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Sports equipment crafted from flexible mechanical metamaterials offers advantages due to its lightweight, comfort, and energy absorption, enhancing athletes' well-being and optimizing their competitive performance. The utilization of metamaterials in sports gear like insoles, protective equipment, and helmets has garnered increasing attention. In comparison to traditional truss and honeycomb metamaterials, the triply periodic minimal surface lattice structure stands out due to its parametric design capabilities, enabling controllable performance. Furthermore, the use of flexible materials empowers this structure to endure significant deformation while boasting a higher energy absorption capacity. Consequently, this study first introduces a parametric method based on the modeling equation of the triply periodic minimal surface structure and homogenization theory simulation. Experimental results demonstrate the efficacy of this method in designing triply periodic minimal surface lattice structures with a controllable and adjustable elastic modulus. Subsequently, the uniform flexible triply periodic minimal surface lattice structure is fabricated using laser selective sintering thermoplastic polyurethane technology. Compression tests and finite element simulations analyze the hyperelastic response characteristics, including the element type, deformation behavior, elastic modulus, and energy absorption performance, elucidating the stress–strain curve of the flexible lattice structure. Upon analyzing the compressive mechanical properties of the uniform flexible triply periodic minimal surface structure, it is evident that the structure's geometric shape and volume fraction predominantly influence its mechanical properties. Consequently, we delve into the advantages of gradient and hybrid lattice structure designs concerning their elasticity, energy absorption, and shock absorption. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials with ultralight and ultrastrong mechanical properties are extensively employed in various industrial sectors, with three-periodic minimal surface (TPMS) structures gaining significant research attention due to their symmetry, equation-driven characteristics, and exceptional mechanical properties. Compared to traditional lattice structures, TPMS structures exhibit superior mechanical performance. The mechanical properties of TPMS structures depend on the base material, structural porosity (volume fraction), and wall thickness. Hard rigid lattice structures such as Gyroid, diamond, and primitive exhibit outstanding performance in terms of elastic modulus, energy absorption, heat dissipation, and heat transfer. Flexible TPMS lattice structures, on the other hand, offer higher elasticity and recoverable large deformations, drawing attention for use in applications such as seat cushions and helmet impact-absorbing layers. Conventional fabrication methods often fail to guarantee the quality of TPMS structure samples, and additive manufacturing technology provides a new avenue. Selective laser sintering (SLS) has successfully been used to process various materials. However, due to the layer-by-layer manufacturing process, it cannot eliminate the anisotropy caused by interlayer bonding, which impacts the mechanical properties of 3D-printed parts. This paper introduces a process data-driven optimization design approach for TPMS structure geometry by adjusting volume fraction gradients to overcome the elastic anisotropy of 3D-printed isotropic lattice structures. Experimental validation and analysis are conducted using TPMS structures fabricated using TPU material via SLS. Furthermore, the advantages of volume fraction gradient-designed TPMS structures in functions such as energy absorption and heat dissipation are explored. [ABSTRACT FROM AUTHOR]