纤维束模型中厚尾无序破坏强度的尺度标度
Size scaling of failure strength with fat-tailed disorder in a fiber bundle model
摘要：
本文研究了当微观无序度受厚尾分布控制时，非均质材料宏观断裂强度的尺寸标度。我们考虑一个纤维束模型，其中单根纤维的强度在有限范围内由幂律分布描述。通过改变幂律指数和纤维强度的上限来调节无序度，在等载荷分担的极限下，揭示了一个惊人的尺寸效应：对于小的系统尺寸，束强度随着纤维的数量而增加，并且非均匀材料的通常减小的尺寸效应仅在超过特征尺寸时恢复。我们分析表明，纤维的强度的极端顺序统计是负责这种特殊的行为。分析计算机模拟的结果，我们推导出一个标度形式，它描述了整个系统尺寸范围内的微观无序的参数上的纤维束的宏观强度的依赖关系。
英文摘要：
We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of disorder by varying the power law exponent and the upper cutoff of fibers' strength, in the limit of equal load sharing an astonishing size effect is revealed: For small system sizes the bundle strength increases with the number of fibers and the usual decreasing size effect of heterogeneous materials is only restored beyond a characteristic size. We show analytically that the extreme order statistics of fibers' strength is responsible for this peculiar behavior. Analyzing the results of computer simulations we deduce a scaling form which describes the dependence of the macroscopic strength of fiber bundles on the parameters of microscopic disorder over the entire range of system sizes.
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