Systematic study of homogenization and the utility of circular simplified representative volume element
Firooz S, Saeb S, Chatzigeorgiou G, Meraghni F, Steinmann P, Javili A (2019)
Publication Type: Journal article
Publication year: 2019
Journal
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.
Authors with CRIS profile
Saba Saeb
Lehrstuhl für Technische Mechanik (LTM)
Paul Steinmann
Lehrstuhl für Technische Mechanik (LTM)
Involved external institutions
Turkey (TR)
France (FR)How to cite
APA:
Firooz, S., Saeb, S., Chatzigeorgiou, G., Meraghni, F., Steinmann, P., & Javili, A. (2019). Systematic study of homogenization and the utility of circular simplified representative volume element. Mathematics and Mechanics of Solids. https://doi.org/10.1177/1081286518823834
MLA:
Firooz, Soheil, et al. "Systematic study of homogenization and the utility of circular simplified representative volume element." Mathematics and Mechanics of Solids (2019).
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