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These artificial materials with maximized operational bandwidth provide the basis for wave manipulation and investigating the topological phase of matter. However, it is still challenging to efficiently design acoustic bandgap crystals via existing topology optimization methods. Most previous studies considering only a volume fraction constraint on the constituent material may have impractical wide band gaps due to the pseudo-air resonant modes. To solve this issue, this paper establishes a new topology optimization method for creating acoustic bandgap crystals periodically composed of solid and air. We adopt a constraint on air permeability to ensure the connective air channels within the periodic microstructures, which is more applicable in engineering practice. The optimized unit cells from the proposed method are further analyzed to realize topologically protected states, providing opportunities for multi-dimensional wave manipulation in acoustic systems. Numerical examples demonstrate the effectiveness of the proposed method in designing acoustic crystals with broad bandgaps on any given band orders, and gapped\/gapless edge states and corner states can be achieved in resulting topological insulators.<\/jats:p>","DOI":"10.1007\/s00366-023-01936-2","type":"journal-article","created":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T03:02:26Z","timestamp":1706324546000},"page":"2581-2594","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Topology optimization of acoustic bandgap crystals for topological insulators"],"prefix":"10.1007","volume":"40","author":[{"given":"Weibai","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoxing","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0176-2686","authenticated-orcid":false,"given":"Xiaodong","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,1,27]]},"reference":[{"issue":"22","key":"1936_CR1","doi-asserted-by":"publisher","first-page":"4400","DOI":"10.1063\/1.1757642","volume":"84","author":"A Khelif","year":"2004","unstructured":"Khelif A, Choujaa A, Benchabane S, Djafari-Rouhani B, Laude V (2004) Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. 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