A systematic study on homogenization and the utility of circular simplified RVE

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.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Cluster of Excellence ‘‘Engineering of Advanced Materials’’ at the University of Erlangen- Nuremberg, funded by the DFG within the framework of its ‘‘Excellence Initiative’’

Influence of microstructural heterogeneity on the scaling between flow stress and relative density in microcellular Al-4,5%Cu

We explore the influence of the metal microstructure on the compressive flow stress of replicated microcellular 400-mu m pore size Al-4.5 wt%Cu solidified at two different solidification cooling rates, in the as-cast and T6 conditions. It is found that the yield strength roughly doubles with age-hardening, but does not depend on the solidification cooling rate. Internal damage accumulation, measured by monitoring the rate of stiffness loss with strain, is similar across the four microstructures explored and equals that measured in similar microcellular pure aluminium. In situ flow curves of the metal within the open-pore microcellular material are back-calculated using the Variational Estimate of Ponte-Castaeda and Suquet. Consistent results are obtained with heat-treated microcellular Al-4.5 wt%Cu and are also obtained with separate data for pure Al; however, for the as-cast microcellular Al-4.5 wt%Cu, the back-calculated in situ metal flow stress decreases, for both solidification rates, with decreasing relative density of the foam. We attribute this effect to an interplay between the microstructural and mesostructural features of the microcellular material: variations in the latter with the former held constant can alter the scaling between flow stress and relative density within microcellular alloys