This research proposes a novel method for designing fracture-resistant structures. By analyzing the relationship between tensile strain energy and phase field brittle fracture, it has been found that minimizing tensile strain energy can delay fracture and enhance resistance. Capitalizing on this insight, a new topology optimization method is proposed. This method focuses on minimizing tensile strain energy to suppress the well-documented tension-dominated fracture behavior observed in phase field brittle fracture analysis. In contrast to traditional topology optimization methods based on von Mises stress, this method generates more robust structures under tension. Furthermore, the method can incorporate stress constraints to mitigate the potential for stress concentrations arising from geometric discontinuities. Numerical results demonstrate the effectiveness of the proposed method. Using phase-field modeling, the mechanical fracture properties of the optimized structures, including peak load, failure displacement, and absorbed elastic energy before fracture, are quantified. Furthermore, experimental tests are also conducted. Both numerical simulations and experimental results are consistently show that structures designed with minimized tensile strain energy exhibit superior fracture toughness. Furthermore, the method offers significant computational efficiency compared to conventional approaches due to its reliance solely on linear elasticity analysis within the optimization process.

中文翻译：

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脆性抗断裂结构设计：一种拉伸应变能最小化拓扑优化


本研究提出了一种设计抗断裂结构的新方法。通过分析拉伸应变能与相场脆性断裂之间的关系，发现最小化拉伸应变能可以延缓断裂并提高抵抗力。利用这一见解，提出了一种新的拓扑优化方法。该方法侧重于最小化拉伸应变能，以抑制在相场脆性断裂分析中观察到的有据可查的以拉伸为主的断裂行为。与基于 von Mises 应力的传统拓扑优化方法相比，这种方法在张力下生成了更坚固的结构。此外，该方法还可以结合应力约束，以减轻几何不连续性引起的应力集中的可能性。数值计算结果验证了所提方法的有效性。使用相场建模，可以量化优化结构的机械断裂特性，包括峰值载荷、失效位移和断裂前吸收的弹性能。此外，还进行了实验测试。数值模拟和实验结果一致表明，以最小拉伸应变能设计的结构表现出优异的断裂韧性。此外，与传统方法相比，该方法在优化过程中仅依赖于线性弹性分析，因此提供了显着的计算效率。