Majari Parisa, Olvera-Trejo Daniel, Estrada-Díaz Jorge A, Elías-Zúñiga Alex, Martinez-Romero Oscar, Ramírez-Herrera Claudia A, Perales-Martínez Imperio Anel
Tecnologico de Monterrey, Institute of Advanced Materials for Sustainable Manufacturing, Ave. Eugenio Garza Sada 2501, Col: Tecnológico, Monterrey 64700, NL, Mexico.
Polymers (Basel). 2025 Feb 28;17(5):654. doi: 10.3390/polym17050654.
Lattice structures offer unique mechanical properties and versatility in engineering applications, yet existing designs often struggle to balance performance and material efficiency. This study introduces the brachistochrone curve as a novel framework for optimizing lattice geometries, enhancing mechanical behavior while minimizing material usage. Using finite element simulations and compressive testing of 3D-printed samples, we analyzed the mechanical response of brachistochrone-based (B-) and standard lattice structures (diamond, IWP, gyroid, and BCC). We investigated the scaling behavior of the volume-to-surface area ratio, incorporated fractal dimension analysis, and compared experimental and numerical results to evaluate the performance of B-lattices versus standard designs (S-). Our findings indicate that brachistochrone-inspired lattices enhance mechanical efficiency, enabling the design of lightweight, high-strength components with sustainable material use. Experimental results suggest that B-gyroid lattices exhibit lower stiffness than S-gyroid lattices under small displacements, highlighting their potential for energy absorption applications.
晶格结构在工程应用中具有独特的力学性能和多功能性，但现有的设计往往难以在性能和材料效率之间取得平衡。本研究引入最速降线曲线作为优化晶格几何形状的新框架，在提高力学性能的同时尽量减少材料使用。通过对3D打印样品进行有限元模拟和压缩测试，我们分析了基于最速降线的（B-）晶格结构和标准晶格结构（菱形、IWP、螺旋面和体心立方）的力学响应。我们研究了体积与表面积比的缩放行为，纳入了分形维数分析，并比较了实验和数值结果，以评估B晶格与标准设计（S-）的性能。我们的研究结果表明，受最速降线启发的晶格提高了力学效率，能够设计出使用可持续材料的轻质、高强度部件。实验结果表明，在小位移下，B-螺旋面晶格的刚度低于S-螺旋面晶格，突出了它们在能量吸收应用中的潜力。
