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Polarization versus Mori-Tanaka approximations for elastic isotropic multicomponent materials

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Abstract

A new method, called the polarization approximation (PA), appears as an interesting technique to calibrate the effective properties of composite materials. Constructed from the minimum energy principle, the popularization approximation is a potential alternative to the popular Mori-Tanka approximation (MTA), and has been derived as an approximation of the macroscopic moduli as well as the microscopic fields. In the literature, MTA has been applied to various homogenization problems of a wide range of composite materials though sometimes, the results lack robust accuracy. It is shown in this paper that PA is more reliable than MTA. The similarity and differences between PA and MTA when applying to elastic modulus will be pointed out using some types of heterogeneous microstructures, which have isotropic macroscopic elastic moduli in 2D or 3D. Results from other methods, such as experiments, the numerical unit cell method and the Hashin-Shtrikman bounds will also be presented as well for comparisons.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.02-2017.309.

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Authors and Affiliations

  1. Hanoi University of Industry, Hanoi, Vietnam

    N. Q. Tran

  2. National University of Civil Engineering, Hanoi, Vietnam

    A. B. Tran & N. Nguyen

  3. VAST-Institute of Mechanics, Hanoi, Vietnam

    D. C. Pham

Authors
  1. N. Q. Tran
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  2. A. B. Tran
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  3. D. C. Pham
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  4. N. Nguyen
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Correspondence to A. B. Tran.

Additional information

Anh-Binh Tran is a Professor at National University of Civil Engineering (NUCE), Hanoi, Vietnam. He received his Ph.D. in Mechanical Engineering from Paris-Est University, France. His research interests include computational mechanics, surrogate model using neural networks, artificial intelligent in construction. He was a member of Vietnam National Foundation for Science and Technology Development. He is now the Head of the Institute of Informatics in Construction (ICC) and of the Faculty of Information Technology in NUCE.

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Tran, N.Q., Tran, A.B., Pham, D.C. et al. Polarization versus Mori-Tanaka approximations for elastic isotropic multicomponent materials. J Mech Sci Technol 35, 3033–3043 (2021). https://doi.org/10.1007/s12206-021-0626-9

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  • DOI: https://doi.org/10.1007/s12206-021-0626-9

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