Cut-Cell Microstructures for Two-scale Structural Optimization

TL;DR

This work tackles the challenge of preserving complex shape boundaries while achieving prescribed deformation in two-scale topology optimization. It introduces cut-cell microstructures that extend regular microstructure families to boundary-adherent tiles, enabling accurate surface preservation in 2D and 3D. The method integrates a five-step pipeline—cell partition, initial material optimization, generation of cut-cell geometry, interior refinement, and surface extraction—paired with a material-to-geometry map to produce manufacturable infill; boundary tiles are constructed via a one-parameter void-size family tied to volume fractions, with an interior optimization refining the rest. The approach is validated through extensive 2D and 3D experiments, including fabrication of TPU specimens, and is shown to outperform baselines like trimmed or solid boundary cells, while maintaining robustness on highly complex geometries. This work enables efficient, automated design of complex, boundary-preserving metamaterials for additive manufacturing with a single base material.

Abstract

Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is important. Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with individually optimized cut-cell tiles adapted to the geometry of the cut-cell. We propose an automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.

Figures (21)

• Figure 1: Two examples comparing simpler baselines, trimming (left) and solid cells (middle), with our approach (right). The scissor is optimized to close when the handles are pulled apart (top row) or pulled together (bottom row). Our approach succeeds in both cases, while trimming performs very poorly, and solid cells are somewhere in-between. We provide a detailed comparison against the solid cells baseline in Section \ref{['sec:results']}.
• Figure 2: Comparison between the solid baseline (left) and our method (right) in 3D. The top row shows both versions seen from the outside (as someone using the gripper would see it), while the bottom row shows section cuts of both shapes. The structure is optimized so that its jaws close together under a compression force on the handle (gripper's right side). The baseline example fails to reach the prescribed deformation.
• Figure 3: Two-scale optimization pipeline. (left) we run material optimization on a bar with square cells; (middle) a map $\mathcal{P}$ is used to map material properties to geometry; and (right) we obtain the final shape, which deforms as expected.
• Figure 4: Cell parameters for 2D and 3D, interior cells.
• Figure 5: Illustration of cell partition. (a) Initial surface mesh with a background regular grid. (b) Triangular/Tetrahedral mesh of the bounding box. (c) Final mesh after removing triangles/tetrahedra outside of the surface mesh.