Pradhan Srutarshi, Hansen Alex
Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026111. doi: 10.1103/PhysRevE.72.026111. Epub 2005 Aug 11.
The presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility--both in an equal load sharing (ELS) model and in a local load sharing (LLS) one using analytic as well as numerical methods. In the ELS model, the critical strength gets modified and, beyond a certain lower cutoff level, the whole bundle fails instantly (brittle failure) after the first fiber ruptures. Although the dynamic exponents for the order parameter, susceptibility, and relaxation time remain unchanged, the avalanche size distribution shows a gradual deviation from the mean field power law. A similar "instant failure" situation occurs in the LLS model at a lower cutoff level, which reduces to that of the equivalent ELS model at higher (high enough) dimensions. Also, the system size variation of the bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.
纤维阈值分布中较低截止值的存在可能会影响一束承受外部载荷的纤维的失效特性。我们通过解析方法和数值方法在等载荷分担（ELS）模型和局部载荷分担（LLS）模型中研究这种可能性。在ELS模型中，临界强度会被修正，并且在超过某个较低截止水平后，在第一根纤维断裂后整个纤维束会立即失效（脆性失效）。尽管序参量、磁化率和弛豫时间的动力学指数保持不变，但雪崩大小分布显示出与平均场幂律的逐渐偏差。在较低截止水平下，LLS模型中会出现类似的“即时失效”情况，在更高（足够高）维度时会简化为等效的ELS模型情况。此外，纤维束强度的系统尺寸变化和雪崩统计显示出对较低截止水平的强烈依赖性。
