[论文解读] How Geometry Tames Disorder in Lattice Fracture

Matthaios Chouzouris, Leo de Waal+4 more|arXiv (Cornell University)|Feb 10, 2026

Microstructure and mechanical properties被引用 0

一句话总结

论文表明在带有Weibull分布失效阈值的带裂纹预裂三角梁晶格中，损伤表达存在三种失序调控的工作状态，受Weibull模量和细长比（Slenderness Ratio）控制，并提供了一个机械信息统计模型来预测损伤演化与状态转变。

ABSTRACT

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.

研究动机与目标

• 了解梁-晶格断裂中的静态无序对几何的依赖。
• 识别失序表达的三种状态：抑制、在裂尖附近局部化、全球扩散性失效。
• 建立一个机械信息驱动的统计框架，将无序与损伤指标及裂纹路径形态联系起来。

提出的方法

• 通过将每个梁离散为三个单元来扩展随机梁模型，以捕捉弯曲主导的变形。
• 对梁使用Weibull分布的失效应力来建模具有模量n的无序。
• 推导一个机械信息统计框架，将SR（细长比）和n与异常失效（散射）与扩散失效的概率联系起来。
• 将裂尖应力层级定义为随SR变化，以预测失效序列和裂纹路径的迂回性。
• 推导P_s(n, λ) = κ_s^n / (1 + κ_s^n)作为裂尖散射概率，以及P_d^(0)作为初始扩散性失效的Weibull重新归一化。
• 在不同SR值和无序水平下用晶格断裂模拟验证预测。

Figure 1 : Problem setup. (a): We consider rectangular domains of triangular lattices, with a half domain horizontal crack along the vertical midpoint, pinned to the horizontal, and with roller constraints along the vertical boundaries. The horizontal boundaries are kept parallel and moved apart to

实验结果

研究问题

• RQ1 几何形状（细长比）如何影响晶格断裂中静态无序的表达？
• RQ2 在Weibull模量与SR的函数下，断裂行为的哪些状态可以被理论预测？
• RQ3 无序如何影响裂尖损伤与扩散损伤，以及这与裂纹路径形态和韧性之间的关系？
• RQ4 是否可以用统计学基础框架预测在断裂起始时 excess 断裂键数量和扩散样损伤？
• RQ5 Weibull应力重新归一化在将微观失败与宏观断裂结果联系起来中扮演何种角色？

主要发现

• 出现三种截然不同的失效状态：无序被有效抑制、无序在裂尖周围局部化改变裂纹形态、无序在全局层面表现为扩散性失效。
• 通过细长比的几何形状重新塑造裂尖应力层级，并控制异常（散射）损伤事件的可能性。
• 一个机械信息驱动的基于Weibull的框架预测散射概率P_s(n, λ)和扩散失效概率P_d^(0)，与模拟结果一致，包括对无序的非单调韧化行为。
• 无序引起的韧化对无序强度呈非单调性，并且依赖晶格几何，挑战仅基于裂纹挠曲度或扩散性损伤的解释。
• SR可作为设计参数，用于在断裂过程中控制无序的表达，从而实现晶格超材料中的几何驱动断裂行为调控。
• 对于过弱到中等无序的情形， excess 断裂键数量和扩散性失效概率的模拟结果与理论预测高度吻合。

Figure 2 : Micromechanics and damage evolution after an anomalous failure event. (a): Crack-tip stress hierarchy and its geometric control. Top: Ratios of the maximum stresses in each of the six crack-tip beams to that of the most highly stressed beam (element 1, shown in blue), plotted as a functio