Isotropy-conditioned density mapping for lattice design using topology optimization

Homogenization-based topology optimization methods used for designing graded lattice structures require multiple scaling laws because of the anisotropic elastic properties of cubic lattice cells. In this study, an isotropy-conditioned density mapping (ICDM) approach is presented to define lattice cells with isotropic elastic properties across the full range of relative densities, enabling the use of a single scaling law in density-based topology optimization. Strut radii for different groups within a cubic lattice cell are determined to satisfy an isotropy condition by evaluating homogenized elastic properties over the entire relative density range required for topology optimization. The resulting isotropy-conditioned lattice cells are used for density mapping in topology optimization based on the solid isotropic material with penalization (SIMP) method. The proposed approach is computationally efficient because it enables macroscopic optimization using the standard SIMP method while ensuring that spatially varying mesoscale lattice configurations satisfy isotropy using a single scaling law. The method is demonstrated through two three-dimensional numerical examples to show its efficacy. The improved structural performance of the optimized designs with the isotropy-conditioned lattice cells is shown by comparing their results with the existing designs.