发表机构
University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结合均匀化与钝裂纹理论的解析模型，预测三角和六边形晶格断裂韧性，发现高密度下节点应力集中主导失效，准脆性PMMA晶格韧性提升约1.6倍，部分可超越基体材料。
AI 中文摘要
晶格材料具有高度可调的力学性能，这些性能由其内部几何结构和基体材料行为控制。虽然低密度晶格的断裂模型已经成熟，但相对密度高于30%的晶格断裂仍 largely 未被探索。在此，我们提出一种解析模型，结合均匀化方法和钝裂纹断裂理论，预测三角形和六边形晶格在广泛相对密度范围内的断裂韧性。有限元建模证实了该解析框架，并展示了低和高相对密度区域之间失效机制的转变。在高相对密度下，失效由节点应力集中主导，这受到局部裂纹尖端几何形状和宏观裂纹路径的强烈影响。随着相对取向和晶格圆角半径的变化，观察到显著的应力重新分布，导致相对于基准几何形状的断裂韧性提高。此外，准脆性聚甲基丙烯酸甲酯（PMMA）晶格相对于完全脆性晶格实现了约1.6倍的断裂韧性增强，因为局部塑性延迟了失效。值得注意的是，一些准脆性晶格的断裂韧性超过了其基体材料——这一特性仅在晶胞尺寸远大于基体材料塑性半径时才有可能。对激光切割PMMA制成的晶格断裂试样的实验验证了有限元结果，但突出了脆性晶格材料中失效的随机性，尤其是在较高相对密度下。
英文摘要
Lattice materials have highly tunable mechanical properties that are controlled by their internal geometry and base material behavior. While fracture models for low-density lattices are well-established, the fracture of lattices at relative densities above 30% remains largely unexplored. Here, we present an analytical model that combines homogenization methods and blunt-crack fracture theory to predict the fracture toughness of triangular and hexagonal lattices over a wide range of relative densities. Finite element modeling corroborates the analytical framework and demonstrates a shift in failure mechanisms between low and high relative density regimes. At high relative densities, failure is dominated by nodal stress concentrations, which are strongly influenced by the local crack-tip geometry and the macroscopic crack path. Significant stress redistribution is observed as the relative orientation and lattice fillet radius are varied, resulting in increased fracture toughness relative to baseline geometries. Furthermore, quasi-brittle poly(methyl methacrylate) (PMMA) lattices achieve about a 1.6x enhancement in fracture toughness relative to perfectly brittle lattices as failure is delayed by localized plasticity. Notably, some quasi-brittle lattices are found to exceed the fracture toughness of their base material -- a feature only possible when the cell size is large compared to the base material's plastic radius. Experiments on lattice fracture specimens made from laser-cut PMMA validate the finite element results, but highlight the stochastic nature of failure in brittle lattice materials, especially at higher relative densities.
Comments22 pages, 14 figures
