{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T13:00:53Z","timestamp":1785416453980,"version":"3.56.0"},"reference-count":53,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T00:00:00Z","timestamp":1781395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12372079"],"award-info":[{"award-number":["12372079"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["12372079"],"award-info":[{"award-number":["12372079"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20201470"],"award-info":[{"award-number":["BK20201470"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20220687"],"award-info":[{"award-number":["BK20220687"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fund of Nanjing Institute of Technology","award":["TB202517071"],"award-info":[{"award-number":["TB202517071"]}]},{"award":["TB202517071"],"award-info":[{"award-number":["TB202517071"]}],"id":[{"id":"https:\/\/ror.org\/00n6txq60","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The objective of this study is to mitigate the bottom-out failure and improve the energy absorption of conventional helmet liners during high-energy impacts, thereby reducing the risk of head injuries. To this end, a locally reinforced Primitive-type triply periodic minimal surface (P-TPMS) energy-absorbing liner is proposed for the helmet forehead region, which facilitates progressive energy dissipation through layer-by-layer buckling deformation. A finite element model of a helmet\u2013head coupling was created based on a previously verified high-fidelity head model and subsequently validated against the ECE 22.06 standard drop-test methodology. Three critical design parameters\u2014outer protective layer thickness, triply periodic minimal surface (TPMS) unit cell size, and wall thickness\u2014were optimized employing the Box\u2013Behnken Design (BBD) response surface methodology, resulting in quadratic regression models for the head injury criteria (HIC) and peak linear acceleration (PLA) with good fit (R2 &gt; 0.97). Optimal parameter combinations were established using multi-objective optimization, with protective efficacy carefully assessed from both head dynamic response and biomechanical response perspectives. The ideal P-TPMS liner possesses an outer protective layer thickness of 14.95 mm, a TPMS unit cell size of 12.23 mm, and a wall thickness of 3.93 mm. Compared to the traditional expanded polystyrene (EPS) liner, the optimized P-TPMS liner significantly reduces HIC (by \u223c16%) and PLA (by \u223c14%) while extending the impact duration. More critically, it transitions both intracranial pressure and brain tissue strain below their respective clinical injury thresholds, substantially lowering the risks of skull fracture and mild traumatic brain injury (mTBI). The P-TPMS construction facilitates continuous energy dissipation during impacts via incremental layer-by-layer buckling deformation, hence extending impact duration and markedly improving helmet protective efficacy. These findings offer theoretical foundations and technical direction for the creation of localized heterogeneous liner designs in advanced high-performance helmets, although the results are limited to frontal flat-anvil impact conditions.<\/jats:p>","DOI":"10.3390\/ma19122571","type":"journal-article","created":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T03:01:27Z","timestamp":1781492487000},"page":"2571","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Objective Optimization Design and Impact Protection Efficacy of Locally Reinforced P-TPMS Forehead Helmet Liner"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5646-2672","authenticated-orcid":false,"given":"Bin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4993-7260","authenticated-orcid":false,"given":"Hao","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5181-5870","authenticated-orcid":false,"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7607-5095","authenticated-orcid":false,"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5694-0850","authenticated-orcid":false,"given":"Li","family":"Li","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5188-9757","authenticated-orcid":false,"given":"Xinyu","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5674-0245","authenticated-orcid":false,"given":"Zongchen","family":"Su","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8726-0167","authenticated-orcid":false,"given":"Qi","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9923-4912","authenticated-orcid":false,"given":"Jiawei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1289-508X","authenticated-orcid":false,"given":"Jianhao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation Engineering, Nanjing Institute of Technology, Nanjing 211167, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,14]]},"reference":[{"key":"ref_1","unstructured":"(2023). 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