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<p>In this paper, we perform plane strain deformation analyses of the lattice spring model using the simplest form of higher-order continuum theory, the skew-symmetric couple stress theory. For plane strain deformation analyses, we present a homogenization process to calculate the values of the constitutive coefficients of the couple stress theory from the lattice spring model. This homogenization process employs problems that achieve equilibrium solely through external forces prescribed on the boundary without body forces, specifically those having simple displacement solutions. After solving the problems using both the lattice spring model and the couple stress theory, we compare the internal energies to determine the constitutive coefficients. These values are validated through numerical examples. The results of the numerical examples demonstrate that the couple stress theory accurately analyzes the behavior of the lattice spring model and can account for size effects in plane strain deformation with minimal additional degrees of freedom.</p>

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Homogenization using lattice spring models for couple stress theory under plane strain deformation

  • 期刊论文

  • 发表日期：

    2025年1月28日

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  • Youngjae Shin,
  • Seunghun Lee,
  • Uk Jin Jung,
  • Moonhong Kim,
  • Dongwoo Sohn

摘要

In this paper, we perform plane strain deformation analyses of the lattice spring model using the simplest form of higher-order continuum theory, the skew-symmetric couple stress theory. For plane strain deformation analyses, we present a homogenization process to calculate the values of the constitutive coefficients of the couple stress theory from the lattice spring model. This homogenization process employs problems that achieve equilibrium solely through external forces prescribed on the boundary without body forces, specifically those having simple displacement solutions. After solving the problems using both the lattice spring model and the couple stress theory, we compare the internal energies to determine the constitutive coefficients. These values are validated through numerical examples. The results of the numerical examples demonstrate that the couple stress theory accurately analyzes the behavior of the lattice spring model and can account for size effects in plane strain deformation with minimal additional degrees of freedom.