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Physics and Mathematics

January 24, 2025; Seoul, South Korea: V International Scientific and Practical Conference «THEORETICAL AND PRACTICAL ASPECTS OF MODERN SCIENTIFIC RESEARCH»


MULTISCALE HOMOGENIZATION OF REINFORCED COMPOSITES


DOI
https://doi.org/10.36074/logos-24.01.2025.053
Published
19.02.2025

Abstract

One of the most effective approaches to computational modeling of composite systems is the homogenization method [1]. A necessary condition for applying the homogenization method is the presence of a certain scale relationship between the components of the reinforced composite and the entire system [2]. Most often, two-scale analytical models are introduced, each of which is associated with a pre-set scale parameter. To implement the effective computational processes, this parameter is specified as a small value, namely, a real number (usually tending to zero). The impossibility of introducing more than two different scales for a local volume of a composite and, in addition, the insufficient sensitivity of the homogenized characteristics of the composite to the geometric relationships of scales can be attributed to the significant disadvantages of such methods [3].

References

  1. Fujii, D., Chen, B. C., & Kikuchi, N. (2001). Composite material design of two‐dimensional structures using the homogenization design method. International Journal for Numerical Methods in Engineering, 50(9), 2031-2051. https://doi.org/10.1002/nme.105.
  2. Oller, S., Miquel Canet, J., & Zalamea, F. (2005). Composite material behavior using a homogenization double scale method. Journal of Engineering mechanics, 131(1), 65-79. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:1(65).
  3. Zhou, X. Y., Qian, S. Y., Wang, N. W., Xiong, W., & Wu, W. Q. (2022). A review on stochastic multiscale analysis for FRP composite structures. Composite Structures, 284, 115132. https://doi.org/10.1016/j.compstruct.2021.115132.
  4. Wu, Z., Huang, N. E., & Chen, X. (2009). The multi-dimensional ensemble empirical mode decomposition method. Advances in Adaptive Data Analysis, 1(03), 339-372. https://doi.org/10.1142/S1793536909000187.

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