This paper addresses the intricate analysis of lattice structures, pivotal components in engineering applications, confronted by challenges arising from their diverse unit cells (UCs) and complex behavior across micromechanical and macro-scale dimensions. The present study deals with a comprehensive analysis of lattice structure with honeycomb and re-entrant auxetic unit cells under large deformation via both a robust finite element analysis (FEA) and experimental tests. The proposed FEA is developed based on the hyperelastic Mooney–Rivlin strain energy function and the novel exact motion field that can fully describe the projection of cross-section. The results demonstrate that mechanical parameters such as Young's modulus, Poisson's ratio, and shear modulus have significant nonlinear behaviors with respect to UC geometrical parameters that are crucial for optimization across varied operational conditions. Additionally, the lattices made of TPU material and fabricated by Fused Deposition Modeling are tested under three-point bending and compression considering contact interaction. The results reveal highly nonlinear responses due to instabilities in some links and material nonlinearity. Furthermore, the behavior of lattice structures is exceedingly dependent on the orientations and types of UCs. It also can be found that both of the proposed FEA and constitutive model are in good agreement with experimental data.

中文翻译：

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有限应变条件下超弹性拉胀晶格结构的微观宏观分析

本文讨论了晶格结构的复杂分析，晶格结构是工程应用中的关键部件，面临着其多样化的晶胞 (UC) 以及跨微观机械和宏观尺度的复杂行为所带来的挑战。本研究通过稳健的有限元分析（FEA）和实验测试，对大变形下蜂窝状和凹入拉胀晶胞的晶格结构进行了全面分析。所提出的有限元分析是基于超弹性门尼-里夫林应变能函数和能够完全描述横截面投影的新型精确运动场而开发的。结果表明，杨氏模量、泊松比和剪切模量等机械参数相对于 UC 几何参数具有显着的非线性行为，这对于不同操作条件下的优化至关重要。此外，考虑接触相互作用，由 TPU 材料制成并通过熔融沉积建模制造的晶格在三点弯曲和压缩下进行了测试。结果揭示了由于某些链接的不稳定性和材料非线性而导致的高度非线性响应。此外，晶格结构的行为很大程度上取决于UC的方向和类型。还可以发现，所提出的有限元分析和本构模型都与实验数据吻合良好。