Fig. 4. Effect of porous, anisotropic microstructural materials in topology optimization.

The multimicrostructure topology optimization scheme selects both the appropriate microstructural materials and their locations. The design in (A) considers a single, solid, isotropic material with objective function value, f₀. The designs in (B to G) each consider a different subset, indicated to their right, of seven porous, anisotropic microstructural materials. A single volume constraint is specified in each case such that the total volume of bulk material occupies, at most, a domain volume fraction of $\overline{\mathit{v}}=0.022$ [the volume constraint is active in all cases, and all designs in (A to G) have the same volume of bulk material within a 4% tolerance after postprocessing]. Normalized directional tensile and shear moduli (based on homogenized properties) are provided in (H) for the solid, isotropic material and in (I) for the seven porous, anisotropic microstructural materials. Variable ${\widehat{\mathit{d}}}_{\mathit{i}}^{\text{bar}}$ is bar diameter, ${\hat{\mathit{v}}}_i$ is unit cell volume, and $\mathit{f}/{\mathit{f}}_0$ is the objective function normalized to that of the structure in (A).