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Original Articles

A diffused material interface based homogenization method for periodic composites

, &
Pages 5979-5992 | Received 24 Jun 2021, Accepted 17 Aug 2021, Published online: 20 Sep 2021

References

  • M. Balasubramanian, Composite Materials and Processing. CRC press, Boca Raton, 2014.
  • ScottJ. Hollister, and Noboru Kikuchi, A comparison of homogenization and standard mechanics analyses for periodic porous composites, Comput. Mech., vol. 10, no. 2, pp. 73–95, 1992. DOI: 10.1007/BF00369853.
  • Ouail Ouchetto, and Brahim Essakhi, Homogenization of periodic bi-isotropic composite materials, Waves Random Complex Media, vol. 28, no. 3, pp. 523–532, 2018. DOI: 10.1080/17455030.2017.1367439.
  • Ankit Srivastava, Elastic metamaterials and dynamic homogenization: a review, Int. J. Smart Nano Mater., vol. 6, no. 1, pp. 41–60, 2015. DOI: 10.1080/19475411.2015.1017779.
  • Jean-Claude Michel, Hervé Moulinec, and Pierre Suquet, Effective properties of composite materials with periodic microstructure: a computational approach, Comput. Methods Appl. Mech. Eng., vol. 172, no. 1-4, pp. 109–143, 1999. DOI: 10.1016/S0045-7825(98)00227-8.
  • T. Iwakuma, and S. Nemat-Nasser, Composites with periodic microstructure, Comput Struct., vol. 16, no. 1-4, pp. 13–19, 1983. DOI: 10.1016/0045-7949(83)90142-6.
  • Hamed Khezrzadeh, A statistical micromechanical multiscale method for determination of the mechanical properties of composites with periodic microstructure, Compos. Part B Eng., vol. 115, pp. 138–143, 2017. DOI: 10.1016/j.compositesb.2016.10.024.
  • R. Luciano, and E. J. Barbero, Formulas for the stiffness of composites with periodic microstructure, Int. J. Solids Struct., vol. 31, no. 21, pp. 2933–2944, 1994. DOI: 10.1016/0020-7683(94)90060-4.
  • Michael Ryvkin, Or Hadar, and Leonid Kucherov, Multiscale analysis of non-periodic stress state in composites with periodic microstructure, Int. J. Eng. Sci., vol. 121, pp. 167–181, 2017. DOI: 10.1016/j.ijengsci.2017.09.002.
  • Yeong-Moo Yi, Sang-Hoon Park, and Sung-Kie Youn, Asymptotic homogenization of viscoelastic composites with periodic microstructures, Int. J. Solids Struct., vol. 35, no. 17, pp. 2039–2055, 1998. DOI: 10.1016/S0020-7683(97)00166-2.
  • John Douglas Eshelby. The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London Ser. A. Math. Phys. Sci., vol. 241, no. 1226, pp. 376–396, 1957.
  • M. R. Delfani, and V. Bagherpour, Overall properties of particulate composites with periodic microstructure in second strain gradient theory of elasticity, Mech. Mater., vol. 113, pp. 89–101, 2017. DOI: 10.1016/j.mechmat.2017.07.013.
  • Tanaka Mori, and Kohichi Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., vol. 21, no. 5, pp. 571–574, 1973. DOI: 10.1016/0001-6160(73)90064-3.
  • Rodney Hill, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids., vol. 11, no. 5, pp. 357–372, 1963. DOI: 10.1016/0022-5096(63)90036-X.
  • Bernard Budiansky, On the elastic moduli of some heterogeneous materials, J. Mech. Phys. Solids., vol. 13, no. 4, pp. 223–227, 1965. DOI: 10.1016/0022-5096(65)90011-6.
  • Chunhui Yang, Hoon Huh, and ThomasH. Hahn, Evaluation of effective material properties of composite materials using special fem, J. Mater. Process. Technol., vol. 140, no. 1-3, pp. 185–190, 2003. DOI: 10.1016/S0924-0136(03)00712-X.
  • Jacob Aboudi, and Michael Ryvkin, The effect of localized damage on the behavior of composites with periodic microstructure, Int. J. Eng. Sci., vol. 52, pp. 41–55, 2012. DOI: 10.1016/j.ijengsci.2011.12.001.
  • Erik Andreassen, and Casper Schousboe Andreasen, How to determine composite material properties using numerical homogenization, Comput. Mater. Sci., vol. 83, pp. 488–495, 2014. DOI: 10.1016/j.commatsci.2013.09.006.
  • Francesca Fantoni, Andrea Bacigalupo, Marco Paggi, and Josè Reinoso, A phase field approach for damage propagation in periodic microstructured materials, Int. J. Fract., vol. 223, no. 1-2, pp. 53–24, 2020. pages DOI: 10.1007/s10704-019-00400-x.
  • Igor Sevostianov, On the shape of effective inclusion in the maxwell homogenization scheme for anisotropic elastic composites, Mech. Mater., vol. 75, pp. 45–59, 2014. DOI: 10.1016/j.mechmat.2014.03.003.
  • Chun-Jen Hsueh, and Kaushik Bhattacharya, Homogenization and Path Independence of the J-Integral in Heterogeneous Materials, J. Appl. Mech., vol. 83, pp. 101012, no. 10, 2016. DOI: 10.1115/1.4034294.
  • Arezoo Emdadi, Jeremy Watts, WilliamG. Fahrenholtz, GregoryE. Hilmas, and Mohsen Asle Zaeem, Predicting effective fracture toughness of ZrB2-based ultra-high temperature ceramics by phase-field modeling, Materials & Design., vol. 192, pp. 108713, 2020. DOI: 10.1016/j.matdes.2020.108713.
  • Gabriela R. Fernandes, Guilherme A. Ohland, and Jordana F. Vieira, A boundary element formulation to perform elastic analysis of heterogeneous microstructures, Eng. Anal. Boundary Elem., vol. 87, pp. 47–65, 2018. DOI: 10.1016/j.enganabound.2017.11.006.
  • Gabriela R. Fernandes, Luis Henrique R. Crozariol, Amanda S. Furtado, and Matheus C. Santos, A 2d boundary element formulation to model the constitutive behavior of heterogeneous microstructures considering dissipative phenomena, Eng. Anal. Boundary Elem., vol. 99, pp. 1–22, 2019. DOI: 10.1016/j.enganabound.2018.10.018.
  • Gabriela R. Fernandes, Maria Júlia Marques Silva, Jordana F. Vieira, and José J. C. Pituba, A 2d rve formulation by the boundary element method considering phase debonding, Eng. Anal. Boundary Elem., vol. 104, pp. 259–276, 2019. DOI: 10.1016/j.enganabound.2019.03.018.
  • Olek C. Zienkiewicz, Robert L. Taylor, and Jian Z. Zhu, The Finite Element Method: its Basis and Fundamentals, Elsevier, Oxford, UK, 2005.
  • Per-Olof Persson, and Gilbert Strang, A simple mesh generator in matlab, SIAM Rev., vol. 46, no. 2, pp. 329–345, 2004. DOI: 10.1137/S0036144503429121.
  • Khennane Amar, Introduction to Finite Element Analysis Using MATLAB[Textregistered] and Abaqus, CRC Press, Florida, USA, 2013.

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