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• W2913376552 endingPage "2985" @default.
• W2913376552 startingPage "2961" @default.
• W2913376552 abstract "Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks." @default.
• W2913376552 created "2019-02-21" @default.
• W2913376552 creator A5001563204 @default.
• W2913376552 creator A5016176581 @default.
• W2913376552 creator A5018399001 @default.
• W2913376552 creator A5044909422 @default.
• W2913376552 creator A5055353787 @default.
• W2913376552 creator A5063664248 @default.
• W2913376552 date "2019-01-30" @default.
• W2913376552 modified "2023-10-15" @default.
• W2913376552 title "Systematic study of homogenization and the utility of circular simplified representative volume element" @default.
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