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<p>Polycrystalline materials with irregular random microstructure may have macroscopic elastic properties scattered over some uncertainty intervals, despite the idealistic uniqueness assumption of the homogenization theory. Theoretical variational bounds, including the Voigt–Reuss–Hill, Hashin–Shtrikman, and the latest Pham’s ones, and the self-consistent estimate are specified and calculated for a number of random aggregates of 2D-orthorhombic crystals, which, for the first time, are compared to the numerical results. Large-scale finite element simulations have been performed on large representative volume elements (RVEs), with periodic boundary conditions, of the 2D random Voronoi polycrystals, indicating that the numerical scatter ranges of both the macroscopic elastic bulk and shear moduli converge toward the hierarchical bounds, including the tightest ones, at increasing sizes of the RVEs.</p>

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Elastic moduli of 2D random Voronoi polycrystals: hierarchical estimates versus numerical simulations

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Duc-Chinh Pham,
  • Anh-Binh Tran,
  • Hai-Nhu T. Nguyen,
  • Lam-Dong Vu,
  • My-Hanh T. Vuong

摘要

Polycrystalline materials with irregular random microstructure may have macroscopic elastic properties scattered over some uncertainty intervals, despite the idealistic uniqueness assumption of the homogenization theory. Theoretical variational bounds, including the Voigt–Reuss–Hill, Hashin–Shtrikman, and the latest Pham’s ones, and the self-consistent estimate are specified and calculated for a number of random aggregates of 2D-orthorhombic crystals, which, for the first time, are compared to the numerical results. Large-scale finite element simulations have been performed on large representative volume elements (RVEs), with periodic boundary conditions, of the 2D random Voronoi polycrystals, indicating that the numerical scatter ranges of both the macroscopic elastic bulk and shear moduli converge toward the hierarchical bounds, including the tightest ones, at increasing sizes of the RVEs.