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<p>This study develops a theoretical framework to evaluate the equivalent bulk and shear moduli of nanoporous materials, incorporating nanoscale surface effects through the Steigmann–Ogden surface mechanics model. By decomposing the spatial gradient into in-plane and out-of-plane components, stress boundary conditions at a spherical nanovoid/matrix interface are derived with improved computational efficiency. A representative volume element (RVE) is modeled as an infinite spherical matrix embedding a concentric nanoinhomogeneity or nanovoid. Generalized displacement solutions, rooted in elasticity theory, are formulated for both domains, with unknown coefficients determined using macroscopic strain conditions, Steigmann–Ogden interface constraints, and displacement finiteness at the nanoinhomogeneity’s center. The Mori–Tanaka homogenization approach is employed to compute the equivalent moduli, with nanovoid-specific results derived by setting the nanoinhomogeneity’s elastic moduli to zero. Numerical experiments, conducted on nanoporous aluminum, investigate the influence of surface bulk modulus, shear modulus, bending modulus, porosity, and nanovoid radius. The results demonstrate that surface effects are pronounced for smaller nanovoids (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(&lt;10\)</EquationSource> </InlineEquation> nm) and higher porosity, significantly deviating from classical predictions due to increased surface-to-volume ratios. The equivalent bulk modulus remains independent of surface bending modulus under hydrostatic loading, while the shear modulus exhibits strong sensitivity to bending stiffness, modulated by surface moduli.</p>

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On the macroscopic elastic moduli of nanoporous materials with surface tensile and bending rigidity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月23日

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  • Chenyi Zheng,
  • Xiangming Ge,
  • Weijiang Chu,
  • Can Wang,
  • Gaohui Li,
  • Jianli Ma,
  • Fei Xie,
  • Changwen Mi

摘要

This study develops a theoretical framework to evaluate the equivalent bulk and shear moduli of nanoporous materials, incorporating nanoscale surface effects through the Steigmann–Ogden surface mechanics model. By decomposing the spatial gradient into in-plane and out-of-plane components, stress boundary conditions at a spherical nanovoid/matrix interface are derived with improved computational efficiency. A representative volume element (RVE) is modeled as an infinite spherical matrix embedding a concentric nanoinhomogeneity or nanovoid. Generalized displacement solutions, rooted in elasticity theory, are formulated for both domains, with unknown coefficients determined using macroscopic strain conditions, Steigmann–Ogden interface constraints, and displacement finiteness at the nanoinhomogeneity’s center. The Mori–Tanaka homogenization approach is employed to compute the equivalent moduli, with nanovoid-specific results derived by setting the nanoinhomogeneity’s elastic moduli to zero. Numerical experiments, conducted on nanoporous aluminum, investigate the influence of surface bulk modulus, shear modulus, bending modulus, porosity, and nanovoid radius. The results demonstrate that surface effects are pronounced for smaller nanovoids ( \(<10\) nm) and higher porosity, significantly deviating from classical predictions due to increased surface-to-volume ratios. The equivalent bulk modulus remains independent of surface bending modulus under hydrostatic loading, while the shear modulus exhibits strong sensitivity to bending stiffness, modulated by surface moduli.