Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.

中文翻译：

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DLP 打印 3D 陀螺仪结构：细观和宏观尺度的机械响应

快速原型（RP）技术可以制造复杂的几何形状，使晶格结构越来越受欢迎。晶格结构，被称为多孔材料，由于其优化组件质量分布的能力，在过去二十年中引起了广泛关注。这些结构具有优异的机械性能，可满足能量吸收（弯曲主导结构）和结构性能（拉伸主导结构）的需求。在本文中，我们使用周期性表面模型研究拉伸主导的晶格结构的行为，特别关注基于片的陀螺仪单元，以实现更有效的宏观建模。我们研究不同尺寸的细胞和支架，考虑各种三周期最小表面厚度和范围从大约 0.2 到 0.65 的相对密度。我们探索了与晶胞主轴不同的方向上的载荷应用，并分析了应变率对散装材料和多孔材料的影响。网格结构采用环氧树脂和数字光处理 (DLP) 技术制造。在研究的相对密度范围内，无论是在准静态还是动态条件下，都观察到杨氏模量和压缩屈服强度呈线性趋势。为了将准静态结果扩展到动态状态，我们采用了更广义的归一化技术。这种方法将杨氏模量和压缩屈服强度除以基材在特定应变率下的行为，从而促进两个加载状态下机械性能的相关性。根据实验结果，我们实现并校准了双线性材料模型，用于在宏观尺度上描述三周期最小表面（TPMS）陀螺仪结构。模型系数根据相对密度进行参数化。此外，还将所提出的物质定律与吉布森-阿什比提出的物质定律进行了比较。此外，我们还评估了基材和晶胞的各向异性。第一个是通过在与打印方向不同的方向测试 3D 打印样本来完成的，后者使用齐纳系数。各向异性评估证实了晶胞在所研究的相对密度和测试条件范围内的各向同性行为。最后，我们使用已实现的双线性材料模型和宏观尺度的各向异性刚度矩阵（通过均匀公式获得）以及细观模型的基础材料，对组合剪切压缩测试进行线弹性 3D 宏观和细观模型模拟。结果证明了所提出的等效材料模型适用于研究弹性状态下的 TPMS 陀螺仪结构，无论是准静态还是动态。这样可以对复杂晶格结构进行高效的有限元建模过程。