. 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. https://doi.org/10.1016/j.commatsci.2004.03.011
  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. 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. https://doi.org/10.1016/j.compstruct.2018.01.038
  21. Mura, T., Micromechanics of Defects in Solids, Kluwer Academic Publishers, Netherlands, 1982.
  22. 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. https://doi.org/10.1016/0167-6636(87)90005-6
  23. 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. https://doi.org/10.1016/0022-5096(65)90010-4
  24. 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. https://doi.org/10.1016/S0022-5096(99)00087-3
  25. 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. https://doi.org/10.1016/j.ijplas.2013.06.006
  26. 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. https://doi.org/10.1016/0022-5096(91)90030-R
  27. 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.
  28. 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. https://doi.org/10.1016/j.ijsolstr.2010.03.002
  29. 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. https://doi.org/10.1115/1.3424140
  30. 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.
  31. 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. https://doi.org/10.1177/1081286518805521
  32. 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. https://doi.org/10.1016/j.euromechsol.2018.02.008
  33. 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. https://doi.org/10.3389/fmats.2019.00001
  34. 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. https://doi.org/10.1016/0020-7683(93)90058-F
  35. 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. https://doi.org/10.1038/35002022
  36. 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. https://doi.org/10.1038/nature13184
  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. https://doi.org/10.1002/pssb.2220670108
  38. 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. https://doi.org/10.1177/0021998306062317