Optimal and continuous multilattice embedding

Abstract

Because of increased geometric freedom at a widening range of length scales and access to a growing material space, additive manufacturing has spurred renewed interest in topology optimization of parts with spatially varying material properties and structural hierarchy. Simultaneously, a surge of micro/nanoarchitected materials have been demonstrated. Nevertheless, multiscale design and micro/nanoscale additive manufacturing have yet to be sufficiently integrated to achieve free-form, multiscale, biomimetic structures. We unify design and manufacturing of spatially varying, hierarchical structures through a multimicrostructure topology optimization formulation with continuous multimicrostructure embedding. The approach leads to an optimized layout of multiple microstructural materials within an optimized macrostructure geometry, manufactured with continuously graded interfaces. To make the process modular and controllable and to avoid prohibitively expensive surface representations, we embed the microstructures directly into the 3D printer slices. The ideas provide a critical, interdisciplinary link at the convergence of material and structure in optimal design and manufacturing.

Inverting the structure–property map of truss metamaterials by deep learning

“…UCs may vary in the shape of their external bounding box (due to the applied affine transformations) and their internal topology, both of which must be considered when introducing spatial gradings between UCs. Without the introduced rotations and affine transformations, a smooth transition from one topology to another could be achieved by grading the diameters of the struts in the UCs ( 23 , 41 , 49 , 64 ), since all topologies have the same cube bounding box and connectivities to the corner vertices. Here, by contrast, smooth transitions between affinely transformed UCs (which maintain their connectivity but alter the bounding box) are challenging.…”

“…Other approaches, like the library of tens of thousands of unique truss lattices introduced recently ( 14 ) with inspiration from molecular structures, do not admit a consistent design parameterization (unlike their molecular analogs). Consequently, existing works ( 23 , 25 , 30 , 41 ) have typically considered only a small number of fixed lattice topologies, whose superposition with different strut thicknesses and/or base materials results in a limited design space for the effective properties—but with the added benefit of enabling spatial gradients. In addition, the common focus on cubic and hence orthotropic UCs ( 26 , 35 ) ignores shear–normal and shear–shear coupling components in the effective stiffness tensor—although it has been recognized that those may be beneficial for, among others, compliance minimization and wave guidance ( 22 , 42 ).…”

Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending

“…4a), our method has 1, 928 design variables. Perhaps the most comparable methods are the multilattice approach (Sanders et al, 2021), which needs 3, 200 variables for the same problem without optimizing the graded volume fractions, and the latent variable multiclass approach (Wang et al, 2020c), which uses 1, 920 variables and includes functionally graded volumes; both, however require predefined classes with fixed connectors. It is important to note that although it is possible for other methods to contain less design variables, they make simplifications that we do not.…”

“…In contrast, the continuous interfaces of FGS can mitigate the errors from homogenization as well as the discrepancies between the intended and manufactured designs (Garner et al, 2019;Panesar et al, 2018). Functional grading can be further categorized into three camps: spatially-varying volume fraction (Wang et al, 2018;Li et al, 2019;Zong et al, 2019;Jansen and Pierard, 2020), topology (Kumar et al, 2020;Sanders et al, 2021), or a hybrid of both (Wang et al, 2020c;Luo et al, 2021). While traditional FGS use the first, recent research is shifting towards the latter two, which have demonstrated that expanding the design space to include multiple topology types can considerably improve the structural performance.…”

“…Similar methods in the general multiscale TO field accomplish connected heterogeneous designs without the above simplifications by: (1) sharing finite elements and design variables at interfaces (Liu et al, 2019), (2) adding connectivity constraints (Du et al, 2018;Garner et al, 2019), (3) controlling the change in the properties of intermediate microstructures (Zhou et al, 2019), (4) creating geometric gradations during pre-or post-processing (Sanders et al, 2021;Zhou et al, 2019;Zobaer and Sutradhar, 2020), and (5) interpolating random field representations of microstructures (Kumar et al, 2020). Of these, Liu et al (2019), Garner et al (2019), and Sanders et al (2021) concurrently design the macrostructure as well as the distributions of multiple microstructures, and only Luo et al (2021) also optimized the graded volume fractions.…”