Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods

• Asymptotic homogenization theory is applied for the characterization of 2D lattice materials.
• Stiffness and yield strength of six lattices are determined for the whole range of relative density.
• Closed-form expressions of the yield loci are provided for a convenient use in multiscale problems.
• A comparative analysis on the accuracy of different homogenization schemes as a function of relative density is presented.

Several homogenization schemes exist in literature to characterize the mechanics of cellular materials. Each one has its own assumptions, advantages, and limitations that control the level of accuracy a method can provide. There is often the need in heavy multiscale analyses of lattice materials to find the method that can provide the best trade-off between accuracy and computational cost.In this paper, asymptotic homogenization (AH) is used as a benchmark to test the accuracy of alternative schemes of homogenization applied to lattice materials. AH is first applied to determine the effective elastic moduli and yield strength of six lattice topologies for the whole range of relative density. Yield surfaces are also obtained under multiaxial loading for square, hexagonal, and Kagome lattices, and closed-form expressions of the yield loci are provided for a convenient use in multiscale material problems. With respect to the relative density, the results are then compared to those obtained with other methods available in literature. The analysis shows that the latter can predict the elastic constants with an error below 10% for ρ<0.25ρ<0.25, whereas for the yield strength the discrepancy is above 20% for ρ≥0.1ρ≥0.1 due to the model assumptions. The results of this work on the effective properties of lattice materials provide not only handy expressions of prompt use in multiscale design problems, but also insight into the level of accuracy that alternative homogenization techniques can attain.