<p>Multi‑material microstructure topology optimization (TO) still suffers from three persistent artifacts—phase overlap, jagged/unsmooth interfaces, and grayscale elements—while gradient‑based schemes incur heavy sensitivity costs that hinder scalability. We develop a level‑set proportional topology‑optimization framework that (1) enforces mutual exclusion via a negative‑mapping interpolation applied locally in overlap cells, (2) decomposes an <i>M</i>-phase design into <i>M</i>(<i>M</i>-1)/2 two‑phase subproblems through an Alternating Active‑Phase Strategy (AAPS) with independent level sets, thereby reducing design variables and constraints, and (3) adopts proportional topology optimization (PTO) updates that eliminate sensitivity evaluations. An element‑wise material‑exclusion (EME) proportion filtering and linear scaling further regularize features and suppress spurious branches. On 2D three‑ and four‑phase benchmarks maximizing bulk or shear modulus, the method yields layouts that are strictly non‑overlapping, exhibit smooth, continuous interfaces, and are free of grayscale elements. The main topology emerges in approximately 40 iterations and then stabilizes; compared with standard AAPS, objective values are matched or improved while eliminating interface mixing, and EME filtering typically outperforms density filtering in both modulus and morphology. Consistency between single‑cell and (2 × 2) tiling is also verified. Unlike conventional density-based multi-material TO methods, the proposed approach explicitly enforces phase exclusivity at the geometric level rather than through penalization or projection. We provide a robust, sensitivity‑free, and computationally efficient route to high‑quality, manufacturable multi‑material microstructures by unifying explicit interface control with reduced‑variable decomposition and fast PTO updates.</p>

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Level-set-based negative-mapping interpolation for non-overlapping multi-material microstructure topology optimization

  • Run Du,
  • Dong Wang,
  • Qianglin Ran,
  • Lingyun Yang,
  • Xiong Rao,
  • Wei Xiang,
  • Xuanliang Wang,
  • Wenming Cheng

摘要

Multi‑material microstructure topology optimization (TO) still suffers from three persistent artifacts—phase overlap, jagged/unsmooth interfaces, and grayscale elements—while gradient‑based schemes incur heavy sensitivity costs that hinder scalability. We develop a level‑set proportional topology‑optimization framework that (1) enforces mutual exclusion via a negative‑mapping interpolation applied locally in overlap cells, (2) decomposes an M-phase design into M(M-1)/2 two‑phase subproblems through an Alternating Active‑Phase Strategy (AAPS) with independent level sets, thereby reducing design variables and constraints, and (3) adopts proportional topology optimization (PTO) updates that eliminate sensitivity evaluations. An element‑wise material‑exclusion (EME) proportion filtering and linear scaling further regularize features and suppress spurious branches. On 2D three‑ and four‑phase benchmarks maximizing bulk or shear modulus, the method yields layouts that are strictly non‑overlapping, exhibit smooth, continuous interfaces, and are free of grayscale elements. The main topology emerges in approximately 40 iterations and then stabilizes; compared with standard AAPS, objective values are matched or improved while eliminating interface mixing, and EME filtering typically outperforms density filtering in both modulus and morphology. Consistency between single‑cell and (2 × 2) tiling is also verified. Unlike conventional density-based multi-material TO methods, the proposed approach explicitly enforces phase exclusivity at the geometric level rather than through penalization or projection. We provide a robust, sensitivity‑free, and computationally efficient route to high‑quality, manufacturable multi‑material microstructures by unifying explicit interface control with reduced‑variable decomposition and fast PTO updates.