Despite substantial advancements in optimizing structural designs for stiffness, the field of design against fracture is still in its early stages. This paper introduces a fundamental and standardized paradigm for structural design against brittle fracture, achieved through the minimization of the energy release rate within the framework of linear elastic fracture mechanics (LEFM). By leveraging the Griffith criterion expression and the total potential energy in LEFM, we propose an efficient approach for structural optimization that enhances the toughness of architected materials. The energy release rate is evaluated a synergistic application of finite element analysis and finite difference methods, yielding a precision of 0.6% compared to benchmarks in published handbooks. We demonstrate significantly reduced values compared to standard stiffness and stress-oriented topology optimization, which directly contributes to increased toughness. To comprehensively analyze the fracture process encompassing damage, crack initiation, propagation, and failure, we employ post-processing phase field fracture modeling on the optimally designed architected materials. By performing multi-objective optimization of the stiffness and energy release rate , the toughness and extreme load-bearing capacity can be simultaneously improved. The resulting perforated architecture effectively outperforms homogeneous structures in both toughness and peak load. Additionally, we extend our analysis to various configurations, such as non-center cracks, pure shear loading, and adherence to the standard 3D compact tension ASTM E-399-72. The designed structures are additively manufactured and experimentally validated, demonstrating a toughness increase of over 10 times compared to stress-based design. These contributions offer promising prospects for advancing the design of future engineering structures and materials with a favorable balance of critical fracture resistance characteristics.

中文翻译：

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抗脆性断裂的结构设计：优化能量释放率和实验

尽管在优化刚度结构设计方面取得了重大进展，但抗断裂设计领域仍处于早期阶段。本文介绍了抗脆性断裂结构设计的基本标准化范式，该范式通过线弹性断裂力学（LEFM）框架内的能量释放率最小化来实现。通过利用格里菲斯准则表达式和 LEFM 中的总势能，我们提出了一种有效的结构优化方法，可增强建筑材料的韧性。能量释放率通过有限元分析和有限差分方法的协同应用进行评估，与已出版手册中的基准相比，精度为 0.6%。我们证明，与标准刚度和应力导向的拓扑优化相比，值显着降低，这直接有助于提高韧性。为了全面分析包括损伤、裂纹萌生、扩展和失效在内的断裂过程，我们对优化设计的建筑材料采用后处理相场断裂建模。通过对刚度和能量释放率进行多目标优化，可以同时提高韧性和极限承载能力。由此产生的穿孔结构在韧性和峰值负载方面均有效地优于均质结构。此外，我们还将分析扩展到各种配置，例如非中心裂纹、纯剪切载荷以及遵守标准 3D 紧凑张力 ASTM E-399-72。所设计的结构经过增材制造并经过实验验证，与基于应力的设计相比，韧性提高了 10 倍以上。这些贡献为推进未来工程结构和材料的设计提供了良好的前景，并实现了关键断裂抗力特性的良好平衡。