强异质纤维丛的普适类
Universality class of fiber bundles with strong heterogeneities
摘要：
我们使用纤维束模型研究了强非均匀性对无序材料断裂的影响。纤维束由两个纤维子集组成，即0<α<1的纤维部分是不可破坏的，而剩余的1-α部分的特征在于断裂阈值的分布。在假设全局负载分担的情况下，我们解析地证明了存在一个临界分量α_c，它将系统的两个性质不同的区域分开：低于α_c时，爆发尺寸分布是一个指数τ=5/2的幂律，而高于α_c时，指数转变到一个较低值τ=9/4，并且出现一个特征尺寸发散的截止函数。分析系统的宏观响应，我们证明了过渡的条件是无序分布的本构曲线有一个单一的最大值和一个定义一个新的普遍性类的击穿现象的临界点。
英文摘要：
We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<α<1 of fibers is unbreakable, while the remaining 1-αfraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components α_c which separates two qualitatively different regimes of the system: below α_c the burst size distribution is a power law with the usual exponent τ=5/2, while above α_c the exponent switches to a lower value τ=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena.
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