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Multi-Objective Optimization Design and Impact Protection Efficacy of Locally Reinforced P-TPMS Forehead Helmet Liner.

Bin Yang | Hao Feng | Xin Li | Peng Zhang | Li Li | Xinyu Wei | Zongchen Su | Qi Jin | Jiawei Zhang | Jianhao Zhang
Materials (Basel, Switzerland) | 2026

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-head 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-outer protective layer thickness, triply periodic minimal surface (TPMS) unit cell size, and wall thickness-were optimized employing the Box-Behnken 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 > 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 ∼16%) and PLA (by ∼14%) 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.

Pubmed ID: 42355153

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Associated grants

  • Agency: National Natural Science Foundation of China,
    Id: 12372079
  • Agency: Natural Science Foundation of Jiangsu Province,
    Id: BK20201470
  • Agency: Fund of Nanjing Institute of Technology,
    Id: TB202517071
  • Agency: Natural Science Foundation of Jiangsu Province,
    Id: BK20220687

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RRID:SCR_011448

The National Natural Science Foundation of China (NSFC) is an organization directly affiliated to the State Council for the management of the National Natural Science Fund. # In accordance with the guiding principles, policies and plans for the development of science and technology in China and by adopting the operating mechanisms for the National Natural Science Fund which conform to the socialism market economic system, NSFC supports basic research and some of applied research, identifies and fosters talented researchers in the realm of science and technology, accelerates the progress of science and technology, and promotes the socioeconomic development in China by giving full play the guidance and coordinating role of the National Natural Science Fund from the central government. # NSFC is in charge of the management of the National Natural Science Fund. It compiles and promulgates the annual Guide to Programs for basic research and some of applied research, handles applications of research projects, and organizes peer review and select the best projects to support. It endeavors to create an academic environment conducive to innovation. # NSFC cooperates with the Ministry of Science and Technology to formulate the principles, policies and plans for the development of basic research in China. When entrusted, it provides consultation and undertakes related assignments on major issues for the development of high technology and applied research in China. # NSFC gives help and support to other Chinese foundations in natural sciences. # NSFC establishes contacts with governmental departments in charge of science and technology, science foundations and related academic organizations in other countries and carries out international cooperation and exchange. # NSFC is responsible for the administration, supervision and guidance of the subordinated bodies. # NSFC undertakes other tasks entrusted by the State Council and the State Leading Group for Science and Technology and Education.

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